Estimate free water excess in hyponatremia, or the free water deficit in hypernatremia, from serum sodium and body weight using a body-water fraction.

Reference assumptions: target sodium 140 mmol/L and body-water fraction 0.60.

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Free Water Excess Formula

The following formula is used to calculate the free water excess (for hyponatremia, this estimates a closed-system comparison volume; it does not prescribe fluid removal, restriction, or a correction rate):

FWE = TBW(1 - (Na) / (Nadesired))

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 (a closed-system comparison volume, not a treatment amount); if Na > Nadesired, the calculator shows the same amount as a free water deficit, TBW × (Na/Nadesired − 1); it is not a hypernatremia treatment plan.

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 illustrates a simplified constant-solute model. Actual treatment depends on the cause, symptoms, duration, and ongoing fluid and electrolyte balance and requires clinician monitoring. (If you use a lower target than the current sodium, the calculator reports the difference as a free water deficit, which should not be used as a hypernatremia treatment plan.)

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.