What this calculator does
When serum sodium is high, the usual problem is not too much sodium but too little water. The free water deficit estimates how much water would be needed to dilute the measured sodium back to a target.
The figures are large. A 75 kg adult with a sodium of 155 mEq/L has an estimated deficit of 4.82 litres against a target of 140, and at 165 mEq/L that rises to 8.04 litres.
The formula
Total body water is body weight multiplied by a factor reflecting age and sex. The deficit is that volume multiplied by the ratio of measured to target sodium, less one.
| Term | Meaning |
|---|---|
| Free water deficit | The water volume needed to bring sodium down to the target. |
| Total body water | Body weight multiplied by a population factor, typically 0.45 to 0.6. |
| Correction rate | How fast sodium may safely be lowered, conventionally about 10 mEq/L per 24 hours. |
The inputs explained
| Field | What to enter |
|---|---|
| Body weight (kg) | Body weight in kilograms. |
| Measured sodium (mEq/L) | Measured serum sodium in mEq/L. |
| Target sodium (mEq/L) | Target sodium in mEq/L, usually 140. |
| Body-water factor | Body water factor, which varies with age and sex. |
When to use it
Planning fluid replacement
The deficit is the starting figure for a correction plan.
Understanding why correction is slow
The volume is large and lowering sodium too quickly carries its own serious risks.
Seeing how weight scales the answer
The deficit is proportional to total body water and therefore to body size.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the sodium level change the deficit?
The same patient at three measured sodium levels.
| Measured sodium | Estimated free water deficit | Total body water used |
|---|---|---|
| 150 mEq/L | 3.21 L | 45.0 L |
| 155 mEq/L | 4.82 L | 45.0 L |
| 165 mEq/L | 8.04 L | 45.0 L |
Questions
Why must correction be slow?
Because brain cells adapt to a high sodium level over hours to days, and lowering it faster than they can readjust risks cerebral oedema. The conventional limit of about 10 mEq/L per 24 hours exists for that reason.
Does this account for ongoing losses?
No, and that is a significant limitation. The figure covers the existing deficit only. Continuing losses through urine, sweat, breathing and the gut must be replaced on top of it.
Which body water factor should be used?
Conventionally 0.6 for adult men and children, 0.5 for adult women and older men, and 0.45 for older women. These are population averages and fit poorly at extremes of body composition.
Is this a treatment plan?
No. It is one estimate feeding into a decision that requires clinical assessment, repeated monitoring and adjustment. Hypernatraemia management belongs in a clinical setting.
For total body water on its own, see the total body water calculator. For sodium adjusted against high glucose, see the corrected sodium calculator.