Free Water Deficit Calculator

Use the Free Water Deficit Calculator

Free water deficit calculator for hypernatremia: get the litres of water to replace, a safe 24-hour correction rate, and the exact fluid volume to infuse.

How to Use Free Water Deficit Calculator

1. Step 1: Enter the current and target sodium

   Type the measured value into Current Serum Sodium and the goal into Target Serum Sodium. 140 mEq/L is the classic denominator; some services stop at 145. If glucose is above 400 mg/dL, correct the sodium for glucose first.

2. Step 2: Set weight, sex, and age group

   Enter Body Weight in kg or lb using the current post-losses weight, then pick Sex and Age Group. The calculator applies a total body water fraction of 0.6 for children and adult males, 0.5 for adult females and elderly males, and 0.45 for elderly females.

3. Step 3: Choose acute or chronic

   Select Chronic / unknown to cap the fall at 0.5 mEq/L per hour and 10 mEq/L per 24 hours, or Acute (under 48 h) to allow up to 1 mEq/L per hour. If onset is unknown, treat it as chronic.

4. Step 4: Add ongoing losses and pick a fluid

   Enter Ongoing Daily Losses in mL, typically 1,000 to 1,500 mL in a stable ward patient, then choose a Replacement Fluid and enter any Potassium Added to the Bag, which is osmotically equal to sodium.

5. Step 5: Read the deficit, schedule, and fluid volume

   The top card gives the free water deficit in litres. The schedule table shows the target sodium at the end of each 24-hour block, and the fluid table gives the litres and mL/h for each infusate. Recheck serum sodium every 4 to 6 hours and adjust to the measured trend.

Key Features

• Free water deficit in litres from serum sodium, weight, sex, and age group
• Total body water fractions of 0.6, 0.5, and 0.45 applied automatically
• Day-by-day correction schedule capped at 10 mEq/L per 24 hours
• Acute versus chronic rate limits of 1.0 and 0.5 mEq/L per hour
• Adrogue-Madias volumes for D5W, 0.225%, 0.45%, and 0.9% saline
• Adjustments for ongoing daily losses and potassium added to the bag

Understanding Results

Formula

The free water deficit formula rearranges a conservation statement: total body sodium stays fixed while water is lost, so total body water multiplied by serum sodium is a constant. Solving for the water needed to reach a chosen target gives:

TBW is total body water: weight in kilograms times 0.6 for children and adult men, 0.5 for adult women and men over 65, and 0.45 for women over 65. Current Na is the measured serum sodium in mEq/L and target Nais usually 140. The second line is the Adrogué–Madias equation, which converts the deficit into a volume of a specific fluid; potassium appears because it is osmotically equivalent to sodium, so KCl added to the bag reduces how much the sodium falls.

Reference Ranges & Interpretation

Normal serum sodium is 135–145 mEq/L. Hypernatremia is graded as mild at 146–149, moderate at 150–159, and severe at 160 mEq/L and above, where reported in-hospital mortality among adults ranges from 40% to 60% — largely driven by the underlying illness rather than the sodium itself. A deficit of 3–4 L in a 70 kg adult is roughly 8% of total body water; anything above 6 L signals days of unreplaced losses and usually an impaired thirst mechanism or no access to water.

The correction rate is a harder limit than the deficit. Chronic hypernatremia, or any case of unknown duration, is capped at 0.5 mEq/L per hour and 10 mEq/L per 24 hours; documented acute onset under 48 hours allows up to 1 mEq/L per hour. Serum sodium is rechecked every 4–6 hours during correction, and the infusion is titrated to the measured fall, not the predicted one. If sodium falls faster than planned, slow or pause the hypotonic fluid rather than waiting for the next lab.

Assumptions & Limitations

This equation models a closed system: fixed body water, no ongoing losses, no solute gain, and a body-water fraction taken from healthy-volunteer studies rather than the dehydrated patient in front of you. All three assumptions fail in practice, which is why the predicted fall in sodium systematically overshoots the observed fall. Ongoing losses of 1,000–1,500 mL per day must be added separately, and far more in diabetes insipidus or osmotic diuresis. Hyperglycaemia above 400 mg/dL depresses measured sodium and must be corrected before the deficit is computed. The formula also says nothing about volume status: a hypotensive hypernatremic patient needs isotonic resuscitation first and free water second. Results here are educational and do not replace bedside assessment, repeat laboratory testing, or a treating clinician.

Complete Guide: Free Water Deficit Calculator

A free water deficit calculatoranswers one narrow question: how many litres of water this patient has lost, relative to their salt, to arrive at the sodium sitting on the lab report. It is a measure of the hole, not a plan for filling it. That distinction is where most bedside errors begin. A resident computes 6.2 L, orders 6.2 L of D5W over 24 hours, and by morning the sodium has fallen 22 mEq/L in a patient whose brain spent four days adapting to 165 — a set-up for cerebral oedema, seizures, and a neurology consult that was entirely avoidable.

The deficit formula and the Adrogué–Madias equation are not competitors; they answer different halves of the same problem. One gives you the destination, the other gives you the speed limit and the fuel. This guide works both, shows how far the answer moves when you change the body-water fraction or the target sodium, and covers the two clinical situations — ongoing renal losses and diabetes insipidus — where a technically correct deficit is a clinically useless number.

Free water deficit calculator vs. Adrogué–Madias: two different questions

The free water deficit equation is a rearranged conservation statement. Total body sodium content stays fixed while water leaves, so TBW × [Na] is constant. Solve for the water you would have to add to drag sodium back to a chosen target and you get:

Adrogué–Madias asks the opposite question — not “how much water is missing” but “what will one litre of this specific bagdo to the serum sodium right now?”:

Three practical differences follow. First, the deficit formula is blind to what you infuse — it assumes pure water, so ordering half-normal saline against a deficit-derived volume under-delivers by half. Second, Adrogué–Madias is blind to the destination — it will happily let you run 8 L if you ask it to. Third, and least appreciated, the potassium term is not decorative: potassium is osmotically equivalent to sodium, so adding 40 mEq/L of KCl to a bag of D5W converts it into something that behaves like quarter-normal saline and cuts its sodium-lowering power by roughly a quarter. The same arithmetic in the opposite direction drives our sodium correction calculator, which handles hyponatremia and the glucose adjustment that must be applied before any deficit is computed.

Worked example: 162 mEq/L in a 70 kg man

A 58-year-old man is admitted after three days of poor oral intake following a stroke. Sodium 162 mEq/L, weight 70 kg, alert but confused. Onset is clearly more than 48 hours ago, so this is chronic hypernatremia.

• TBW: 70 × 0.6 = 42 L
• Deficit: 42 × (162 ÷ 140 − 1) = 42 × 0.157 = 6.6 L
• Gap to close: 162 − 140 = 22 mEq/L, which at a 10 mEq/L daily ceiling takes 3 days
• Day 1 target: 162 → 152 mEq/L, which is 10 of the 22 mEq/L, so 10/22 of the deficit = 3.0 L
• Plus ongoing losses: 3.0 + 1.5 = 4.5 L in 24 hours, about 188 mL/h

Now cross-check with Adrogué–Madias. One litre of D5W in this patient produces (0 − 162) ÷ (42 + 1) = −3.77 mEq/L. To drop sodium 10 points you need 10 ÷ 3.77 = 2.65 L, plus 1.5 L for losses — call it 4.2 L. The two methods land within 8% of each other, which is the expected agreement, not a coincidence: both are algebraic rearrangements of the same conservation assumption. When they disagree by more than about 10%, one of the inputs is wrong.

Order that as D5W at 190 mL/h, recheck sodium at 6 hours, and expect roughly a 2.5 mEq/L fall. If the 6-hour value is 157 instead of 159.5, the patient is losing more water than assumed and the rate needs to come down, not up — the overshoot is already in progress.

How much does each assumption move the answer?

Clinicians treat the deficit as a hard number because it arrives with two decimal places. It is not. Below is the same 70 kg patient at 162 mEq/L, with one assumption changed at a time. The spread across reasonable inputs is 4.7 L — roughly 70% of the base answer.

Two lessons fall out of that table. The body-water fraction is the softest input and the one most often set by reflex — and a 0.6-versus-0.45 mistake changes the deficit by a quarter. Yet none of that variation matters much on day one, because the rate cap, not the deficit, determines what you actually infuse. The deficit sets how many days you will be doing this; the ceiling sets what happens tonight. Choose the fraction carefully for prognosis, and stop agonising over it for the first order.

One caveat the table cannot show: hypernatremic patients are volume-depleted by definition, and a dehydrated body carries a lowerwater fraction than the textbook value derived from healthy volunteers. Several nephrology texts recommend dropping the coefficient by 0.05 in overtly dehydrated patients, which biases the estimate toward under-, not over-, replacement — the safer direction.

The term the equation leaves out: ongoing losses

The deficit formula describes a sealed system at a single instant. Real patients keep leaking. Insensible losses through skin and breath run about 500–1,000 mL per day in an afebrile adult and rise roughly 100–150 mL per day for each degree Celsius of fever. Urinary free water clearance adds more, and stool losses in osmotic diarrhoea can add litres. A common, defensible starting assumption is 1,000–1,500 mL per 24 hours in a stable ward patient, but the number should be measured as soon as urine output is being charted.

This is the single most common reason a correction stalls. The sodium sits at 158 for two days despite “full replacement,” and the chart shows 3 L in against 3.4 L of urine out. Nothing about the deficit calculation was wrong; the patient was simply never in net positive free-water balance. Whenever the measured fall lags the predicted fall, check the output side of the ledger before touching the formula. Daily fluid balance and body-weight trends are the fastest audit, and for a general picture of baseline requirements the hydration calculator covers maintenance needs in patients who are not acutely ill.

10 mEq/L a day, and why the brain sets that number

Brain cells do not tolerate shrinking. Within hours of a rising serum sodium they pull in electrolytes, and over 24–48 hours they synthesise organic osmolytes — myo-inositol, taurine, glutamine, often called idiogenic osmoles — to restore their volume against a hypertonic plasma. Those osmolytes cannot be dumped quickly. Lower the plasma sodium faster than the brain can dismantle its own solute and water floods back in: cerebral oedema, raised intracranial pressure, seizures.

That adaptation timeline is the entire basis for the two-tier rate rule:

• Chronic or unknown duration: maximum 0.5 mEq/L per hour and no more than 10 mEq/L in any 24-hour block. Some services use 8 mEq/L in the elderly.
• Acute, documented under 48 hours (post-operative hypertonic saline, salt poisoning, accidental sodium bicarbonate load): up to 1 mEq/L per hour, because the osmolytes have not yet accumulated.
• Either way: recheck sodium every 4–6 hours during active correction, more often if the patient is symptomatic.

“Unknown duration” means chronic. A patient found down at home has, for planning purposes, been hypernatremic long enough to adapt, and the 10 mEq/L ceiling applies. Note that the asymmetry with hyponatremia is real and often confused: too-fast correction of low sodium causes osmotic demyelination, too-fast correction of high sodium causes cerebral oedema. Different lesion, different mechanism, same underlying rule that the brain needs days, not hours.

Why normal saline is not a treatment for hypernatremia

Every fluid can be scored by its free-water fraction, calculated as 1 minus its sodium concentration divided by 154. D5W is 100% free water. Half-normal saline (77 mEq/L) is 50%. Quarter-normal (38.5 mEq/L) is 75%. Normal saline is 0% — it is isotonic to plasma, and infusing it into a patient at 162 mEq/L lowers sodium by (154 − 162) ÷ 43 = 0.19 mEq/L per litre. Closing a 22-point gap that way would take 118 L.

Normal saline still has a role, and this is where the nuance sits: a hypernatremic patient who is also hypotensive needs perfusion restored first. Give isotonic crystalloid until the blood pressure and mentation are stable, then switch to hypotonic fluid for the free-water deficit. Treating the sodium in a shocked patient is the wrong order of operations. Enteral water down a nasogastric tube is also underused — it is free, carries no glucose load, and in a patient with a working gut it corrects just as reliably as D5W without the risk of infusion-related hyperglycaemia, which itself worsens the osmotic diuresis driving the hypernatremia in the first place.

Diabetes insipidus breaks the whole plan

In a patient producing 6 L of dilute urine per day, the deficit is the least of the arithmetic. Urine osmolality below 300 mOsm/kg against a serum sodium above 145 is the diagnostic pattern — the kidney is failing to concentrate in the face of a stimulus that should maximally concentrate it. Central diabetes insipidus responds to desmopressin; nephrogenic does not, and is managed by removing the offending drug where possible (lithium, demeclocycline), plus thiazides and a low-solute diet.

The planning consequence: replacement must equal deficit correction plus hourly urine output, matched close to real time. A patient on 190 mL/h of D5W for a calculated deficit while passing 250 mL/h of dilute urine is getting further from target every hour, and the sodium will rise on a chart that says the deficit is being replaced. Any hypernatremia that fails to respond to an adequately calculated plan should trigger a urine osmolality and urine sodium before the infusion rate is increased. Renal concentrating ability sits behind all of this, and the picture is worth pairing with an estimate of kidney function when the creatinine is also moving.

Five errors that turn a correct number into a wrong dose

1. Giving the whole deficit in 24 hours. The output of the formula is a total, not a daily dose. A 6.6 L deficit across a 22 mEq/L gap is a three-day plan; infusing it in one produces a 22 mEq/L fall, more than double the ceiling.
2. Using deficit-derived volume with half-normal saline.The deficit assumes pure water. Order 3.0 L of 0.45% NaCl against a 3.0 L free-water requirement and you have delivered 1.5 L of free water — half the intended correction, which then reads as a mysterious plateau.
3. Ignoring hyperglycaemia. Glucose above 400 mg/dL pulls water into the vascular space and depresses measured sodium. Compute the deficit on the uncorrected value in a patient at 800 mg/dL and you will understate it substantially; correct the sodium for glucose first, then run the deficit on the corrected figure.
4. Forgetting the potassium in the bag.A litre of D5W with 40 mEq of KCl is not free water. In the 42 L patient above it produces −2.84 mEq/L per litre instead of −3.77 — 25% less correction than the order implies.
5. Trusting the prediction over the lab. Every one of these equations models a closed system with fixed body water and no ongoing losses, so the predicted fall systematically overshoots the observed one. The 6-hour sodium is data; the formula is a hypothesis. When they disagree, the formula is wrong.

Used the way it is meant to be used — as the first line of a plan rather than the whole of it — the free water deficit is one of the more reliable estimates in electrolyte medicine. It tells you the size of the problem in a single number, the rate cap tells you how long you will be at it, and the 6-hour sodium tells you which of your assumptions was wrong.

References

1. Adrogué HJ, Madias NE. Hypernatremia. New England Journal of Medicine. 2000;342(20):1493–1499. NEJM
2. Muhsin SA, Mount DB. Diagnosis and treatment of hypernatremia. Best Practice & Research Clinical Endocrinology & Metabolism. 2016;30(2):189–203. PubMed
3. Chauhan K, et al. Rate of correction of hypernatremia and health outcomes in critically ill patients. Clinical Journal of the American Society of Nephrology. 2019;14(5):656–663. PubMed

Frequently Asked Questions