Calculated
Hydrostatic Pressure Calculator
Sign up to favourite this calculatorCalculate pressure at depth, depth from pressure, or fluid density, using the hydrostatic pressure formula P = ρgh.
Your values
Entered
The pressure already acting on the fluid's surface — commonly standard atmospheric pressure.
A fluid of density 1,000 kg/m³ at a depth of 10.00 m has a gauge pressure of 98,070 Pa.
Formula used
P = ρ × g × h
P = 1,000 kg/m³ × 9.80665 m/s² × 10 m = 98,070 Pa
Step-by-step calculation
- Convert the known values to SI units — Depth (h): 10 m → 10.0000 m; Fluid density (ρ): 1,000 kg/m³ → 1,000.00 kg/m³; Gravitational acceleration (g): 9.80665 m/s².
- Substitute into the formula: P = 1,000 kg/m³ × 9.80665 m/s² × 10 m = 98,070 Pa.
- Result: Pressure = 98,070 Pa.
Values used
| Quantity | Display value | Base SI value | Status |
|---|---|---|---|
| Pressure (P) | 98,070 Pa | 98,066.5 Pa | Calculated |
| Depth (h) | 10 m | 10.0000 m | Entered |
| Fluid density (ρ) | 1,000 kg/m³ | 1,000.00 kg/m³ | Entered |
Assumptions
Based on P = ρgh. Depth is measured vertically downward from the free surface, and the fluid is assumed static with constant density.
Hydrostatic pressure rises linearly with depth in a static fluid of constant density.
Absolute pressure equals the surface pressure plus the fluid (gauge) pressure at that depth.
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Assumptions and limits
- An estimate from the numbers you entered, for guidance only. It is not financial, tax or medical advice.
- Calculator version 1, last updated 25 October 2026.
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How to use this calculator
Select what you want to calculate, choose gauge or absolute pressure, and enter the other two values with the units they were measured in. The result updates automatically as you type — there is no separate calculate step.
- Choose "Pressure", "Depth" or "Fluid density" as the quantity to calculate — the other two quantity cards become editable inputs.
- Choose gauge pressure (fluid only) or absolute pressure (fluid plus surface pressure). In absolute mode, enter the surface pressure acting on the fluid.
- Enter each known value and choose its unit, or pick a fluid preset for density. The missing quantity recalculates as soon as both known values are entered.
- Review the formula used, the step-by-step calculation, and the values-used table showing each quantity's exact SI value.
- Change the mode at any time — your entered values are kept — or select "Reset" to start over, or "Use example" to load a worked example.
What do I need to enter?
- What do you want to calculate? — Pressure, Depth or Fluid density. The other two quantities become the inputs.
- Pressure type — Gauge is the fluid's own pressure; Absolute adds the surface pressure on top.
- Pressure (P) — in pascals, kilopascals, bar, atmospheres or psi. Must be greater than zero, up to the equivalent of 1,000,000,000 Pa.
- Depth (h) — in metres, centimetres or millimetres, measured vertically down from the free surface. Must be greater than zero, up to 20,000 m.
- Fluid density (ρ) — a Water or Seawater preset, or a custom value in kg/m³ up to 25,000.
- Gravitational acceleration (g) — standard gravity (9.80665 m/s²) or a custom value above zero, up to 1,000 m/s².
- Surface pressure — shown in Absolute mode only: the pressure already acting on the fluid's surface, zero or more, in the same pressure units.
What do the results show?
- Calculated quantity — the pressure, depth or density you chose to solve for, with a one-line statement of the result.
- Formula used and Step-by-step calculation — the rearranged formula, then your values substituted in and worked through.
- Values used — each quantity's display value, its exact SI value, and whether it was entered or calculated.
- Assumptions — the fluid, gravity and surface pressure behind the result.
What is hydrostatic pressure?
Hydrostatic pressure is the pressure exerted by a fluid at rest, caused by the weight of the fluid above the point in question. In a static fluid of constant density, it rises linearly with depth:
P = ρgh
- P — gauge pressure, in pascals (Pa)
- ρ (rho) — fluid density, in kilograms per cubic metre (kg/m³)
- g — gravitational acceleration, in metres per second squared (m/s²)
- h — depth below the free surface, in metres (m)
This is gauge pressure — the pressure due to the fluid alone. If a pressure already acts on the fluid's surface, such as the atmosphere above a lake, absolute pressure adds it in:
P₍abs₎ = P₍surface₎ + ρgh
- P₍abs₎ — absolute pressure, in pascals (Pa)
- P₍surface₎ — pressure acting on the fluid's surface, in pascals (Pa)
How is pressure calculated at a given depth?
For 10 m of water (density 1,000 kg/m³) under standard gravity (9.80665 m/s²), gauge pressure is:
P = 1,000 kg/m³ × 9.80665 m/s² × 10 m = 98,066.5 Pa ≈ 98.1 kPa.
In absolute mode, this gauge pressure is added to whatever pressure already acts on the water's surface — typically standard atmospheric pressure, 101,325 Pa — giving an absolute pressure of about 199,391.5 Pa.
How do you rearrange P = ρgh for depth or density?
Starting from P = ρgh, the same relationship rearranges to solve for either input:
| Solving for | Gauge mode | Absolute mode |
|---|---|---|
| Pressure | P = ρgh | P₍abs₎ = P₍surface₎ + ρgh |
| Depth | h = P ÷ (ρg) | h = (P₍abs₎ − P₍surface₎) ÷ (ρg) |
| Fluid density | ρ = P ÷ (gh) | ρ = (P₍abs₎ − P₍surface₎) ÷ (gh) |
Depth is measured vertically downward from the free surface, and the fluid is assumed static with constant density throughout — this calculator does not model a fluid whose density changes with depth.
What units does this calculator use?
Pressure can be entered and displayed in pascals, kilopascals, bar, atmospheres or pounds per square inch (psi). Depth uses metres, centimetres or millimetres. Fluid density is entered in kilograms per cubic metre and gravitational acceleration in metres per second squared. Every figure is converted to pascals, metres and kg/m³ before the formula runs, so mixing units within one calculation still gives the correct result.
What does this calculator assume, and what does it not do?
This calculator models an incompressible, static fluid of uniform density using P = ρgh. It does not infer a fluid type, density, gravity or surface pressure for you — every value used comes from what you enter or from a preset you explicitly select, and the assumptions used in each result are listed beneath it. It does not model a compressible fluid, a moving or turbulent fluid, a density that varies with depth, or advanced thermodynamics, and it is a general physics calculation, not a scientific reference or an engineering design tool.
Frequently asked questions
What is the formula for hydrostatic pressure?
Gauge pressure at depth is P = ρgh, where ρ (rho) is fluid density in kg/m³, g is gravitational acceleration in m/s², and h is depth below the free surface in metres. If a surface pressure acts on the fluid — usually atmospheric pressure — absolute pressure is P₍abs₎ = P₍surface₎ + ρgh.
What is the difference between gauge and absolute pressure?
Gauge pressure is the pressure due to the fluid alone, ρgh, measured relative to whatever pressure already exists at the surface. Absolute pressure adds that surface pressure in: P₍abs₎ = P₍surface₎ + ρgh. Most everyday pressure gauges — including diving depth gauges and car tyre gauges — read gauge pressure, since they are zeroed against atmospheric pressure before use.
How do I calculate pressure at a given depth?
Choose "Pressure" as what to calculate, then enter the depth and fluid density (or pick a fluid preset). In gauge mode the calculator applies P = ρgh. For example, 10 m of water (1,000 kg/m³) under standard gravity gives P = 1,000 × 9.80665 × 10 = 98,066.5 Pa (about 98.1 kPa). Switch to absolute mode and enter a surface pressure to add it to this figure.
How do I calculate depth from a known pressure?
Choose "Depth" as what to calculate, then enter the pressure and fluid density. In gauge mode the calculator applies h = P ÷ (ρg). In absolute mode it first subtracts the surface pressure: h = (P₍abs₎ − P₍surface₎) ÷ (ρg). If the entered pressure is at or below the surface pressure, there is no positive depth that satisfies the equation.
How do I calculate fluid density from pressure and depth?
Choose "Fluid density" as what to calculate, then enter the pressure and depth. In gauge mode the calculator applies ρ = P ÷ (gh). In absolute mode it subtracts the surface pressure first: ρ = (P₍abs₎ − P₍surface₎) ÷ (gh). Depth must be above zero here, since it is a divisor in this formula.
What fluid density and gravity does this calculator use?
Nothing is assumed silently. Fluid density defaults to a water preset (1,000 kg/m³) with a seawater preset (1,025 kg/m³) also available, or you can enter a custom density for any fluid. Gravitational acceleration defaults to standard gravity (9.80665 m/s²) but can be set to a custom value. Every figure used in the result is shown in the assumptions list beneath it.
What units does this calculator support?
Pressure: pascals, kilopascals, bar, atmospheres and pounds per square inch (psi). Depth: metres, centimetres and millimetres. Fluid density is entered in kilograms per cubic metre and gravity in metres per second squared. Every figure is converted to pascals, metres and kg/m³ before the formula runs.
Does hydrostatic pressure depend on the shape or width of the container?
No. Hydrostatic pressure at a given depth depends only on the fluid density, gravity and the vertical depth below the free surface — never on the shape, width or total volume of the container. A narrow tube and a wide tank filled with the same fluid to the same depth have the same pressure at that depth.
Last updated 25 October 2026.