Free water deficit calculator
With sodium at 160 mEq/L, a target of 140 and a 70 kg man, the water deficit is 6 litres out of 42 litres of body water. A teaching estimate for hypernatremia worksheets, never a treatment plan. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Sodium
- 160
- Target sodium
- 140
- Weight
- 70
- Sex
- Male
- Tbw fraction
- 0.6 L
- Tbw
- 42
- Delta sodium
- 20
- Water deficit
- 6
The free water deficit calculator estimates how many liters of electrolyte-free water would be required, in a teaching identity, to lower serum sodium from a current high laboratory value to a chosen target while holding estimated total body water as a sex-specific fraction of body weight. Educators, nursing students, and product teams use that identity when teaching hypernatremia, checking electrolyte worksheets, or embedding a small educational calculator. Send current serum sodium, target sodium, weight in kilograms, and sex; the response reports the deficit in liters together with total body water and the fraction used. Weight that is not a positive number also fails. Validation errors are not billed. Figures are educational estimates and never replace serial sodium checks, fluid choice, or professional medical advice.
What the free water deficit formula measures and how total body water is estimated
The free water deficit is the textbook teaching identity used when a serum sodium sits above a chosen target: litres of electrolyte-free water theoretically needed to close that gap while holding estimated total body water fixed. Water deficit equals total body water in litres times current sodium divided by target sodium minus one, which is algebraically the same as total body water times the difference between current sodium and target sodium, all divided by the target.
Both sodium values are milliequivalents per litre, total body water is litres, and the product is litres of free water. Total body water is not measured here and is not the Watson equation; it is estimated as a sex-specific fraction of body weight in kilograms. Adult male teaching default is zero point six times weight.
Adult female teaching default is zero point five times weight. When current sodium is one hundred sixty milliequivalents per litre, the target is one hundred forty, and a seventy kilogram man is entered, total body water is forty-two litres and the water deficit is six litres. When current sodium already equals the target, the identity returns zero litres.
Weight that is missing, zero, negative, or not a finite number is also rejected, because a non-positive mass cannot yield a usable total-body-water volume. The arithmetic is deterministic.
Practical limits of this teaching estimate
Call the free in-browser free water deficit calculator for classroom demos, nursing homework, and quick personal learning without reimplementing the sex-specific total-body-water identity in every spreadsheet. Keep requests small, pin the numeric fields in tests with the documented rounding, and you get reproducible figures for edge workers, LMS plugins, and consumer health funnels without standing up clinical decision support you are not licensed to offer.
Always disclose that the numbers are educational estimates: the fractions ignore age and body composition, the identity ignores ongoing urinary losses and insensible water, and the result does not replace serial sodium checks, a chosen correction limit, or clinician-prescribed fluids. People with symptoms, known sodium disorders, kidney disease, heart failure, or medication changes should follow professional medical advice rather than any single automated number alone.
What you can do with it
Hypernatremia teaching worksheets
Education apps show how a seventy kilogram man at one hundred sixty milliequivalents per litre toward a target of one hundred forty yields six litres without recoding the fractions on every client.
FAQ
What happens if current serum sodium is below the target?
Free water deficit is the hypernatremia teaching identity; a current sodium below the target is a different problem and is not charged.
Does this replace medical advice or choose a correction rate?
No. Results are educational estimates using adult teaching fractions 0.6 and 0.5, not a fluid order. People with sodium disorders should follow professional guidance, not this calculator alone.
What is the formula for the water deficit?
Total body water times current sodium divided by target sodium, minus one. With sodium at 160, a target of 140 and 42 litres of body water, the deficit is 6 litres.
How is total body water estimated?
As a share of body weight, 0.6 for men and 0.5 for women in this teaching version, so a 70 kg man has 42 litres. Age, height and body fat are deliberately left out.
What if sodium already equals the target?
The result is zero litres, because there is no gap to close. The calculator only works when current sodium is at or above the target, which is the hypernatremia case.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/health/water-deficit \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"sodium":160,"target_sodium":140,"weight":70,"sex":"male"}'const res = await fetch("https://api.kit.forhosting.com/health/water-deficit", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"sodium": 160,
"target_sodium": 140,
"weight": 70,
"sex": "male"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/health/water-deficit",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"sodium": 160,
"target_sodium": 140,
"weight": 70,
"sex": "male"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/health/water-deficit", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"sodium":160,"target_sodium":140,"weight":70,"sex":"male"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"sodium":160,"target_sodium":140,"weight":70,"sex":"male"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/health/water-deficit", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"sodium": 160,
"target_sodium": 140,
"weight": 70,
"sex": "male"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "health.water_deficit",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
If current sodium is below the target, the request fails because the identity describes a water deficit of hypernatremia, not a sodium deficit of hyponatremia.
What the free water deficit formula measures and how total body water is estimated
Those fractions ignore age, height, and adiposity on purpose so the endpoint stays a four-field calculator rather than a full body-composition model. When current sodium is below the target, the same identity would produce a negative volume that describes water excess rather than a deficit; this endpoint rejects that case with invalid_input instead of returning a signed surplus, because the search intent and the teaching formula are for hypernatremia. Identical numbers always produce identical JSON, with stable rounding so automated tests can pin water_deficit across runtimes without floating-point surprises between engines.
Input contract, response fields, and error behaviour
Target sodium must also be a strictly positive finite number, because the identity divides by that target. Optional output keys are omitted rather than set to null. POST a JSON body with four required fields. Field sodium is current serum sodium in milliequivalents per litre; aliases include current_sodium, na, Na, serum_sodium, and sodium_meq. It must be a strictly positive finite number inside the declared teaching range. Field target_sodium is the desired serum sodium in the same units; aliases include desired_sodium, na_target, goal_sodium, and target_na. Field weight is body mass in kilograms; aliases include weight_kg, kg, mass, and w. Weight must be a finite positive number inside the declared teaching range; zero, negative, missing, empty, or non-numeric weight fails with invalid_input and is not billed. Field sex selects the total-body-water fraction and is a closed enumeration: male, female, m, f, man, or woman, case-insensitive; alias gender. Anything outside that set fails with invalid_input. Each numeric field may arrive as a JSON number or as a numeric string. On success the body echoes the four inputs, reports tbw_fraction as zero point six or zero point five, reports tbw as that fraction times weight in litres, reports water_deficit as tbw times the sodium ratio minus one in litres, sets unit to L, restates the formula string, and sets method to free_water_deficit so clients can branch on algorithm identity. Pair this endpoint with serial sodium checks of your own; this calculator does not prescribe a correction rate or choose an intravenous fluid.
API usage, pricing, product workflows, and practical limits
Use the prepaid API when a health SaaS, electronic worksheet, simulation lab, tutoring platform, or school LMS needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after the engine rejects the request. Typical workflows send a hypernatremia panel with a male or female weight and a target of one hundred forty to show how many litres the textbook formula attributes to the free-water gap, then pin water_deficit in automated checkers. Do not treat a large computed deficit as a bolus of free water; correction rate, fluid choice, and monitoring remain clinical decisions outside this endpoint.
Integration use cases
Nursing and medical-school homework
Students submit current sodium, target sodium, weight, and sex and pin water_deficit JSON in automated checkers with deterministic TBW-times-ratio outputs.
Simulation labs and SaaS backends
Server pipelines that already store electrolyte panels, weight, and sex call a prepaid endpoint for water_deficit instead of duplicating the textbook identity in every language.
Technical questions
How is the free water deficit calculated?
water_deficit = TBW × (sodium / target_sodium − 1), with TBW = 0.6 × weight kg for males and 0.5 × weight kg for females. The result is litres (L). The response also returns tbw, tbw_fraction, and delta_sodium.
What fields are required?
Four required fields: sodium (current serum Na in mEq/L, must be a positive number and at least the target), target_sodium (desired Na in mEq/L), weight (kilograms, must be a positive number), and sex (male or female). Missing fields return invalid_input and are not billed.
What does the free water deficit calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.