Estimate free water excess in hyponatremia from serum sodium, target sodium, body weight, and patient type; results show liters, mL, and cups.

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

Educational closed-system estimate. This is not a fluid-removal or restriction prescription. Hyponatremia requires clinician assessment and monitored treatment.

Related Calculators

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 result is negative (a signed model difference; 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 calculation will produce a negative value, which is a signed model difference and 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.