Fluid Mechanics

Hydrostatic Pressure Calculator

Calculate gauge pressure, absolute pressure, fluid depth, or fluid density using the constant-density hydrostatic relation for a fluid at rest.

Formula Delta p = rho g h; p = p0 + rho g hReviewed Sep 8, 2026

Hydrostatic pressure is the pressure increase caused by the weight of a fluid above a point. For a constant-density fluid at rest, pressure rises linearly with vertical depth according to p = p0 + ρgh, where p0 is the surface pressure reference. This calculator lets you work in either gauge-pressure mode or absolute-pressure mode so you can solve for pressure, depth, or density without mixing the two concepts.

Calculation Bench

Pressure Reference

Solve for

01Density

ρ · Mass density of the fluid, assumed constant over the depth being analyzed.

02Gravity

g · Local gravitational acceleration magnitude.

03Depth Below Surface

h · Vertical distance from the free surface down to the point where pressure is evaluated.

Depth is vertical below the free surface. This tool assumes a fluid at rest with constant density; it does not model compressibility, layering, or flowing-fluid effects.

Solution

Enter the required values to calculate gauge pressure.

p = ρ g h

Formula Sheet

p = \rho g h

h = \dfrac{p}{\rho g}

\rho = \dfrac{p}{g h}

p = p_0 + \rho g h

h = \dfrac{p-p_0}{\rho g}

\rho = \dfrac{p-p_0}{g h}

pPressure at Depth
p0Surface Pressure
ρDensity
gGravity
hDepth Below Surface

Variables & Units

Symbol	Variable	Description	Common Units
p	Pressure at Depth	Pressure at the point of interest. In gauge mode this is pressure rise above the free surface; in absolute mode it is the total absolute pressure at depth.	Pa, kPa, bar, psi
p0	Surface Pressure	Pressure at the liquid free surface, used only when working in absolute-pressure mode.	Pa, kPa, atm, bar
ρ	Density	Mass density of the fluid, assumed constant over the depth being analyzed.	kg/m³, g/cm³, lb/ft³
g	Gravity	Local gravitational acceleration magnitude.	m/s², ft/s², g
h	Depth Below Surface	Vertical distance from the free surface down to the point where pressure is evaluated.	m, ft, in

How to Use This Calculator

01Choose Gauge Pressure mode when you want pressure rise relative to the free surface only. Choose Absolute Pressure mode when you know the surface pressure as well and want the total pressure at depth.
02Select whether you want to solve for pressure, depth, or density. The calculator will show only the inputs required for that case.
03Enter depth as a vertical distance below the free surface, not pipe length or distance along a sloped wall.
04Use a constant-density fluid value. If the tank is open to atmosphere, the surface pressure in absolute mode is usually 101.325 kPa at standard atmospheric pressure.
05Pick a realistic fluid density from the reference table or your fluid data sheet. Fresh water is about 1000 kg/m³, seawater about 1025-1030 kg/m³, light oils often 850-950 kg/m³, and mercury about 13,600 kg/m³.

How the Formula Works

A fluid at rest develops pressure because each deeper layer supports the weight of the fluid above it. For a liquid whose density stays essentially constant with depth, that pressure rise is linear: gauge pressure equals ρgh. If you also include the surface pressure reference p0, the total absolute pressure becomes p = p0 + ρgh.

That means hydrostatic pressure depends only on vertical depth, density, and gravity. It does not depend on the shape of the tank or the total volume of liquid. This calculator uses that ideal constant-density relation directly, which makes it well suited to liquids such as water, oil, and glycerin over ordinary engineering depths, but not to strongly compressible gases or layered fluids with changing density.

Worked Example 01

Gauge pressure 10 m below a freshwater surface

Known

Density (ρ): 1000 kg/m³
Gravity (g): 9.81 m/s²
Depth (h): 10 m

Formula

p = ρ g h

Substitution

p = 1000 × 9.81 × 10

Result

p = 98.1 kPa gauge

Ten meters below the free surface of fresh water, the hydrostatic pressure rise is 98.1 kPa above the surface reference.

Worked Example 02

Absolute pressure 5 m below the surface of seawater

Known

Surface Pressure (p0): 101.325 kPa
Density (ρ): 1030 kg/m³
Gravity (g): 9.81 m/s²
Depth (h): 5 m

Formula

p = p0 + ρ g h

Substitution

p = 101,325 + 1030 × 9.81 × 5

Result

p ≈ 151.85 kPa absolute

The liquid column adds about 50.52 kPa above atmospheric pressure, giving a total absolute pressure of roughly 151.85 kPa.

Worked Example 03

Depth from a measured absolute pressure in glycerin

Known

Pressure at Depth (p): 163.128 kPa
Surface Pressure (p0): 101.325 kPa
Density (ρ): 1260 kg/m³
Gravity (g): 9.81 m/s²

Formula

h = (p - p0) / (ρ g)

Substitution

h = (163,128 - 101,325) / (1260 × 9.81)

Result

h ≈ 5.00 m

Subtracting the surface pressure first leaves the hydrostatic pressure rise due to the glycerin column alone.

Worked Example 04

Density from pressure rise over a known depth

Known

Gauge Pressure (p): 37.278 kPa
Gravity (g): 9.81 m/s²
Depth (h): 4 m

Formula

ρ = p / (g h)

Substitution

ρ = 37,278 / (9.81 × 4)

Result

ρ ≈ 950 kg/m³

A 37.278 kPa pressure rise over 4 m corresponds to a fluid density of about 950 kg/m³, typical of some light oils.

Applications

01Estimating pressure at the bottom of tanks, reservoirs, and open channels
02Checking how deep a sensor or outlet sits below a liquid surface from a measured pressure
03Back-calculating approximate fluid density from a measured pressure rise over a known depth

Typical Fluid Densities for Hydrostatic Estimates

Fluid	Density (kg/m³)
Fresh water (4°C)	1000
Sea water (0°C)	1030
Olive oil	920
Glycerin	1260
Mercury	13600

Assumptions

01The fluid is at rest, so the relation is hydrostatic rather than dynamic.
02Fluid density is treated as constant over the depth range entered.
03Depth is measured vertically below the free surface.

Where This Model Stops

01Does not model layered fluids, temperature-driven density gradients, or compressibility effects in deep gas columns.
02Does not calculate total force on a wall, center of pressure, or buoyant force on a submerged body.
03Absolute-pressure mode requires a consistent surface-pressure reference; do not mix gauge and absolute inputs in the same calculation.
04Does not include fluid motion, pump head losses, pipe friction, water hammer, waves, sloshing, or acceleration of the container.
05Does not decide pressure-vessel, tank-wall, pipe, or sensor ratings. Compare the calculated pressure with rated working pressure and required safety factors separately.

References

[1]
University Physics Volume 1, Section 14.1: Fluids, Density, and Pressure
OpenStax
Defines pressure and presents pressure variation with depth for a constant-density fluid, plus representative fluid densities.
[2]
Pressure Effects, Hydrostatic Equation, and Gauge/Vacuum Pressure
MIT OpenCourseWare
MIT reference covering the hydrostatic equation and the distinction between gauge and absolute pressure.

Frequently Asked Questions

What is the difference between gauge pressure and absolute pressure?

Gauge pressure measures pressure above the local surface reference, often atmospheric pressure. Absolute pressure includes that reference itself, so in an open tank the absolute pressure at depth equals atmospheric pressure plus the hydrostatic pressure rise.

Why does tank shape not appear in the formula?

Hydrostatic pressure at a point depends only on fluid density, gravity, and vertical depth below the free surface. Tank shape affects total liquid volume and total wall force distribution, but not the local pressure at a given depth.

Can I use this for gases?

Only with caution over small height changes where density remains nearly constant. For deeper gas columns, density changes significantly with pressure and temperature, so the constant-density hydrostatic equation becomes less accurate.

How is this different from the Buoyant Force Calculator?

Hydrostatic Pressure finds pressure at a depth from rho g h. Buoyant Force uses the displaced fluid volume to calculate upward force, F_B = rho g V. Pressure can vary over a surface, while buoyancy depends on displaced volume.

Should I use gauge or absolute pressure?

Use gauge pressure when comparing to most pressure gauges or pressure rise due to a liquid column. Use absolute pressure when the surface pressure matters, such as sealed tanks, vacuum conditions, or calculations that must include atmospheric pressure.

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