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.
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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:
- First, determine the current sodium level (Na) in mmol/L.
- Next, determine the desired sodium level (Nadesired) in mmol/L.
- Next, determine the patient’s weight in kilograms (or convert from pounds).
- Estimate total body water (TBW) in liters using a TBW factor: TBW ≈ (TBW factor) × weight (kg).
- Use the formula: FWE = TBW × (1 − Na/Nadesired).
- Finally, calculate the Free Water Excess (FWE) in liters.
- 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.
