Advertisement

Free water deficit calculator

Estimate the free water needed to reach a chosen sodium concentration in a closed-system model, or solve for sodium or body weight.

Calculator

Estimated free water deficit
4.2
Estimated initial body water (L)
42.000
Body weight (kg)
70.000
Current sodium (mmol/L)
154.000
Desired sodium (mmol/L)
140.000

Advertisement

How this calculator works

The closed-system equation estimates a net water gain while solute content stays constant. It excludes ongoing losses and maintenance requirements. The cited review uses 140 mmol/L as the reference; entering another target is an algebraic generalization of that same mass-balance equation. The target does not specify how quickly to correct sodium. The result is an estimate for information only and is not medical advice.

Formula

Water deficit (L) = TBW × (current Na / desired Na - 1). TBW = weight (kg) × body-water fraction. Current Na = desired Na × (1 + deficit/TBW).

Worked example

At 70 kg and fraction 0.60, TBW is 42 L. Current Na 154 and desired Na 140 give 42 × 0.1 = 4.2 L. At 60 kg and fraction 0.50, Na 168 to 140 gives 6 L.

Advertisement

Frequently asked questions

Is this a daily drinking target?

No. It is a modelled deficit, and route, timing and ongoing losses require individual clinical assessment.

Why can a body-water fraction be changed?

Age, body composition and water depletion alter body water. The approximate adult presets may not fit an individual.

What if current and desired sodium are equal?

The deficit is zero. That zero difference cannot identify body weight in an inverse calculation.

Sources

Advertisement