Free Water Deficit Calculator (Hypernatremia)

What is free water deficit?

Free water deficit is an estimate of how much electrolyte-free water a patient has lost relative to solute, typically in the setting of hypernatremia (elevated serum sodium). It represents the volume of pure water that would need to be given to bring the serum sodium back toward a chosen target (often 140 mEq/L), assuming no ongoing losses or gains.

This calculator implements commonly used formulas (including Adrogue–Madias) and lets you adjust:

• Patient type (adult vs pediatric)
• Sex and total body water (TBW) fraction
• Weight in kg or lb
• Current and target serum sodium
• Desired maximum correction rate per 24 hours

Free water deficit formulas

1. Total body water (TBW)

First, estimate total body water as a fraction of body weight:

Common TBW fractions used clinically:

• Adult men: 0.6 (younger), 0.5 (elderly or frail)
• Adult women: 0.5 (younger), 0.45–0.5 (elderly or frail)
• Children: 0.6–0.7 depending on age

The calculator pre-populates a reasonable default based on patient type and sex, but you can override it.

2. Adrogue–Madias free water deficit formula

• Serum Na = current sodium (mEq/L)
• Target Na = desired sodium (often 140 mEq/L)
• TBW in liters

This formula estimates how much free water is needed to dilute the current sodium down to the target, assuming no ongoing losses or gains and that sodium content stays constant.

3. Simplified formula (fixed target 140 mEq/L)

Many references use a simplified version with a fixed target of 140 mEq/L:

This is mathematically identical to the Adrogue–Madias formula when the target is 140 mEq/L. The calculator shows both the general and the simplified estimates for transparency.

How to use the free water deficit calculator

1. Select patient type and sex. The tool will suggest a TBW fraction (e.g., 0.6 for adult male, 0.5 for adult female). Adjust if the patient is elderly, obese, or very lean.
2. Enter weight. You can use kg or lb; the calculator converts lb to kg internally.
3. Enter current serum sodium. Only use this tool for hypernatremia (Na > 145 mEq/L). If sodium is normal or low, a free water deficit formula is not appropriate.
4. Choose a target sodium. 140 mEq/L is a common default. In some high-risk patients, you may choose a higher intermediate target (e.g., 145 → 150).
5. Set a maximum correction rate. For chronic or unknown-duration hypernatremia, many guidelines suggest no more than 10–12 mEq/L per 24 hours.
6. Click “Calculate”. The tool will display:
   • Estimated TBW
   • Free water deficit (Adrogue–Madias)
   • Simplified deficit (target 140 mEq/L)
   • A rough suggestion for how much water to give per 24 hours based on your chosen correction rate

Worked example

Case: 70 kg adult man with chronic hypernatremia, serum Na = 160 mEq/L, target Na = 140 mEq/L.

1. Estimate TBW (adult male): TBW fraction ≈ 0.6.
   TBW = 70 kg × 0.6 = 42 L
2. Apply Adrogue–Madias:
   Free water deficit = 42 × \(\left(\dfrac{160}{140} - 1\right)\) = 42 × (1.1429 − 1) ≈ 42 × 0.1429 ≈ 6.0 L
3. If you aim to correct by 10 mEq/L in the first 24 hours (160 → 150), you might initially plan to give roughly:
   6.0 L × \(\dfrac{10}{20}\) ≈ 3.0 L free water over 24 hours
   plus replacement of ongoing losses, with frequent sodium checks and adjustments.

Clinical considerations and limitations

• Formulas are approximations. They assume stable sodium content and no ongoing losses. Real patients often have ongoing renal, GI, or insensible losses that must be added to the plan.
• Correction rate matters. Rapid correction of chronic hypernatremia can cause cerebral edema and neurologic injury. For chronic or unknown-duration hypernatremia, many experts recommend limiting correction to about 10–12 mEq/L per 24 hours.
• Acute hypernatremia (developing over < 48 hours) may be corrected more rapidly, but this should be done in a monitored setting with specialist input.
• Choice of fluid. Free water can be given as:
  • Enteral water (via mouth or feeding tube)
  • Intravenous 5% dextrose in water (D5W)
  • Sometimes 0.45% saline, depending on volume status and concurrent needs
• Volume status. In hypovolemic hypernatremia, initial resuscitation is usually with isotonic saline to restore perfusion, followed by hypotonic fluids to correct sodium.
• Pediatrics. Children are at particularly high risk of complications from both hypernatremia and its correction. Always involve pediatric or nephrology specialists.

Frequently asked questions

Is free water deficit the same as dehydration?

Not exactly. Free water deficit specifically refers to loss of water relative to solute, leading to hypernatremia. A patient can be volume depleted without hypernatremia, and some hypernatremic patients may be euvolemic or even hypervolemic depending on the underlying cause.

Which TBW fraction should I choose?

The TBW fraction is an estimate. Use higher values for younger, lean patients and lower values for elderly, obese, or very frail patients. When in doubt, many clinicians use:

• 0.6 for adult men
• 0.5 for adult women
• 0.45–0.5 for elderly of either sex

How often should I re-check sodium during correction?

In moderate to severe hypernatremia, sodium is often checked every 2–4 hours during active correction, then less frequently once the rate of change is stable and within the desired range. Follow your institution’s protocol.

Can I use this calculator for hyponatremia?

No. The free water deficit formulas here are intended for hypernatremia. Hyponatremia management uses different concepts (e.g., sodium deficit, tonicity, and specific correction limits) and requires separate tools and guidelines.

Disclaimer

This free water deficit calculator is provided for educational and decision-support purposes only. It does not replace clinical judgment, institutional protocols, or specialist consultation. Always verify calculations, monitor the patient closely, and adjust therapy based on serial labs and clinical response.