Free Water Deficit Calculator
Calculate the free water deficit in hypernatremia with the Adrogue-Madias formula — a clinical reference for doctors and trainees.
Your latest serum sodium result in mmol/L. Normal is roughly 135-145.
Free water deficit
4.5 L
Adrogue-Madias formula
In millilitres
4,500 ml
Replacement volume estimate
Estimated TBW
42 L
60% of body weight
For clinicians and informed patients only. Hypernatremia correction is medical care — rehydration rate and monitoring must be decided by a physician, never by a calculator.
Last updated: August 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
This calculator is a ward-round companion for doctors, residents and medical students managing hypernatremia. The free water deficit anchors the initial fluid prescription in adults with elevated serum sodium, whether the cause is poor intake in the elderly, fever or diarrhoea losses, or diabetes insipidus. It is also a teaching tool: medical students repeatedly work the Adrogue-Madias formula in exams and in the ICU, and having the arithmetic automated leaves room to think about the harder parts — the correction rate, the fluid choice and the underlying cause. Nurses and physicians' assistants use it to double-check orders and to explain to families why a patient is receiving a particular volume of water. It is deliberately a reference tool; the individualised plan remains with the treating clinician, who folds in comorbidities and monitoring intervals the formula cannot see.
How to Use This Calculator
- Step 1: Select the patient's sex — TBW is estimated as 60% of weight in men and 50% in women.
- Step 2: Enter body weight in kilograms and the latest serum sodium in mmol/L.
- Step 3: Read the free water deficit in litres and millilitres, plus the estimated TBW.
- Step 4: Use the number as one input to a clinical correction plan — never as a standalone prescription.
Worked Example
A 70 kg man with a serum sodium of 155 mmol/L has an estimated TBW of 42 litres. The Adrogue-Madias deficit is 42 × (155 ÷ 140 − 1), which works out to 4.5 litres — a substantial deficit that needs slow, monitored correction. The same formula for a 55 kg woman at 160 mmol/L gives a 27.5-litre TBW and a deficit of about 3.93 litres (3,930 ml). At or below 140 mmol/L the deficit reads zero, correctly, because no free-water replacement is indicated from the formula's perspective.
Tips and Common Mistakes
- •Tip 1: Recalculate as sodium changes — the deficit shrinks as correction proceeds.
- •Tip 2: Pair the deficit with the patient's ongoing losses; insensible and GI losses continue during treatment.
- •Tip 3: Use the same sodium measurement basis (venous, arterial or capillary) for trend comparisons.
- ✗Mistake 1: Correcting the full deficit rapidly — the rate of sodium correction, not the volume alone, drives outcome.
- ✗Mistake 2: Forgetting that TBW estimates assume average body composition; obesity and oedema skew them.
Frequently Asked Questions
What is free water deficit?
It is the volume of pure water an adult needs to correct hypernatremia — high serum sodium — assuming the sodium stays constant. The deficit is estimated from body weight and serum sodium using the Adrogue-Madias formula.
What is the Adrogue-Madias formula?
The free water deficit is TBW × (measured Na ÷ 140 − 1), where TBW is estimated as 60% of weight in men and 50% in women. It estimates how many litres of water are 'missing' at a sodium level above 140 mmol/L.
Who should use this calculator?
It is a clinical reference for doctors, residents and medical students planning hypernatremia correction. It should not be used by patients to self-treat, because the rate of correction, the choice of fluids and monitoring are medical decisions.
How is hypernatremia treated?
Treatment replaces the deficit with oral water or intravenous fluids while the underlying cause is addressed, and serum sodium is rechecked frequently. Correction is done gradually to avoid cerebral oedema — the deficit is a planning estimate, not a one-shot prescription.
Why is the sodium capped at 140 mmol/L in the formula?
140 mmol/L is the reference value in the Adrogue-Madias convention, close to the middle of the normal range (135-145 mmol/L). At or below 140 the calculated deficit is zero, meaning no replacement is needed from the formula's perspective.
What causes hypernatremia?
Common causes include inadequate water intake (especially in the elderly or unconscious), heavy water loss through fever, diarrhoea or burns, diabetes insipidus, and diuretic use. Symptoms range from thirst to confusion and seizures in severe cases.
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