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Hydrostatic-pressure calculator

Calculate the pressure increase with depth in a constant-density static liquid; examine surface pressure, density and units.

From a liquid column to pressure

Calculate the pressure rise below a free surface or between layer interfaces. See each layer’s contribution, and add an absolute surface pressure only when you know it.

Δp = Σ(ρᵢ g hᵢ) pabsolute = psurface, absolute + Δp

Inputs and assumptions

Use a decimal dot or comma, with no thousands separators. Scientific notation is accepted. Values are not inferred from a fluid name.

Number of layersEnter layers in top-to-bottom order. Only active layers are used.

Layer 1

Density ρ1kg/m³100–20000 kg/m³. Use the value at the relevant temperature, salinity and pressure.

Vertical layer thickness h1m0–1000 m per layer; total ≤ 1000 m. Nonzero minimum: 0.000001 m.

Gravitational accelerationm/s²0.1–30 m/s². The initial 9.80665 is conventional standard gravity, not a local measurement.

Surface absolute pressure (optional)kPa0–1000000 kPa absolute; leave blank if unknown. There is no automatic atmospheric-pressure assumption. Nonzero minimum: 0.000001 kPa.

Calculated result

Illustrative starting example. Edit the inputs to explore the model.

Quantity	Value	Unit
Hydrostatic pressure rise	100.5182	kPa
Δp	100518.2	Pa
Δp	1.005182	bar
Absolute pressure at the bottom	Not calculated	kPa
Total vertical depth	10	m
Column mass per area	10250	kg/m²

This surface-referenced rise equals gauge pressure only if the surface is exposed to the local atmosphere. A pressurized or evacuated surface needs its own pressure reference.

Layer pressure contribution
Layer	ρ · kg/m³	h · m	Δp · kPa	ΣΔp · kPa
1	1025	10	100.5182	100.5182

Depth increases downward. The horizontal axis shows pressure rise relative to the top surface; slopes change with density. The layer table gives the same values.

Calculation trace

Δp1 = 1025 kg/m³ × 9.80665 m/s² × 10 m = 100518.2 Pa
Δp = 100518.2 = 100518.2 Pa
100518.2 Pa ÷ 1000 = 100.5182 kPa; ÷ 100000 = 1.005182 bar

Numerical checks

Δp − gΣ(ρᵢhᵢ) = 0.00000000001455192 Pa

Displayed values are rounded; computation and CSV use unrounded values. A small arithmetic residual checks implementation consistency, not physical accuracy.

Sensitivity: change one assumption

All active layer thicknesses are multiplied together, preserving their proportions. Densities, gravity and any entered surface pressure stay fixed. Rows beyond the input envelope are omitted from calculation.
Depth scale	h · m	Δp · kPa	p · kPa absolute	Status
0.5×	5	50.25908	Not calculated	Calculated
0.75×	7.5	75.38862	Not calculated	Calculated
1×	10	100.5182	Not calculated	Calculated
1.25×	12.5	125.6477	Not calculated	Calculated
1.5×	15	150.7772	Not calculated	Calculated

The calculation and CSV are created in this page in your browser. This calculator does not transmit or store the inputs.

How the calculation works

1. Choose the pressure reference. The displayed Δp is the increase relative to the pressure at the top surface. Gauge pressure is relative to the surrounding atmosphere; these are the same reference only for an open surface at local atmospheric pressure.

2. Measure vertical thickness, not the length of a sloping pipe or tank wall. For a static layer with uniform density, the weight per unit area is ρgh. Container shape and horizontal area do not enter the pressure-at-a-point relation.

3. Add the layer contributions. With constant gravity, Δp = g(ρ₁h₁ + ρ₂h₂ + ρ₃h₃). Pressure is continuous at an ideal flat interface; its rate of increase with depth changes when density changes.

4. Convert units after summation: 1 kPa = 1000 Pa and 1 bar = 100000 Pa. Pressure has dimensions kg/(m·s²), equivalent to N/m².

5. If the actual top-surface absolute pressure is available, add it in pascals. Leaving the field blank is different from entering zero. Zero is an ideal absolute vacuum boundary, whose physical feasibility this liquid model does not establish.

Worked examples and interpretation

Single-layer example: ρ = 1025 kg/m³, g = 9.80665 m/s² and h = 10 m. Δp = 1025 × 9.80665 × 10 = 100518.1625 Pa = 100.5181625 kPa = 1.005181625 bar. The density is an illustrative seawater value; it is not calculated from temperature or salinity.

For an explicitly assumed example surface pressure of 101.325 kPa absolute, that same column gives 201.8431625 kPa absolute. This is a hypothetical boundary value, not a measurement or assumption about your location.

The companion pressure-testing guide uses ρ = 1000 kg/m³, g = 9.81 m/s² and a vertical water column of 12 m: Δp = 117720 Pa = 117.72 kPa. This static elevation contribution must not be confused with a flowing pipe’s frictional loss.

Two-layer example: 2 m of a liquid at 850 kg/m³ above 3 m at 1000 kg/m³. Contributions are 16.671305 and 29.41995 kPa, giving 46.091255 kPa. The load-example button reproduces these inputs without assuming an absolute surface pressure.

Doubling every layer thickness doubles Δp. It does not double absolute pressure when a fixed nonzero surface pressure is added. For a supported static arrangement, swapping layer order keeps the bottom pressure sum unchanged, but can change stability.

Model boundaries

Static, single-phase liquids with constant density in each of one to three horizontal layers and constant gravity. Properties remain user inputs; there is no water, seawater, oil or temperature-property database.
The model excludes vessel acceleration, heel and trim geometry, sloshing, waves, dynamic pressure, gas compression, capillary jumps and pressure-dependent density. Enter the actual vertical thickness for the idealized condition.
The tool envelope is a numerical and educational bound, not a statement that every permitted density, depth or surface pressure is physically attainable. Phase stability and vapor pressure are not checked.
A point pressure is not a tank design load, window force or plate-stress result. Structural capacity, corrosion allowance, classification rules and equipment pressure ratings require separate verification.
No result is a diving limit, operating instruction, equipment selection, safety approval or certification.

Method sources

Primary technical references for the equations. The input envelope, transition hold and solver tolerances are conservative implementation choices, not certification criteria.

fluids-1.0.0

Read the method and its limits

Related project: ShipExact

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