Health calculators

Free Water Deficit Calculator

Updated Aug 28, 2026 By Jehan Wadia
Rate Formulas Medical disclaimer
Calculation Method & Patient Profile
Calculation Method
Weight-Based derives total body water from weight × demographic coefficient. TBW-Based uses a TBW value you enter directly.
Patient Type / Demographic
Selection sets the total body water fraction applied to weight.
Mode: Weight-Based · Adult Male · TBW coefficient 0.60
Patient Values
Typical adult range: 1–300 kg (2.2–661 lb). Value auto-converts when you switch units.
This calculator is clinically indicated for serum sodium above 140 mEq/L (hypernatremia).
Normal range: 136–145 mEq/L. For sodium, mEq/L and mmol/L are numerically equivalent (valence 1).
Normal range: 136–145 mEq/L. Pre-filled at 140 mEq/L; override as needed. Unit stays synchronized with current sodium.
Used to convert the deficit into an hourly rate and to check correction velocity. Common: 48–72 hours.
Liters and milliliters are always shown; this adds a third unit of your choice.
Free Water Deficit Result
Free Water Deficit (Liters) — rounded to 2 decimals
Free Water Deficit (Milliliters) — nearest whole mL — order-ready
In selected unit — from the output unit selector
—
Total Body Water used —  
Sodium gap (current − target) —  
Replacement rate over plan —  
Minimum duration at 10 mEq/L per 24 h —  
Correction Rate Safety Guidance: Serum sodium should be corrected at a rate no greater than 10–12 mEq/L per 24 hours to reduce the risk of osmotic demyelination syndrome (central pontine myelinolysis). Consider distributing the calculated free water deficit over 48–72 hours and reassessing sodium frequently.
Step-by-Step Solution
Show / hide calculation steps
TBW Coefficient Reference
Total body water fraction by demographic. The row applied to your current selection is marked “Applied”.
Patient Type TBW Fraction TBW at entered weight Status
Projected Correction Timeline
Projected sodium assumes an even correction across the planned duration; the limit line shows the fastest correction consistent with 10 mEq/L per 24 hours.
Replacement Rate by Duration

Introduction

The Free Water Deficit Calculator tells you how much water the body is missing when blood sodium is too high. High sodium is called hypernatremia. It usually means the body lost water, not that it gained salt. This tool shows the water gap in liters, milliliters, and other units you pick.

To use it, enter the patient's weight (or total body water), the current sodium level, and the target sodium level. Pick the patient type — adult male, adult female, elderly male, elderly female, or child. Each type has its own total body water fraction, since bodies hold different amounts of water. The math uses this simple formula:

Free Water Deficit = Total Body Water × (Current Sodium ÷ Target Sodium − 1)

You also enter how long you plan to replace the water. The calculator then gives an hourly rate in mL/h and checks your speed against the safe limit of 10–12 mEq/L per 24 hours. Fixing sodium too fast can hurt the brain, so this check matters. Most plans spread the water over 48 to 72 hours. Once you know the volume and the time frame, an IV Infusion Rate Calculator or an Infusion Drip Calculator can turn that plan into a pump setting or drip rate.

You get a full step-by-step solution, a chart of the projected sodium over time, and a chart comparing rates at 24, 48, and 72 hours. Remember: this deficit does not include ongoing losses from urine, sweat, or breathing. Those need extra fluid on top. This tool is for learning and planning support, not a substitute for a doctor's judgment.

How to use our Free Water Deficit Calculator

Enter the patient's body water details, current and target sodium, and how long you plan to replace fluid. The calculator shows the free water deficit in liters, milliliters, and one unit you pick, plus the hourly rate and a safety check on correction speed.

Calculation Method: Pick "Weight-Based" to work out total body water from weight, or "TBW-Based" to type in a total body water value you already have.

Patient Type / Demographic: Choose adult male, adult female, elderly male, elderly female, or child. This sets the body water fraction used with weight.

Patient Weight: Type the weight and choose kg or lb. The number changes on its own when you switch units, and you can double-check any conversion with the Kg to Lbs Calculator. This box only shows in Weight-Based mode. For dosing work that needs a body-size estimate instead of raw weight, see the Ideal Body Weight Calculator and the Adjusted Body Weight Calculator.

Total Body Water (TBW): Type the known total body water and pick L, mL, fl oz, pt, or gal. This box only shows in TBW-Based mode. The Volume Conversion Calculator helps if your source value is in another unit.

Current Serum Sodium: Enter the patient's latest sodium level in mEq/L or mmol/L. The two units are the same number for sodium. Sodium also drives the Serum Osmolality Calculator, which is a useful companion reading.

Target Serum Sodium: Enter the sodium level you want to reach. It starts at 140 mEq/L, and you can change it.

Planned Replacement Duration: Enter how long the fluid will be given and pick hours, days, or minutes. Most plans use 48 to 72 hours.

Additional Output Volume Unit: Choose one more unit for the answer, such as fluid ounces or cups. Liters and milliliters always show, and the Liters to Gallons Calculator covers larger volumes.

Calculate and Reset: Results update as you type, but you can press Calculate to refresh them. Press Reset to bring back the starting values.

What Is Free Water Deficit?

Free water deficit is the amount of plain water the body is missing. When the body loses more water than salt, the sodium in the blood goes up. This is called hypernatremia (blood sodium above 145 mEq/L). The free water deficit tells doctors how many liters of water are needed to bring sodium back down to a safe level. For healthy day-to-day drinking goals rather than a clinical deficit, use the Water Intake Calculator.

The Free Water Deficit Formula

The standard formula is:

Free Water Deficit (L) = Total Body Water × [(Current Sodium ÷ Target Sodium) − 1]

Total body water (TBW) is a share of body weight. That share changes with age and sex, because muscle holds more water than fat:

  • Adult male: 60% of body weight (0.60)
  • Adult female: 50% of body weight (0.50)
  • Elderly male: 50% of body weight (0.50)
  • Elderly female: 45% of body weight (0.45)
  • Child: 60% of body weight (0.60)

Example: a 70 kg adult male has about 42 L of body water. If his sodium is 158 and the goal is 140, his free water deficit is about 5.4 L. Because muscle mass drives how much water a body holds, the Lean Body Weight Calculator and the Body Fat Calculator help explain why the fractions differ between patients.

Why High Sodium Happens

Blood sodium rises when water leaves the body or when a person does not drink enough. Common causes include:

  • Fever, sweating, or hot weather — see the Heat Index Calculator for risky conditions
  • Vomiting and diarrhea
  • Diabetes insipidus or high blood sugar (track control with the A1C Calculator)
  • Water pills (diuretics)
  • Older adults or babies who cannot ask for water
  • Tube feeding without enough free water

Signs can include thirst, dry mouth, weakness, confusion, and in bad cases, seizures. Kidney function shapes how the body handles water, so the GFR Calculator, the Creatinine Clearance Calculator, and the BUN Creatinine Ratio Calculator are often reviewed alongside sodium.

Correcting Sodium Safely

Fixing sodium too fast is dangerous. Fast changes can make brain cells swell and cause cerebral edema or osmotic demyelination syndrome. Because of this, sodium should drop no faster than 10 to 12 mEq/L in 24 hours. Most plans spread the water over 48 to 72 hours, with blood tests every few hours to check progress. Repeat labs often include the Anion Gap Calculator, the Corrected Calcium Calculator, and the Osmolality Calculator to see the whole electrolyte picture. Blood pressure trends from the MAP Calculator can also guide how quickly fluid is given.

Things the Number Does Not Include

The free water deficit only covers water that is already missing. It does not count water the body keeps losing. You must also replace:

  • Urine losses that keep happening — measure them with the Urine Output Calculator and check sodium handling with the FENa Calculator
  • Insensible losses from breathing and skin (about 500–1000 mL a day)
  • Extra losses from fever, diarrhea, drains, or burns

Water can be given by mouth, through a feeding tube, or by IV using D5W or half-normal saline, depending on the patient. If you need to mix or check a solution's strength, the Dilution Calculator and the Molarity Calculator can help, and body-size dosing often starts with the BSA Calculator.

Important Note

This tool gives an estimate, not a treatment plan. Real body water can differ from the formula, and each patient needs lab checks and a doctor's judgment. Always work with a health care provider before giving fluids. For other bedside calculations, browse related tools such as the Heparin Drip Calculator, the QTc Calculator, and the Cardiac Index Calculator.

Formulas used

Total Body Water (weight-based)
TBW = k \times W
Free Water Deficit
FWD = TBW \times \left( \frac{Na_{current}}{Na_{target}} - 1 \right)
Sodium gap
\Delta Na = Na_{current} - Na_{target}
Correction velocity (per 24 h)
v = \frac{|\Delta Na|}{t_{h}} \times 24
Replacement rate
\text{Rate} = \frac{|FWD_{mL}|}{t_{h}}
Minimum safe duration at 10 mEq/L per 24 h
t_{min} = \frac{|\Delta Na|}{10} \times 24
Projected serum sodium during correction
Na(t) = Na_{current} + (Na_{target} - Na_{current}) \times \frac{t}{t_{h}}
Fastest safe sodium change limit line
Na_{limit}(t) = Na_{current} \pm 10 \times \frac{t}{24}

Frequently asked questions

Why is my result a negative number?

A negative answer means there is no water deficit. It shows a free water excess instead. This happens when the current sodium is lower than the target sodium. In that case the patient may need fluid limits, not extra water. Check that you typed the two sodium numbers in the right boxes.

Should I use actual body weight or ideal body weight?

Most clinicians use actual body weight for this formula. But fat holds much less water than muscle, so the answer can be too high in very obese patients. Some teams use a lower water fraction or an adjusted weight in that case. Ask the treating provider which weight to enter.

What target sodium should I enter?

The box starts at 140 mEq/L, which is the middle of the normal range. Some plans aim only for a safe drop in the first 24 hours, such as 10 mEq/L below the current level, rather than full normal. You can type any target you want and the numbers update right away.

Does the calculator work if sodium is normal or low?

It will still do the math, but the answer is not useful. This tool is built for high sodium (hypernatremia), usually above 145 mEq/L. If you type 140 or less, the tool shows a note telling you so. Low sodium needs a different approach and different formulas.

What does the "Minimum duration at 10 mEq/L per 24 h" box mean?

It shows the shortest safe time to reach your target. The tool takes your sodium gap and spreads it out at 10 mEq/L per day. If your planned duration is shorter than this number, you are correcting too fast. Extend the plan to at least that many hours.

Why do mEq/L and mmol/L give the same number?

Sodium carries one charge, so one millimole equals one milliequivalent. The two units are the same number for sodium. Switching the toggle changes only the label, not the math. Both sodium boxes stay on the same unit so you cannot mix them up.

Is the free water deficit the total IV fluid I should give?

No. The deficit is only the plain water already missing. You must add fluid for urine, sweat, breathing, fever, and any drains on top of it. The final IV order is almost always larger than the number this tool gives.

What is the difference between Weight-Based and TBW-Based mode?

Weight-Based takes the weight you type and multiplies it by the water fraction for that patient type. TBW-Based skips that step and uses a total body water value you already have, such as one from a body composition scan. In TBW mode the patient type fraction is not used at all.

What do the three lines on the timeline chart show?

The blue line is the projected sodium if you correct evenly over your planned time. The green line is the cumulative water given in mL. The orange dashed line is the fastest safe change, 10 mEq/L per 24 hours. If the blue line dips below the orange line, your plan is too fast.

Why is the rate chart showing 24, 48, and 72 hours?

Those are the common correction windows. The chart lets you compare the mL per hour needed for each one, plus your own plan. It makes it easy to see how much slower the drip becomes when you stretch the time out.

What happens if I switch from kg to lb?

The number in the box converts on its own. Type 70 kg, switch to lb, and you will see about 154.32 lb. The result does not change because it is the same weight. The same thing happens with the TBW and duration units.

Which fluid do I use to replace the deficit?

That is a clinical choice. Plain water by mouth or feeding tube is used when the patient can take it. For IV, teams often use D5W or half-normal saline. Saline has salt in it, so it replaces less free water per liter. This tool only gives the water volume, not the fluid type.

How often should sodium be rechecked during treatment?

Usually every 4 to 6 hours at first, then less often once the trend is steady. The body keeps losing water while you treat, so the real sodium rarely follows the straight line on the chart. Recalculate with each new lab value.

Why does the calculator use a lower water fraction for older patients?

People lose muscle and gain fat as they age, and fat holds much less water. So an 80-year-old man holds a smaller share of water than a 30-year-old man at the same weight. Using the lower fraction keeps the deficit from being overstated.

Can I use this for a baby or a small child?

Pick Child / Pediatric and the tool uses 0.60. A green badge shows that pediatric mode is on. Note that newborns hold even more water, closer to 0.70 to 0.75, and children need very careful fluid orders. Always confirm with a pediatric provider.

Why do I see a yellow "Note" under a box instead of a red error?

Yellow notes are warnings. The value is still used and results still show, but the number looks unusual, such as a weight over 300 kg or a sodium outside 100–200. Red errors mean the value cannot be used at all and results are paused until you fix it.

Does this tool replace the Adrogué–Madias formula?

No. The free water deficit tells you how much water is missing. Adrogué–Madias predicts how much one liter of a chosen fluid will change sodium. Many teams use both, one to size the deficit and one to pick the fluid and rate.

Can I use this calculator on myself at home?

No. You need a lab sodium result to use it, and high sodium is a hospital problem. This tool is for learning and for planning support by trained staff. If you feel very thirsty, weak, or confused, get medical help right away.

Why does my answer change so much when I switch patient type?

The water fraction changes the total body water, and the deficit is built on that. At 70 kg, a 0.60 fraction gives 42 L but a 0.45 fraction gives only 31.5 L. That is a third less water, so the deficit drops by a third too. Pick the type that fits the patient.

Can I print or save my results?

Use your browser's print option to save the page as a PDF. The step-by-step section, the result tiles, and both charts are part of the page, so they print with it. Open the steps first if you want them included.

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