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Bicarbonate · compensation · anion gap

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Traditional worked examples

22 worked blood gases covering single and mixed disorders, albumin correction, delta analysis, respiratory time course and incomplete measurements.

Work through a reference gas, single disturbances and mixed disorders. Open any case in the calculator to inspect each step and change its measurements.

22 synthetic teaching cases. Results are generated by the current Traditional calculation engine; these are not patient records or an independent clinical-validation dataset.

Traditional · reference

A reference gas

pH, carbon dioxide, bicarbonate and the anion gap are within the selected ranges.

pH 7.396PaCO₂ 40 mmHgHCO₃⁻ 24.0 mmol/L
No disorder identified from pH, PaCO₂ and HCO₃⁻

No compensation assessment needed. All three gas values are within the screening ranges. Review the anion gap before concluding that there is no metabolic disturbance.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: unknown. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.396—
PCO₂40mmHg
Reported gas HCO₃⁻24mmol/L
Chemistry total CO₂ / HCO₃⁻24mmol/L
Sodium140mmol/L
Chloride107.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻24.00mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. Calculated bicarbonate is approximately 24 mmol/L. A reference-range pH must still be read alongside PaCO₂, bicarbonate and the anion gap.
  2. AG = 140 − 107.5 − 24 = 8.5 mmol/L. Albumin is 40 g/L, so correction adds zero.
  3. No acid–base disorder is demonstrated by this synthetic panel. This does not establish that a patient is clinically well.

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Traditional · metabolic acidosis

High-gap acidosis with raised lactate

A low bicarbonate, raised corrected gap and PaCO₂ within Winter’s range.

pH 7.282PaCO₂ 26 mmHgHCO₃⁻ 12.0 mmol/L
High anion gap metabolic acidosis

Expected response. PaCO₂ is compatible with the expected respiratory response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.282—
PCO₂26mmHg
Reported gas HCO₃⁻12mmol/L
Chemistry total CO₂ / HCO₃⁻12mmol/L
Sodium140mmol/L
Chloride107.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate12mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻12.00mmol/L
Anion gap, without potassium20.50mmol/L
Albumin-corrected anion gap20.50mmol/L
Delta ratio1.00—
Delta gap0.00mmol/L
Delta-adjusted bicarbonate24.00mmol/L

Expected PaCO₂: 24.0–28.0 mmHg. Observed: 26.0 mmHg. PaCO₂ is compatible with the expected respiratory response. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The ratio is compatible with a high-gap metabolic acidosis. It does not prove that only one metabolic process is present.

  1. The low pH and bicarbonate support metabolic acidosis. AG = 140 − 107.5 − 12 = 20.5 mmol/L; albumin correction is zero.
  2. Winter’s expected PaCO₂ is 1.5 × 12 + 8 = 26 mmHg, with a range of 24–28. The measured 26 is compatible with compensation.
  3. Delta ratio = (20.5 − 8.5) / (24 − 12) = 1.0. This is compatible with high-gap acidosis without a second metabolic process being demonstrated.
  4. Lactate is measured at 12 mmol/L. It is a contributor; the number alone does not identify its cause or exclude other anions.

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Traditional · metabolic acidosis

Normal-gap metabolic acidosis

Bicarbonate has fallen while chloride has risen; the corrected gap remains within range.

pH 7.317PaCO₂ 32 mmHgHCO₃⁻ 16.0 mmol/L
Normal anion gap metabolic acidosis

Expected response. PaCO₂ is compatible with the expected respiratory response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.317—
PCO₂32mmHg
Reported gas HCO₃⁻16mmol/L
Chemistry total CO₂ / HCO₃⁻16mmol/L
Sodium140mmol/L
Chloride115.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻16.00mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Expected PaCO₂: 30.0–34.0 mmHg. Observed: 32.0 mmHg. PaCO₂ is compatible with the expected respiratory response. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. The bicarbonate is 16 mmol/L and the pH is low. AG = 140 − 115.5 − 16 = 8.5 mmol/L.
  2. Winter’s predicted PaCO₂ is 32 ±2 mmHg; the measured value is 32.
  3. The normal-gap pattern directs attention to gastrointestinal bicarbonate loss, impaired renal acid handling, and chloride-rich fluids. The panel does not distinguish these causes.
  4. A delta ratio is not used to classify an isolated normal-gap acidosis.

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Traditional · metabolic acidosis

High-gap acidosis with normal lactate

The raised gap requires an explanation beyond the measured lactate.

pH 7.256PaCO₂ 23 mmHgHCO₃⁻ 10.0 mmol/L
High anion gap metabolic acidosis

Expected response. PaCO₂ is compatible with the expected respiratory response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.256—
PCO₂23mmHg
Reported gas HCO₃⁻10mmol/L
Chemistry total CO₂ / HCO₃⁻10mmol/L
Sodium140mmol/L
Chloride102.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻10.00mmol/L
Anion gap, without potassium27.50mmol/L
Albumin-corrected anion gap27.50mmol/L
Delta ratio1.36—
Delta gap5.00mmol/L
Delta-adjusted bicarbonate29.00mmol/L

Expected PaCO₂: 21.0–25.0 mmHg. Observed: 23.0 mmHg. PaCO₂ is compatible with the expected respiratory response. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The ratio is compatible with a high-gap metabolic acidosis. It does not prove that only one metabolic process is present.

  1. AG = 140 − 102.5 − 10 = 27.5 mmol/L. Albumin is normal, so the corrected gap is unchanged.
  2. Expected PaCO₂ is 23 ±2 mmHg; the measured value is 23.
  3. The delta ratio is 19 / 14 = 1.36. The selected screen is compatible with high-gap acidosis.
  4. Normal lactate does not identify the anion. Relevant next information includes blood ketones, glucose, renal function and an exposure history.

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Traditional · metabolic acidosis

A gap concealed by low albumin

The uncorrected gap is within range; albumin correction reveals an increase.

pH 7.317PaCO₂ 32 mmHgHCO₃⁻ 16.0 mmol/L
High anion gap metabolic acidosis

Expected response. PaCO₂ is compatible with the expected respiratory response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.317—
PCO₂32mmHg
Reported gas HCO₃⁻16mmol/L
Chemistry total CO₂ / HCO₃⁻16mmol/L
Sodium140mmol/L
Chloride111.5mmol/L
Potassium4mmol/L
Albumin20g/L
Lactate4mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻16.00mmol/L
Anion gap, without potassium12.50mmol/L
Albumin-corrected anion gap17.50mmol/L
Delta ratio1.13—
Delta gap1.00mmol/L
Delta-adjusted bicarbonate25.00mmol/L

Expected PaCO₂: 30.0–34.0 mmHg. Observed: 32.0 mmHg. PaCO₂ is compatible with the expected respiratory response. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The ratio is compatible with a high-gap metabolic acidosis. It does not prove that only one metabolic process is present.

  1. The raw AG is 140 − 111.5 − 16 = 12.5 mmol/L, inside the selected 4–13 interval.
  2. At albumin 20 g/L, add 0.25 × (40 − 20) = 5. The corrected AG is 17.5 mmol/L, above the interval.
  3. Expected PaCO₂ is 32 ±2 mmHg; the measured 32 is compatible with respiratory compensation.
  4. The delta ratio is (17.5 − 8.5) / 8 = 1.13. A reference-range raw gap would have obscured this high-gap pattern.

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Traditional · metabolic alkalosis

Metabolic alkalosis with low chloride

Raised bicarbonate, alkalaemia and a compatible compensatory rise in PaCO₂.

pH 7.493PaCO₂ 48 mmHgHCO₃⁻ 36.0 mmol/L
Metabolic alkalosis

Expected response. PaCO₂ is compatible with the expected respiratory response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.493—
PCO₂48mmHg
Reported gas HCO₃⁻36mmol/L
Chemistry total CO₂ / HCO₃⁻36mmol/L
Sodium140mmol/L
Chloride95.5mmol/L
Potassium3.2mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻36.00mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Expected PaCO₂: 47.2–49.0 mmHg. Observed: 48.0 mmHg. PaCO₂ is compatible with the expected respiratory response. Expected PaCO₂ = 40 + (0.6–0.75) × (gas HCO₃⁻ − 24) mmHg, with an additional ±2 mmHg screening allowance. At severe alkalosis, the linear rule is less reliable; PaCO₂ above 55 alone does not prove another respiratory disorder.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. Bicarbonate is 36 mmol/L and pH is raised. A low chloride and potassium provide context for a metabolic alkalosis.
  2. Expected PaCO₂ = 40 + (0.6–0.75) × (36 − 24) = 47.2–49.0 mmHg. The measured 48 is within that band.
  3. Review vomiting or gastric drainage, diuretics, prior hypercapnia and volume status. A suitably interpreted urine chloride can help if the cause remains unclear.
  4. The CO₂ rise fits compensation here. It does not create a separate diagnosis of primary respiratory acidosis.

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Traditional · respiratory

Acute respiratory acidosis

An acute PaCO₂ rise with the expected smaller bicarbonate response.

pH 7.271PaCO₂ 60 mmHgHCO₃⁻ 27.0 mmol/L
Acute respiratory acidosis

Expected response. HCO₃⁻ is compatible with the expected acute response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.271—
PCO₂60mmHg
Reported gas HCO₃⁻27mmol/L
Chemistry total CO₂ / HCO₃⁻27mmol/L
Sodium140mmol/L
Chloride104.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻27.00mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Acute: 26.0–28.0 mmol/L. Observed: 27.0 mmol/L. HCO₃⁻ is compatible with the expected acute response. Expected HCO₃⁻ change per 10 mmHg PaCO₂ rise: acute +1 to +2; chronic +3 to +4 mmol/L, from PaCO₂ 40 and HCO₃⁻ 24. An additional ±2 mmol/L screening allowance is used before suggesting another process; it is not a validated prediction interval.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. The PaCO₂ is 20 mmHg above the 40 mmHg anchor. The pH is low.
  2. The acute rule predicts HCO₃⁻ 24 + (1–2) × 2 = 26–28 mmol/L. The observed 27 fits that band.
  3. The chronic band would be 30–32. The clinical time course is selected from the history, not established by this gas alone.
  4. Raised bicarbonate is the expected secondary response in this example; it is not sufficient evidence for metabolic alkalosis.

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Traditional · respiratory

Chronic respiratory acidosis

The larger bicarbonate response fits a known chronic course; pH remains low.

pH 7.331PaCO₂ 60 mmHgHCO₃⁻ 31.0 mmol/L
Chronic respiratory acidosis

Expected response. HCO₃⁻ is compatible with the expected chronic response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: chronic. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.331—
PCO₂60mmHg
Reported gas HCO₃⁻31mmol/L
Chemistry total CO₂ / HCO₃⁻31mmol/L
Sodium140mmol/L
Chloride100.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻31.00mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Chronic: 30.0–32.0 mmol/L. Observed: 31.0 mmol/L. HCO₃⁻ is compatible with the expected chronic response. Expected HCO₃⁻ change per 10 mmHg PaCO₂ rise: acute +1 to +2; chronic +3 to +4 mmol/L, from PaCO₂ 40 and HCO₃⁻ 24. An additional ±2 mmol/L screening allowance is used before suggesting another process; it is not a validated prediction interval.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. With PaCO₂ 60, the chronic rule predicts HCO₃⁻ 24 + (3–4) × 2 = 30–32 mmol/L.
  2. Bicarbonate 31 is within that range. Compensation is compatible even though pH remains below 7.35.
  3. A change from a previous stable gas can reveal an acute deterioration that a single value cannot establish.

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Traditional · respiratory

Chronic hypercapnia with pH in range

A pH inside 7.35–7.45 does not mean the respiratory disorder has disappeared.

pH 7.358PaCO₂ 50 mmHgHCO₃⁻ 27.5 mmol/L
Chronic respiratory acidosis

Expected response. HCO₃⁻ is compatible with the expected chronic response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: chronic. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.358—
PCO₂50mmHg
Reported gas HCO₃⁻27.5mmol/L
Chemistry total CO₂ / HCO₃⁻27.5mmol/L
Sodium140mmol/L
Chloride104mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻27.50mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Chronic: 27.0–28.0 mmol/L. Observed: 27.5 mmol/L. HCO₃⁻ is compatible with the expected chronic response. Expected HCO₃⁻ change per 10 mmHg PaCO₂ rise: acute +1 to +2; chronic +3 to +4 mmol/L, from PaCO₂ 40 and HCO₃⁻ 24. An additional ±2 mmol/L screening allowance is used before suggesting another process; it is not a validated prediction interval.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. PaCO₂ remains elevated at 50 mmHg. The chronic expected bicarbonate band is 27–28 mmol/L.
  2. Bicarbonate 27.5 fits that band and the calculated pH is approximately 7.358.
  3. Describe the chronic respiratory disorder and its compatible compensation. The reference-range pH should not erase the abnormal PaCO₂.

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Traditional · respiratory

Acute respiratory alkalosis

A fall in PaCO₂ with the expected acute reduction in bicarbonate.

pH 7.493PaCO₂ 30 mmHgHCO₃⁻ 22.5 mmol/L
Acute respiratory alkalosis

Expected response. HCO₃⁻ is compatible with the expected acute response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.493—
PCO₂30mmHg
Reported gas HCO₃⁻22.5mmol/L
Chemistry total CO₂ / HCO₃⁻22.5mmol/L
Sodium140mmol/L
Chloride109mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻22.50mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Acute: 22.0–23.0 mmol/L. Observed: 22.5 mmol/L. HCO₃⁻ is compatible with the expected acute response. Expected HCO₃⁻ change per 10 mmHg PaCO₂ fall: acute −1 to −2; chronic −4 to −5 mmol/L, from PaCO₂ 40 and HCO₃⁻ 24. An additional ±2 mmol/L screening allowance is used before suggesting another process; it is not a validated prediction interval.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. PaCO₂ is 10 mmHg below 40 and pH is high. The acute bicarbonate band is 22–23 mmol/L.
  2. Bicarbonate 22.5 fits the acute response. A small bicarbonate fall does not establish an additional metabolic acidosis.
  3. Assess the reason for increased ventilation, including hypoxaemia, pain, systemic illness, drugs and ventilator settings where relevant.

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Traditional · respiratory

Chronic respiratory alkalosis

A lower bicarbonate is compatible with the known chronic respiratory disturbance.

pH 7.431PaCO₂ 30 mmHgHCO₃⁻ 19.5 mmol/L
Chronic respiratory alkalosis

Expected response. HCO₃⁻ is compatible with the expected chronic response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: chronic. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.431—
PCO₂30mmHg
Reported gas HCO₃⁻19.5mmol/L
Chemistry total CO₂ / HCO₃⁻19.5mmol/L
Sodium140mmol/L
Chloride112mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻19.50mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Chronic: 19.0–20.0 mmol/L. Observed: 19.5 mmol/L. HCO₃⁻ is compatible with the expected chronic response. Expected HCO₃⁻ change per 10 mmHg PaCO₂ fall: acute −1 to −2; chronic −4 to −5 mmol/L, from PaCO₂ 40 and HCO₃⁻ 24. An additional ±2 mmol/L screening allowance is used before suggesting another process; it is not a validated prediction interval.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. The chronic rule predicts HCO₃⁻ 24 − (4–5) × 1 = 19–20 mmol/L for PaCO₂ 30.
  2. Bicarbonate 19.5 lies inside that range. Although it is below the routine bicarbonate interval, it can be explained by chronic respiratory compensation.
  3. The anion gap is 8.5 mmol/L. A low bicarbonate alone would incorrectly turn this example into a primary normal-gap metabolic acidosis.

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Traditional · respiratory

Hypercapnia with an unknown course

The same gas has different implications under acute and chronic hypotheses.

pH 7.331PaCO₂ 60 mmHgHCO₃⁻ 31.0 mmol/L
Respiratory acidosis

Time course needed. The gas alone does not establish acute or chronic duration. Use the history and previous gases.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: unknown. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.331—
PCO₂60mmHg
Reported gas HCO₃⁻31mmol/L
Chemistry total CO₂ / HCO₃⁻31mmol/L
Sodium140mmol/L
Chloride100.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻31.00mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Acute: 26.0–28.0 mmol/L; Chronic: 30.0–32.0 mmol/L. Observed: 31.0 mmol/L. The gas alone does not establish acute or chronic duration. Use the history and previous gases. Expected HCO₃⁻ change per 10 mmHg PaCO₂ rise: acute +1 to +2; chronic +3 to +4 mmol/L, from PaCO₂ 40 and HCO₃⁻ 24. An additional ±2 mmol/L screening allowance is used before suggesting another process; it is not a validated prediction interval.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. PaCO₂ is 60 and bicarbonate is 31 mmol/L. The acute band is 26–28; the chronic band is 30–32.
  2. These values fit the chronic band, but the measurements do not supply the missing clinical history.
  3. If the hypercapnia is known to be new, the high bicarbonate raises the possibility of a second metabolic process. If chronic, the values fit the expected response.
  4. Leave the course uncertain until a previous gas or reliable history resolves it.

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Traditional · mixed

Metabolic and respiratory acidosis

A PaCO₂ of 40 is too high for this degree of metabolic acidosis.

pH 7.095PaCO₂ 40 mmHgHCO₃⁻ 12.0 mmol/L
High anion gap metabolic acidosis + respiratory acidosis

Additional process suggested. PaCO₂ is above the expected response: an additional respiratory acidosis is suggested.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.095—
PCO₂40mmHg
Reported gas HCO₃⁻12mmol/L
Chemistry total CO₂ / HCO₃⁻12mmol/L
Sodium140mmol/L
Chloride107.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate12mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻12.00mmol/L
Anion gap, without potassium20.50mmol/L
Albumin-corrected anion gap20.50mmol/L
Delta ratio1.00—
Delta gap0.00mmol/L
Delta-adjusted bicarbonate24.00mmol/L

Expected PaCO₂: 24.0–28.0 mmHg. Observed: 40.0 mmHg. PaCO₂ is above the expected response: an additional respiratory acidosis is suggested. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The ratio is compatible with a high-gap metabolic acidosis. It does not prove that only one metabolic process is present.

  1. The bicarbonate is 12 and the corrected gap is 20.5 mmol/L.
  2. Winter’s range is 24–28 mmHg. A measured PaCO₂ of 40 exceeds the expected range.
  3. There is an additional respiratory acidosis relative to the metabolic disturbance, even though 40 falls inside the routine PaCO₂ interval.
  4. Both processes contribute to the low pH. The cause and clinical response require the patient context.
  • Marked pH abnormality. A real patient sample requires prompt clinical assessment.

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Traditional · mixed

Metabolic acidosis and respiratory alkalosis

Opposing processes produce a pH near the upper end of the reference interval.

pH 7.442PaCO₂ 18 mmHgHCO₃⁻ 12.0 mmol/L
High anion gap metabolic acidosis + respiratory alkalosis

Additional process suggested. PaCO₂ is below the expected response: an additional respiratory alkalosis is suggested.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.442—
PCO₂18mmHg
Reported gas HCO₃⁻12mmol/L
Chemistry total CO₂ / HCO₃⁻12mmol/L
Sodium140mmol/L
Chloride107.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate12mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻12.00mmol/L
Anion gap, without potassium20.50mmol/L
Albumin-corrected anion gap20.50mmol/L
Delta ratio1.00—
Delta gap0.00mmol/L
Delta-adjusted bicarbonate24.00mmol/L

Expected PaCO₂: 24.0–28.0 mmHg. Observed: 18.0 mmHg. PaCO₂ is below the expected response: an additional respiratory alkalosis is suggested. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The ratio is compatible with a high-gap metabolic acidosis. It does not prove that only one metabolic process is present.

  1. Bicarbonate is 12 mmol/L and corrected AG is 20.5 mmol/L. The metabolic acidosis persists despite a pH around 7.442.
  2. Winter’s predicted PaCO₂ is 24–28. The measured 18 is below that range, supporting an additional respiratory alkalosis.
  3. The normal-range pH reflects opposing processes and must not be labelled a normal gas or used alone to claim complete compensation.

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Traditional · mixed

Metabolic alkalosis and respiratory acidosis

Neither the carbon dioxide nor the bicarbonate is explained by compensation alone.

pH 7.420PaCO₂ 60 mmHgHCO₃⁻ 38.0 mmol/L
Metabolic alkalosis + respiratory acidosis

Additional process suggested. PaCO₂ is above the expected response: an additional respiratory acidosis is suggested.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: chronic. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.420—
PCO₂60mmHg
Reported gas HCO₃⁻38mmol/L
Chemistry total CO₂ / HCO₃⁻38mmol/L
Sodium140mmol/L
Chloride93.5mmol/L
Potassium3.1mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻38.00mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Expected PaCO₂: 48.4–50.5 mmHg. Observed: 60.0 mmHg. PaCO₂ is above the expected response: an additional respiratory acidosis is suggested. Expected PaCO₂ = 40 + (0.6–0.75) × (gas HCO₃⁻ − 24) mmHg, with an additional ±2 mmHg screening allowance. At severe alkalosis, the linear rule is less reliable; PaCO₂ above 55 alone does not prove another respiratory disorder.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. For bicarbonate 38, expected PaCO₂ is 48.4–50.5 mmHg. The measured 60 is substantially above that band.
  2. For a chronic PaCO₂ of 60, expected bicarbonate is 30–32; the observed 38 is also above the chronic band and its screening margin.
  3. The combined picture supports metabolic alkalosis with respiratory acidosis. A history of chronic hypercapnia plus diuresis or gastric losses is one possible clinical setting, not a diagnosis supplied by the gas.

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Traditional · mixed

Metabolic and respiratory alkalosis

Both a raised bicarbonate and a low PaCO₂ push the pH upwards.

pH 7.546PaCO₂ 33 mmHgHCO₃⁻ 28.0 mmol/L
Metabolic alkalosis + respiratory alkalosis

Additional process suggested. PaCO₂ is below the expected response: an additional respiratory alkalosis is suggested.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.546—
PCO₂33mmHg
Reported gas HCO₃⁻28mmol/L
Chemistry total CO₂ / HCO₃⁻28mmol/L
Sodium140mmol/L
Chloride103.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻28.00mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Expected PaCO₂: 42.4–43.0 mmHg. Observed: 33.0 mmHg. PaCO₂ is below the expected response: an additional respiratory alkalosis is suggested. Expected PaCO₂ = 40 + (0.6–0.75) × (gas HCO₃⁻ − 24) mmHg, with an additional ±2 mmHg screening allowance. At severe alkalosis, the linear rule is less reliable; PaCO₂ above 55 alone does not prove another respiratory disorder.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. Bicarbonate is 28 mmol/L and PaCO₂ is 33. Both changes support the observed alkalaemia.
  2. Metabolic alkalosis would predict PaCO₂ 42.4–43.0 mmHg. The measured value is below this range.
  3. The low PaCO₂ cannot be compensatory for metabolic alkalosis; an additional respiratory alkalosis is present.

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Traditional · mixed

High-gap and possible normal-gap acidosis

Bicarbonate has fallen more than the increase in the corrected gap.

pH 7.282PaCO₂ 26 mmHgHCO₃⁻ 12.0 mmol/L
High anion gap metabolic acidosis

Expected response. PaCO₂ is compatible with the expected respiratory response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.282—
PCO₂26mmHg
Reported gas HCO₃⁻12mmol/L
Chemistry total CO₂ / HCO₃⁻12mmol/L
Sodium140mmol/L
Chloride111.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate4mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻12.00mmol/L
Anion gap, without potassium16.50mmol/L
Albumin-corrected anion gap16.50mmol/L
Delta ratio0.67—
Delta gap-4.00mmol/L
Delta-adjusted bicarbonate20.00mmol/L

Expected PaCO₂: 24.0–28.0 mmHg. Observed: 26.0 mmHg. PaCO₂ is compatible with the expected respiratory response. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The bicarbonate fall exceeds the gap increase. An additional normal-gap metabolic acidosis is suggested; urinary anion losses and the selected baseline can also alter this ratio.

  1. AG is 16.5 mmol/L, above the selected upper limit of 13. The increase above the 8.5 anchor is 8.
  2. The bicarbonate fall is 24 − 12 = 12. Delta ratio = 8 / 12 = 0.67.
  3. This pattern suggests an additional normal-gap component. It should be checked against baseline results, fluid exposure, renal function and gastrointestinal losses.
  4. The measured PaCO₂ of 26 remains within Winter’s range. A delta screen describes a possible second metabolic process; it is not proof of its cause.

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Traditional · mixed

High-gap acidosis with possible metabolic alkalosis

The rise in the gap is large compared with the fall in bicarbonate.

pH 7.329PaCO₂ 35 mmHgHCO₃⁻ 18.0 mmol/L
High anion gap metabolic acidosis · additional metabolic alkalosis possible

Expected response. PaCO₂ is compatible with the expected respiratory response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.329—
PCO₂35mmHg
Reported gas HCO₃⁻18mmol/L
Chemistry total CO₂ / HCO₃⁻18mmol/L
Sodium140mmol/L
Chloride95.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate6mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻18.00mmol/L
Anion gap, without potassium26.50mmol/L
Albumin-corrected anion gap26.50mmol/L
Delta ratio3.00—
Delta gap12.00mmol/L
Delta-adjusted bicarbonate36.00mmol/L

Expected PaCO₂: 33.0–37.0 mmHg. Observed: 35.0 mmHg. PaCO₂ is compatible with the expected respiratory response. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The gap increase exceeds the bicarbonate fall. Consider an additional metabolic alkalosis or a previously raised bicarbonate from chronic CO₂ retention.

  1. Corrected AG is 140 − 95.5 − 18 = 26.5 mmol/L. The rise above 8.5 is 18.
  2. Delta ratio = 18 / (24 − 18) = 3.0. Delta-adjusted bicarbonate is 18 + 18 = 36 mmol/L.
  3. The high ratio and adjusted bicarbonate suggest an additional alkalinising metabolic process, or a previously raised bicarbonate. A prior gas and the history distinguish these possibilities.
  4. Winter’s range is 33–37 mmHg; measured PaCO₂ 35 is compatible with respiratory compensation.

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Traditional · mixed

Normal pH and bicarbonate, raised gap

A reassuring-looking gas can coexist with an abnormal anion gap.

pH 7.396PaCO₂ 40 mmHgHCO₃⁻ 24.0 mmol/L
Possible high-gap metabolic acidosis + metabolic alkalosis

Mixed metabolic process possible. The increased gap and delta-adjusted HCO₃⁻ 34.0 mmol/L suggest an acidifying process offset by alkalinisation or a previously raised bicarbonate. The numerical screen does not prove two causes.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.396—
PCO₂40mmHg
Reported gas HCO₃⁻24mmol/L
Chemistry total CO₂ / HCO₃⁻24mmol/L
Sodium140mmol/L
Chloride97.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate5mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻24.00mmol/L
Anion gap, without potassium18.50mmol/L
Albumin-corrected anion gap18.50mmol/L
Delta ratioNot available—
Delta gap10.00mmol/L
Delta-adjusted bicarbonate34.00mmol/L

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

Bicarbonate is near normal or raised, so the denominator is small or non-positive. Use the delta-adjusted bicarbonate as a cautious screen; no delta ratio is assigned.

  1. The gas resembles the reference case: PaCO₂ 40 and bicarbonate 24. Corrected AG is nevertheless 18.5 mmol/L.
  2. Delta-adjusted bicarbonate is 24 + (18.5 − 8.5) = 34 mmol/L. Opposing metabolic processes are a possibility to investigate.
  3. A delta ratio would divide by 24 − 24 = 0 and is therefore not reported. The gap finding remains useful without a ratio.
  4. Repeat or confirm an unexpected gap, then assess the measured lactate and other possible anions in context.

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Traditional · mixed

Two processes, a possible third

High-gap acidosis and respiratory alkalosis, with a delta pattern suggesting metabolic alkalosis.

pH 7.442PaCO₂ 18 mmHgHCO₃⁻ 12.0 mmol/L
High anion gap metabolic acidosis + respiratory alkalosis · additional metabolic alkalosis possible

Additional process suggested. PaCO₂ is below the expected response: an additional respiratory alkalosis is suggested.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.442—
PCO₂18mmHg
Reported gas HCO₃⁻12mmol/L
Chemistry total CO₂ / HCO₃⁻12mmol/L
Sodium140mmol/L
Chloride90mmol/L
Potassium3.1mmol/L
Albumin40g/L
Lactate8mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻12.00mmol/L
Anion gap, without potassium38.00mmol/L
Albumin-corrected anion gap38.00mmol/L
Delta ratio2.46—
Delta gap17.50mmol/L
Delta-adjusted bicarbonate41.50mmol/L

Expected PaCO₂: 24.0–28.0 mmHg. Observed: 18.0 mmHg. PaCO₂ is below the expected response: an additional respiratory alkalosis is suggested. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The gap increase exceeds the bicarbonate fall. Consider an additional metabolic alkalosis or a previously raised bicarbonate from chronic CO₂ retention.

  1. AG is 38 mmol/L. Bicarbonate is 12, with PaCO₂ 18 below Winter’s 24–28 range: high-gap metabolic acidosis and respiratory alkalosis coexist.
  2. Delta ratio = (38 − 8.5) / 12 = 2.46. Delta-adjusted bicarbonate is 41.5 mmol/L.
  3. The delta result raises the possibility of a third process, metabolic alkalosis, or a higher starting bicarbonate. Treat the third label as a hypothesis requiring history and earlier results.
  4. A near-normal pH does not remove the need to account for each component.

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Traditional · reference

A venous sample stays venous

Numeric calculations are retained without assigning an arterial compensation diagnosis.

pH 7.363PCO₂ 45 mmHgHCO₃⁻ 25.0 mmol/L
Venous sample · descriptive results

Arterial compensation withheld. No fixed conversion to an arterial gas is applied. Arterial compensation and primary-disorder assignment are withheld; use sample-specific interpretation.

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Inputs, calculations and explanation

Synthetic venous sample at 37°C. Respiratory course: unknown. Chemistry collection: same time as the gas. reported chemistry total CO₂

Entered measurements
MeasurementValueUnit
pH7.363—
PCO₂45mmHg
Reported gas HCO₃⁻25mmol/L
Chemistry total CO₂ / HCO₃⁻25mmol/L
Sodium140mmol/L
Chloride106.5mmol/L
Potassium4mmol/L
Albumin40g/L
Lactate1mmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻25.00mmol/L
Anion gap, without potassium8.50mmol/L
Albumin-corrected anion gap8.50mmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

The albumin-corrected gap is not above the selected upper limit; a delta ratio is not indicated.

  1. This example is explicitly venous. Its pH and PCO₂ describe the collected sample; they are not converted to arterial values.
  2. Calculated bicarbonate and the chemistry-based AG remain visible. Arterial compensation labels should be withheld.
  3. Use a sample-appropriate assessment and obtain an arterial sample when the clinical question requires it.

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Traditional · reference

An incomplete panel can still be useful

pH and PaCO₂ support a gas assessment; anion-gap analysis awaits electrolytes.

pH 7.282PaCO₂ 26 mmHgHCO₃⁻ 12.0 mmol/L
Metabolic acidosis

Expected response. PaCO₂ is compatible with the expected respiratory response.

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Inputs, calculations and explanation

Synthetic arterial sample at 37°C. Respiratory course: acute. Chemistry collection: not confirmed. gas-calculated HCO₃⁻

Entered measurements
MeasurementValueUnit
pH7.282—
PCO₂26mmHg
Reported gas HCO₃⁻12mmol/L
Chemistry total CO₂ / HCO₃⁻Not suppliedmmol/L
SodiumNot suppliedmmol/L
ChlorideNot suppliedmmol/L
PotassiumNot suppliedmmol/L
AlbuminNot suppliedg/L
LactateNot suppliedmmol/L
Calculated values
MeasurementValueUnit
Gas-derived HCO₃⁻12.00mmol/L
Anion gap, without potassiumNot availablemmol/L
Albumin-corrected anion gapNot availablemmol/L
Delta ratioNot available—
Delta gapNot availablemmol/L
Delta-adjusted bicarbonateNot availablemmol/L

Expected PaCO₂: 24.0–28.0 mmHg. Observed: 26.0 mmHg. PaCO₂ is compatible with the expected respiratory response. Expected PaCO₂ = 1.5 × gas HCO₃⁻ + 8 ±2 mmHg. Use the current arterial gas; chemistry total CO₂ is not substituted into this compensation check.

Selected no-potassium AG interval: 4.0–13.0 mmol/L. Delta anchor: 8.5 mmol/L. RCPA adult interval without K: 4–13 mmol/L. Delta anchor 8.5 is a selected value.

Sodium, chloride and bicarbonate are needed for the anion gap.

  1. The gas gives a calculated bicarbonate around 12 mmol/L. PaCO₂ 26 is compatible with Winter’s expected 24–28 range.
  2. Sodium and chloride are missing, so the anion gap is unavailable. Missing albumin also prevents correction.
  3. The available gas supports metabolic acidosis with compatible respiratory compensation. Its gap subtype and cause remain unassessed.
  4. Blank measurements are never replaced by reference values.

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