Hydrostatic pressure calculator
Ten metres down in water of 1000 kg/m³ with gravity at 9.81 m/s², the gauge pressure is 98100 Pa. Enter density, depth and gravity, and add the atmospheric pressure if you want the absolute value instead. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Density
- 1,000
- Depth
- 10
- Gravitational acceleration g
- 9.81
- Atmospheric
- 0
- Gauge pressure
- 98,100
- Pressure
- 98,100
Hydrostatic pressure is the pressure exerted by a static fluid column at a given depth below a free surface. For an incompressible fluid of constant density under uniform gravity, the gauge pressure at depth h is simply density times gravity times depth—P equals rho g h—because the weight of the fluid above a unit area balances the pressure difference. Engineers, divers, civil designers, and students use this relation constantly to size tanks, rate submersible housings, and check textbook pool and dam problems. This calculator takes fluid density, depth, and gravitational acceleration, multiplies them, and optionally adds an atmospheric (or other reference) pressure so you can report either gauge or absolute pressure in one call. Negative depth is rejected with a clear validation error: a point above the free surface is outside the hydrostatic column model.
How hydrostatic pressure follows from density, depth, and gravity
Start from equilibrium in a vertical fluid column that is at rest. The net force on a thin horizontal slab of thickness dh and area A must vanish: the pressure increase dP times A equals the weight of the slab, which is density times g times A times dh. Canceling area and integrating from the free surface down to depth h yields the classic hydrostatic relation for constant density and constant g: the gauge pressure equals rho times g times h.
Gauge pressure is zero at the free surface when the surface is open to the reference atmosphere; absolute pressure is then gauge plus the atmospheric offset. Density may be expressed in kilograms per cubic metre, grams per cubic centimetre, or any other mass-per-volume unit as long as gravity and depth use matching length and time units so that the product has a coherent pressure unit.
Gravity is usually 9.81 metres per second squared near Earth's surface, but the field accepts any non-negative finite value so lunar, planetary, or centrifuge problems stay valid. The calculator does not integrate stratified density profiles, does not apply Bernoulli terms for flowing fluids, does not convert pascals to bars or psi, and does not correct for surface tension or compressibility. It answers only the algebraic definition that secondary-school physics, fluid-mechanics courses, and field engineering call hydrostatic pressure.
What you send and what you get back
Send finite numbers under the fields density, depth, and gravity. Density is the fluid mass per volume and must be non-negative; typical freshwater is near one thousand kilograms per cubic metre and seawater is often near one thousand twenty-five. Depth is the distance below the free surface in a consistent length unit and must be zero or positive—negative depth fails with a message that names the negative-depth rule.
Gravity is the gravitational acceleration in a consistent unit and must be non-negative. Optionally send atmospheric as a finite pressure offset to add after the gauge term; when omitted, atmospheric is treated as zero and the response reports gauge pressure only.
Classic textbook checks include ten metres of fresh water at 9.81 metres per second squared yielding about ninety-eight thousand one hundred pascals of gauge pressure, or the same column plus one atmosphere of one hundred one thousand three hundred twenty-five pascals for absolute pressure near the bottom of a pool.
Where hydrostatic pressure calculations show up in real work
Secondary-school and university physics courses constantly assign pool, dam, and diving-bell problems that give density, depth, and g and ask for the pressure at a submerged point, often distinguishing gauge from absolute by adding atmospheric pressure. Civil and mechanical engineers size thin-walled tanks, retaining walls, and buried pipes by estimating lateral fluid loads from rho g h at the design depth. Scuba and commercial diving training materials map depth to ambient pressure so tables and computers stay consistent with the simple column model for seawater.
Aquarium and aquaculture designers check glass and liner loads at the deepest waterline. If you later need Bernoulli streamline energy balances, manometer differential readings with multiple fluids, compressible atmospheric stratification, unit conversion between pascals and psi, or buoyant force on submerged bodies, treat those as separate search intents and landings rather than overloading this hydrostatic pressure calculator page.
What you can do with it
Homework and lab answer keys
Compute P = ρ·g·h (and optional +P_atm) for textbook pool and dam problems so teachers and auto-graders share one ground truth, including negative-depth rejection.
Tank, wall, and diving depth estimates
Estimate gauge or absolute pressure at a design depth for tanks, retaining walls, pipes, or dive planning under constant density and gravity.
FAQ
What formula does this hydrostatic pressure calculator use?
Gauge pressure is P = ρ · g · h. When you supply the optional atmospheric field, absolute (or reference-offset) pressure is P = ρ · g · h + P_atm. Density, gravity, and depth must share consistent units.
What happens if depth is negative?
Negative depth would place the point above the free surface, which is outside the hydrostatic fluid-column model used here.
Is atmospheric pressure required?
No. If you omit atmospheric, the calculator returns gauge pressure only (offset zero). Provide atmospheric when you need absolute pressure or another reference offset.
What units should I use?
Any consistent set. For SI, density in kg/m³, depth in m, and gravity in m/s² give pressure in pascals (N/m²). The tool does not convert units for you.
What does it cost?
The browser tool is free and runs locally.
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/thermo/hydrostatic-pressure \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"density":1000,"depth":10,"gravity":9.81}'const res = await fetch("https://api.kit.forhosting.com/thermo/hydrostatic-pressure", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"density": 1000,
"depth": 10,
"gravity": 9.81
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/thermo/hydrostatic-pressure",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"density": 1000,
"depth": 10,
"gravity": 9.81
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/thermo/hydrostatic-pressure", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"density":1000,"depth":10,"gravity":9.81}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"density":1000,"depth":10,"gravity":9.81}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/thermo/hydrostatic-pressure", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"density": 1000,
"depth": 10,
"gravity": 9.81
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "thermo.hydrostatic_pressure",
"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
How hydrostatic pressure follows from density, depth, and gravity
Depth is the vertical distance below the free surface and must be zero or positive; a negative depth would place the evaluation point above the surface, where this simple column model does not apply and the request fails with invalid input.
What you send and what you get back
Missing fields, non-numeric strings, NaN, and Infinity fail with invalid_input and are not charged. On success the response echoes cleaned density, depth, gravity, and atmospheric, sets has_atmospheric true when you supplied an offset, reports gauge_pressure as rho times g times h, reports pressure as gauge plus atmospheric, and includes a formula string plus method hydrostatic_pressure. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where hydrostatic pressure calculations show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.
Integration use cases
Curriculum widgets and API fixtures
Drive browser demos and CI golden tests from the same isomorphic solver so classroom tools never disagree with backend grading.