Manometer calculator
A 0.2 m difference in a water column, at 1000 kg/m³ and 9.81 m/s², means 1962 Pa. Enter the column height difference, the liquid density and gravity to turn a U-tube or inclined gauge reading into pressure. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Height
- 0.2
- Density
- 1,000
- Gravity
- 9.81
- Pressure
- 1,962 Pa
A manometer is the classic laboratory and process instrument that turns a visible liquid-column height difference into a fluid pressure. Given the height difference of the manometer liquid, the liquid density, and gravitational acceleration, the hydrostatic manometer relation is simply P equals ρ times g times h, and the SI product is pascals. Students checking U-tube homework, HVAC technicians reading an inclined water gauge, and process engineers converting a mercury column into a vessel gauge pressure all need that same three-number contract and one reproducible result. This calculator accepts the column height difference, the manometer-liquid density, and gravity, multiplies them, and returns the pressure in pascals together with the echoed inputs and the textbook formula.
What P = ρ · g · h means for a manometer and which quantities you need to send
A manometer converts a visible height difference between two liquid columns into a fluid pressure through the hydrostatic relation P equals ρ times g times h. In a U-tube, well-type, or inclined-tube instrument the working liquid—water, mercury, oil, or a gauge fluid of known density—rises on one limb and falls on the other until the column difference balances the applied pressure. Search intent clusters around phrases such as manometer calculator, U-tube manometer pressure, convert column height to pascals, mercury manometer ρ g h, and liquid-column gauge pressure.
That is a different query from hydrostatic pressure at a depth under a free surface: here the height is the instrument reading, not the submersion of a point in a tank, and the result is the pressure implied by that reading. Students checking a fluids-lab write-up, HVAC technicians reading a water-column duct gauge, and process engineers converting a mercury manometer into vessel gauge pressure all want a numeric P in pascals they can pin against a worksheet.
Sign is part of the contract: a positive height difference yields a positive gauge pressure; a negative height difference yields a negative vacuum reading on the same formula; equal columns yield zero. Keep the unit basis honest: height in metres, density in kilograms per cubic metre, and gravity in metres per second squared yield pascals by construction.
What you can do with it
Homework and U-tube lab checks
Students and graders confirm manometer pressure from column height, liquid density, and gravity, with clear rejection when density or gravity is zero, negative, or a field is missing.
HVAC and process gauge sketches
Technicians and educators get structured pascal pressure from a water or mercury column without standing up a full instrumentation model or unit-conversion table.
FAQ
How do I compute manometer pressure from column height, density, and gravity?
Send finite numbers height, density, and gravity, with density and gravity strictly positive.
Which units yield pressure in pascals?
Use metres for the column height difference, kilograms per cubic metre for liquid density, and metres per second squared for gravity. The product ρ·g·h is then pascals by construction; mixed units are not converted automatically.
What does a negative height difference mean?
It means the opposite limb is higher, so the reading is a vacuum and the pressure comes out negative from the same formula. Equal columns give a height difference of zero and a gauge pressure of zero.
What density should I enter for water or mercury?
Water is about 1000 kg/m³ and mercury is often near 13595 kg/m³. Use the density of the liquid actually inside your manometer, because the pressure scales in direct proportion to it.
Can I enter the column in millimetres of mercury?
Not directly. The calculator does not convert units, and mixing millimetres with an SI density silently scales the answer. Enter the height in metres, the density in kg/m³ and gravity in m/s² to get pascals.
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/phys/manometer \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"height":0.2,"density":1000,"gravity":9.81}'const res = await fetch("https://api.kit.forhosting.com/phys/manometer", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"height": 0.2,
"density": 1000,
"gravity": 9.81
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/phys/manometer",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"height": 0.2,
"density": 1000,
"gravity": 9.81
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/phys/manometer", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"height":0.2,"density":1000,"gravity":9.81}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"height":0.2,"density":1000,"gravity":9.81}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/phys/manometer", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"height": 0.2,
"density": 1000,
"gravity": 9.81
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "phys.manometer",
"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
Density or gravity that is zero or negative is rejected with invalid_input instead of a non-physical pressure.
What P = ρ · g · h means for a manometer and which quantities you need to send
Delivering height, density, gravity, pressure, unit, formula, and method as JSON makes the result easy to paste into notes, diff in automated tests, or reuse across languages without reimplementing the three-factor product. Mixing millimetres of mercury with SI density without converting first will silently scale the answer and is not a unit-conversion service this endpoint provides.
How this calculator validates input and applies P = ρ · g · h
Numeric strings that parse to finite numbers are accepted so forms and CSV-style pipelines can pass values without an extra cast. Density must be strictly positive. Gravity must likewise be strictly positive: a zero or negative g is rejected for the same reason, since the hydrostatic product is not a laboratory pressure when gravity is not a positive acceleration. Height may be any finite value, including zero, which means equal columns and zero gauge pressure, and negative, which means the opposite limb is higher so the signed pressure is negative. There is no unit-conversion table, no temperature correction for mercury expansion, and no differential-versus-absolute switch; this is ideal manometer pressure from three known quantities. Send a JSON body with three required fields: height, density, and gravity. Every field must be finite: missing fields, empty strings, non-numeric text, NaN, and Infinity all fail immediately with invalid_input before any result is returned, and failed validation is not charged. Aliases are supported: h, delta_h, and height_difference for height; rho and liquid_density for density; g for gravity. A zero or negative density is always rejected as invalid_input because a manometer liquid with non-positive density is not a physical working fluid for P equals ρ g h, and that failure is the product contract named in the capability brief. After validation the engine multiplies density by gravity by height and rounds to a stable decimal precision so the same input always yields the same JSON across JavaScript engines. The same pure function powers the free in-browser tool and the API path, so homework checks and production pipelines never disagree on a column reading.
Practical use, limits, pricing, and delivery channels
Use the browser tool when you want an immediate P equals ρ g h check while grading a fluids homework set, reducing a U-tube reading from a lab notebook, converting a water-column HVAC gauge into pascals, or sanity-checking a mercury manometer against a known atmospheric scale. Choose units consistently—if height is in metres, density in kilograms per cubic metre, and gravity in metres per second squared, pressure is in pascals and ready for textbook comparison. Results are fully deterministic: the same three inputs always yield the same pressure, the same unit label, and the same formula and method strings. There is no language model, no external fluid-property service, and no randomness, so the capacity is safe to pin in continuous-integration checks and reproducible lesson materials. Each successful request is one billable item at $0.002; failed validation does not consume balance. Wire the endpoint into manometer drills, contest answer checkers, gauge-calibration helpers, or preprocessing steps where you already prefer explicit domain errors—such as rejecting a non-positive density—over opaque black-box widgets that cannot explain why a bad input was refused.
Integration use cases
Deterministic fixtures for fluids pipelines
Scripts that later convert a gauge reading into process pressure can call a pure P=ρ·g·h oracle instead of reimplementing the three-factor product in every language.
Technical questions
What happens if density or gravity is zero or negative?
The task fails with invalid_input. A manometer liquid with non-positive density, or a non-positive gravitational acceleration, is not a physical hydrostatic column, so the request is rejected and is not billed.
Does a negative height difference mean vacuum?
Yes in the signed-column convention used here: a positive Δh yields positive gauge pressure, a negative Δh yields a negative (vacuum) reading, and equal columns (Δh=0) yield zero gauge pressure.
What does the manometer calculator cost?
The browser tool is free. API requests use prepaid KIT balance at $0.002 per successful call; invalid input is not billed.