What is the exact free-water-deficit formula?

This hypernatremia model requires current sodium >145 mmol/L or mEq/L. Estimated TBW (L) = normalized weight (kg) × the explicit coefficient selected outside this page. Estimated deficit (L) = TBW × (current sodium ÷ selected lower target sodium − 1). Pounds use 0.45359237 kg per lb, and intermediate values are not rounded.

Is free water deficit the same as the volume to administer?

No. It is a static estimate under submitted assumptions, not a fluid prescription, infusion volume, route, correction rate, or treatment plan. Ongoing losses, intake, volume status, and serial response are separate.

Why is the TBW coefficient entered explicitly?

The coefficient directly changes estimated TBW and the deficit. An explicit input makes that external assumption visible instead of silently applying a default based on incomplete demographic or body-composition data.

Which TBW coefficient should be entered?

The applicable external protocol or clinical workflow must select it. Traditional 0.6 and 0.5 values and lower estimates in some older or water-depleted groups are population approximations, not a universal personal selection table.

How should target sodium be selected?

Target selection depends on context absent from this page, including onset, symptoms, serial sodium, volume status, and treatment history. The calculator neither prefills 140 nor recommends another target.

Does the formula include ongoing losses?

No. It omits later urine, gastrointestinal, skin, respiratory, and insensible losses, intake, and urine electrolyte-free water clearance. It is not a complete 24-hour water requirement.

Can it be used with sodium loss or volume depletion?

The constant-total-sodium equation is most direct for pure-water loss. Sodium loss and extracellular-volume depletion are distinct problems and can make the simple estimate too low.

Can hyperglycemia or pseudohypernatremia change interpretation?

Yes. Glucose-related sodium redistribution, pseudohypernatremia, and direct-versus-indirect measurement questions require separate evaluation; this page uses the submitted sodium without resolving them.

Can the same assumptions be used in pregnancy, children, or neonates?

This page does not establish that. Those populations require population-specific assessment, and the calculator has no pregnancy, gestational-age, pediatric, or neonatal inputs and supplies no universal coefficient.

Do edema, ascites, obesity, frailty, or altered body composition matter?

They can change how a weight-based TBW approximation relates to an individual. The page cannot determine whether a submitted coefficient is appropriate from weight and sodium alone.

Can it select a fluid, amount, rate, correction time, or monitoring plan?

No. It does not choose fluid type, oral or IV route, administration amount, rate, duration, monitoring, medicine, dialysis, referral, or another treatment action.

Educational reference only. Not a diagnostic tool. See full disclaimer.

NephrologyFree Water Deficit

Free Water Deficit Calculator (Explicit TBW Coefficient)

Estimate a static positive free water deficit for hypernatremia when current sodium is >145 mmol/L or mEq/L, using an explicitly selected lower target, kg or lb weight, and an explicit TBW coefficient, with estimated TBW and results in L and mL—not an infusion volume or treatment output.

Content updated: August 8, 2026View sources

QuickMedCalc is developed and maintained by an independent developer. Medical content is not independently reviewed by a physician.

Formula and medical content are based on the references listed on this page. See sources, About, and Sources and Review Process.

About

This page calculates a static, positive free-water-deficit estimate for hypernatremia when current sodium is greater than 145 mmol/L or mEq/L. It uses a lower target sodium selected in an external workflow, weight, and an explicit TBW coefficient. It displays estimated TBW and the same deficit in liters and milliliters. It automatically selects neither target nor coefficient, and it does not diagnose the cause, duration, urgency, or treatment of hypernatremia.[1, 2, 3]

Weight multiplied by the explicit coefficient estimates TBW; it does not measure body water. Traditional background commonly includes 0.6 and 0.5, with lower estimates in older or markedly water-depleted groups. These are population approximations, not a universal personal table, so the page does not infer a coefficient from age, sex, BMI, obesity, frailty, or diagnosis.[1, 3]

The arithmetic assumes constant total body sodium and is most direct for a pure-water-loss model. It omits sodium loss, ongoing renal and extrarenal losses, insensible loss, intake, urine electrolyte-free water clearance, and changes during treatment. The output is not an infusion volume, fluid choice, correction rate, correction time, or treatment plan.[3, 4, 5]

Formula

Estimated TBW (L) = normalized weight (kg) × explicit TBW coefficient. The coefficient must be selected outside this page; there is no default. The output is an estimate, not a measurement.[1, 3]

Estimated deficit (L) = estimated TBW × (current sodium ÷ selected target sodium − 1). This hypernatremia model requires current sodium >145 mmol/L or mEq/L. The target must be strictly lower than current sodium. Equal target does not return zero; higher target does not calculate water excess; and the target is not recommended by this site.[2, 3]

Unit normalization: weight lb × 0.45359237 = weight kg; deficit mL = deficit L × 1000. Sodium mmol/L and mEq/L are numerically equivalent here. Normalization precedes calculation, without intermediate rounding.

Display contract: deficit liters use two decimals, milliliters use a whole number, and TBW and normalized kilograms use two decimals. Tiny positive results use a less-than display instead of false zero. Software input boundaries are not physiologic ranges, target recommendations, or treatment thresholds.

Interpretation

Quantity	What it represents	Calculated here
Current sodium	Submitted sodium for one clinical assessment	Input
Selected target sodium	External workflow’s lower sodium target	Input
Protocol-selected TBW coefficient	External assumption for estimated body-water fraction	Input
Estimated TBW	Weight multiplied by the submitted coefficient	Yes
Static positive water deficit	Estimated TBW multiplied by the sodium-ratio term	Yes
Measured total body water	Direct body-composition or dilution measurement	No
Ongoing and insensible losses	Water continuing to leave after the submitted assessment	No
Sodium deficit / ECF volume deficit	Separate sodium and extracellular-volume problem	No
Fluid type, administration volume or correction rate	Individual treatment plan	No

Target sodium and the TBW coefficient are inputs, not calculator outputs. Estimated TBW is not measured TBW. Deficit liters and milliliters represent the same static arithmetic quantity, not an actual fluid prescription; this page generates no treatment plan.

What this calculator computes

This is a hypernatremia free-water-deficit model: the submitted current sodium must be greater than 145 mmol/L or mEq/L. That numeric guard defines this calculator's model scope; it does not diagnose the cause, duration, urgency, or treatment of hypernatremia.[1, 3]

Normalize the submitted weight to kilograms.
Read the explicit total-body-water coefficient selected outside this page.
Estimate total body water by multiplying normalized weight by that coefficient.
Calculate the current-to-target sodium ratio.
Calculate only the positive static water-deficit domain.
Show estimated TBW, deficit in liters and milliliters, and the raw audit details.

The calculator does not read volume status, urine output, urine sodium or potassium, urine osmolality, glucose, ongoing losses, fluid intake, the sodium trend, symptoms, or acuity.

Why the page only calculates a positive deficit

The frozen runtime requires the selected target to be strictly below the current sodium. An equal target is rejected rather than displayed as a zero deficit, and a higher target is rejected rather than relabeled as a negative deficit or water excess. This is the software scope of the named positive-deficit task, not clinical advice.

How the formula is assembled

Convert pounds to kilograms when needed.
Multiply kilograms by the submitted coefficient to estimate TBW.
Divide current sodium by the selected lower target sodium.
Subtract one from the sodium ratio.
Multiply that term by estimated TBW.
Multiply liters by 1000 for the milliliter view.
Round only the final displayed quantities.

Why target sodium is explicit

Target selection depends on information this page does not collect, including symptoms, onset, serial sodium results, volume status, and the treatment record. The page does not prefill 140 or derive a target from current sodium. An applicable external workflow must select it first; this calculator performs arithmetic only on that submitted target.[3, 5]

Why the TBW coefficient is explicit

The coefficient directly determines estimated TBW and therefore changes the deficit linearly. This page cannot infer an individual coefficient reliably from age, sex, BMI, obesity, frailty, edema, or diagnosis. An explicit input makes the assumption visible instead of hiding it in a default.

Conventional coefficient background without automatic selection

Traditional references commonly show approximations near 0.6 and 0.5, with lower estimates in older or water-depleted populations. They are population-level approximations, not a universal individual selection table. This page has no automatic male/female or adult/elderly selector, calls no coefficient “correct,” and provides no green, yellow, red, or recommended label.[1, 3]

Static deficit versus an actual fluid prescription

This deficit is static arithmetic under the submitted assumptions. Actual replacement may also depend on ongoing and insensible losses, intake, volume status, route, fluid composition, and serial response. The result must not be copied into “give this many liters.” This page selects no oral, enteral, or IV route; no D5W, saline, or other fluid; and no rate, duration, or monitoring schedule.[3, 4, 5]

Constant-total-sodium and pure-water-loss assumptions

The equation assumes total body sodium remains constant and is most direct for a pure-water-loss model. Hypernatremia may instead involve hypotonic fluid loss with a sodium deficit or hypertonic sodium gain. The same sodium concentration therefore does not establish the same total body sodium or volume status, and this page does not classify euvolemic, hypovolemic, or hypervolemic hypernatremia.[1, 3, 4]

Volume depletion and sodium loss

Volume depletion is a total-body-sodium and extracellular-fluid-volume problem. When hypernatremia accompanies sodium loss, the simple water- deficit formula may underestimate water loss. Intravascular and ECF assessment is a different task from this arithmetic. The page has no vital signs, examination, urine sodium, or hemodynamics and cannot infer dehydration severity or resuscitation needs.[1, 4, 6]

Ongoing and insensible losses

The formula describes a static difference at the submitted time. Later urine, gastrointestinal, skin, respiratory, and insensible losses are not included. Ongoing urine electrolyte-free water clearance requires urine volume and urine sodium and potassium, none of which are inputs here. The result is not a complete 24-hour requirement.[3, 4]

Hyperglycemia and pseudohypernatremia are separate questions

This page uses the submitted sodium as-is. It does not perform Katz or Hillier glucose adjustment, determine direct versus indirect ion-selective electrode measurement, exclude pseudohypernatremia, or assess hyperglycemic redistribution. Those questions must be addressed outside this calculator when relevant.[3]

Worked examples from the frozen implementation

Principal vector

Current sodium 160, selected target 140, 70 kg, and coefficient 0.60 produce estimated TBW 42 L, raw deficit about 6 L, and displays of 6.00 L, 6000 mL, and 42.00 L TBW.