Enter the current sodium level, desired sodium level, weight, and a total body water (TBW) factor into the calculator to estimate the free water excess (the approximate liters of electrolyte-free water contributing to hyponatremia). This calculator provides an educational estimate commonly used in clinical learning and decision-support.

Free Water Excess Calculator

Enter Current Sodium, Desired Sodium, Weight, and a TBW factor to estimate Free Water Excess (FWE).

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Free Water Excess Formula

The following formula is used to calculate the free water excess (for hyponatremia, this estimates electrolyte-free water to remove/restrict to reach a higher sodium target):

\mathrm{FWE}=\mathrm{TBW}\left(1-\frac{\mathrm{Na}}{\mathrm{Na}_{\mathrm{desired}}}\right)

Variables:

  • FWE is the free water excess (liters)
  • Na is the current sodium level (mmol/L)
  • Nadesired is the desired sodium level (mmol/L)
  • TBW is total body water (liters), commonly estimated as: TBW ≈ (TBW factor) × weight (kg)

To calculate the free water excess, estimate total body water (TBW) and multiply it by (1 − Na/Nadesired). For hyponatremia (Na < Nadesired), this gives a positive value (liters of electrolyte-free water to remove/restrict); if Na > Nadesired, the result is negative (a relative water deficit vs the target).

Important context: This “free water excess” framing is primarily used for hyponatremia estimation. Hypernatremia evaluation/treatment is typically approached using a free water deficit framework and should be guided by clinician oversight.

What is Free Water Excess?

Free water excess is an estimate of how much electrolyte-free water is contributing to a low serum sodium relative to a chosen target. It is used in the management of electrolyte imbalances such as hyponatremia, where the sodium concentration in the blood is abnormally low. (If you use a lower target than the current sodium, the calculation will produce a negative value, which corresponds to a water deficit relative to that target.)

How to Calculate Free Water Excess?

The following steps outline how to calculate the Free Water Excess:

  1. First, determine the current sodium level (Na) in mmol/L.
  2. Next, determine the desired sodium level (Nadesired) in mmol/L.
  3. Next, determine the patient’s weight in kilograms (or convert from pounds).
  4. Estimate total body water (TBW) in liters using a TBW factor: TBW ≈ (TBW factor) × weight (kg).
  5. Use the formula: FWE = TBW × (1 − Na/Nadesired).
  6. Finally, calculate the Free Water Excess (FWE) in liters.
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Current sodium level (Na) = 125 mmol/L

Desired sodium level (Nadesired) = 135 mmol/L

Weight of the patient = 70 kg

Assume TBW factor = 0.60 (typical adult male). Then TBW ≈ 0.60 × 70 = 42 L.

FWE = 42 × (1 − 125/135) ≈ 3.111 L.