Water Deficit, Free Water Calculations

Human Physiology • Fluid, Electrolyte, and Acid–base Physiology

Written by STEM Calculators Team Published April 26, 2026 Updated April 26, 2026

Estimate free water deficit from current sodium, target sodium, body weight, and a total body water assumption. This educational tool is designed for physiology learning and does not replace clinical judgment.

Core inputs

Current serum sodium (mmol/L)

Desired serum sodium (mmol/L)

Body weight (kg)

Total body water assumption

Replacement planning

Planned correction time (days)

Maximum sodium change used for warning (mmol/L/day)

Optional ongoing free-water loss (mL/day)

Optional interpretation note

The daily plan is a teaching estimate: deficit divided across the chosen days, plus optional ongoing losses.

Preset cases

Use a preset to compare mild dehydration, severe water loss, or a slower staged correction plan.

Paste or import CSV values

Paste either a header row plus one data row, or key-value pairs. Supported keys: currentNa, targetNa, weightKg, tbwFraction, planDays, maxDailyChange, ongoingLoss.

Ready

Interactive visualizations and simulation

Hover over plotted elements to inspect values. Use the zoom control if labels are easier to read at a larger scale, then scroll horizontally if needed.

Zoom 100% Simulation day Day 0

Body-water container

Target correction bar

Staged correction timeline

TBW assumption comparison

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Water deficit and free water replacement

A water deficit calculator estimates how much free water is missing when serum sodium is higher than the desired target. The core idea is that hypernatremia usually reflects too little water relative to body sodium, so correcting the water balance can move serum sodium toward a safer target.

The calculation depends on current serum sodium, desired serum sodium, body weight, and an assumed total body water fraction. This makes the result an estimate, because total body water changes with age, sex, body composition, and clinical condition.

Core formulas

Total body water is estimated from body weight and the selected total body water fraction:

\[ \begin{aligned} TBW &= \text{body weight} \cdot \text{TBW fraction} \end{aligned} \]

The free water deficit is then estimated by comparing the current sodium concentration with the desired sodium concentration:

\[ \begin{aligned} \text{Free water deficit} &= TBW \cdot \left(\frac{Na_{\text{current}}}{Na_{\text{target}}} - 1\right) \end{aligned} \]

Here, \(TBW\) is total body water in liters, \(Na_{\text{current}}\) is the measured serum sodium, and \(Na_{\text{target}}\) is the desired serum sodium. If the result is positive, the model estimates a free water deficit. If the result is negative, the target sodium is above the current sodium and the usual hypernatremia water-deficit interpretation does not apply.

How to interpret the result

A larger free water deficit means more water would be needed to shift the sodium concentration toward the selected target. The calculator also estimates the sodium difference and divides the deficit across a planned correction time when a replacement plan is entered.

The daily replacement estimate is a teaching model. A faster planned sodium change produces a stronger caution because overly rapid correction can be unsafe in real clinical settings.

Use kilograms for body weight, not pounds.
Choose a total body water fraction that matches the teaching case.
Do not treat the equation as a complete clinical fluid order.
Check whether ongoing losses should be added to the daily plan.

Micro example

For a 70 kg adult with a total body water fraction of 0.60, \(TBW = 70 \cdot 0.60 = 42\ \text{L}\).

If current sodium is \(158\ \text{mmol/L}\) and the target is \(145\ \text{mmol/L}\), the estimated free water deficit is:

\[ \begin{aligned} \text{Deficit} &= 42 \cdot \left(\frac{158}{145} - 1\right) \\ &\approx 3.77\ \text{L} \end{aligned} \]

This tool is best used for learning the relationship between hypernatremia, total body water, water loss, and staged correction planning. More advanced interpretation should also consider ongoing losses, urine concentration, glucose correction, kidney function, and the broader fluid and electrolyte picture.

Frequently Asked Questions

What does a free water deficit calculator estimate?

It estimates how much water is missing when serum sodium is above a selected target. The common formula is TBW x (current sodium / target sodium - 1).

Why does total body water fraction matter?

The same sodium values can produce different deficit estimates depending on body water assumptions. Lower TBW fractions usually produce smaller calculated deficits, while higher TBW fractions produce larger deficits.

How is the daily replacement estimate calculated?

The calculator divides the estimated free water deficit by the planned correction time and then adds any ongoing free-water loss entered by the user. This is an educational estimate, not a complete clinical prescription.

Why does the calculator warn about correction rate?

Rapid changes in serum sodium can be unsafe. The warning compares the planned daily sodium change with the maximum daily change entered in the calculator.

When is the water deficit formula most useful?

It is most useful for teaching hypernatremia and altered body water states where the target sodium is lower than the current sodium. It should be interpreted together with clinical context, ongoing losses, and other electrolyte data.

Core inputs

Replacement planning

Preset cases

Paste or import CSV values

Interactive visualizations and simulation

Body-water container

Target correction bar

Staged correction timeline

TBW assumption comparison

Calculation steps

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Frequently Asked Questions

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