Hydraulic Pressure Calculator — P = ρgh
Find the hydrostatic (fluid) pressure at any depth using the classic formula P = ρgh. Choose from common fluids (water, seawater, mercury, oil) or enter a custom density, and see the result in pascals, kilopascals, bar, psi, atmospheres, and mmHg.
m
Fluid type
Pa
Pressure due to the fluid column above the point, excluding atmosphere
- 1
Fluid density
ρ = 1,000 kg/m³ = 1,000 - 2
g × depth
9.81 × 10 m = 98.1 - 3
Gauge pressure
P = 1,000 × 98.1 = 98,100Hydrostatic pressure from the fluid column: P = ρ × g × h.
How does this calculator work?
Hydrostatic pressure P = ρgh grows linearly with fluid depth h. For water (ρ = 1000 kg/m³) and g = 9.81 m/s², every 10 m of depth adds ≈ 98 kPa (≈ 1 atm) of gauge pressure. Enter depth and fluid type to get results in Pa, kPa, bar, psi and atm.
Formula
How this is calculated
Hydrostatic pressure is the pressure exerted by a stationary fluid on a submerged object or surface. It increases linearly with depth h according to P = ρgh, where ρ is the fluid density and g = 9.81 m/s² is the gravitational acceleration. This pressure acts equally in all directions at any given depth (Pascal's principle).
Gauge pressure is the excess above atmospheric pressure P₀. Absolute pressure adds the atmospheric pressure back: P_abs = ρgh + P₀. For many engineering applications (pipe design, dam safety, diving physiology) gauge pressure is the relevant quantity; absolute pressure is used in thermodynamics and gas-law calculations.
Density values used here are approximate constants at room temperature: water at 15 °C (1000 kg/m³), seawater at 3.5% salinity (1025 kg/m³), mercury (13 600 kg/m³), a typical petroleum oil (850 kg/m³), and glycerol (1260 kg/m³). Real densities vary with temperature and composition.
Frequently asked questions
Every additional metre of fluid above a point adds the weight of that fluid layer to the pressure below it. Since weight = ρgV (density × gravity × volume), the pressure contribution per unit area at depth h is exactly ρgh.
Gauge pressure is the pressure relative to the local atmosphere (what a tyre gauge reads). Absolute pressure includes the atmospheric pressure: P_abs = P_gauge + P_atm. At sea level, standard atmosphere is 101325 Pa ≈ 1 bar ≈ 14.7 psi.
At 10 m in fresh water, the gauge pressure is ρgh = 1000 × 9.81 × 10 = 98 100 Pa ≈ 0.97 atm ≈ 14.2 psi. The absolute pressure (including atmosphere) is roughly 2 atm — which is why divers must decompress carefully when surfacing.
Also known as
TG we-Calculate Editorial Team. (2026). Hydraulic Pressure Calculator — P = ρgh [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hydraulic-pressure-calculator
TG we-Calculate Editorial Team. "Hydraulic Pressure Calculator — P = ρgh." TG we-Calculate. 2026. https://we-calculate.com/calculator/hydraulic-pressure-calculator.
TG we-Calculate Editorial Team, "Hydraulic Pressure Calculator — P = ρgh," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hydraulic-pressure-calculator
@misc{wecalculate_hydraulic_pressure_calculator, title = {Hydraulic Pressure Calculator — P = ρgh}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hydraulic-pressure-calculator}}, year = {2026}, note = {TG we-Calculate} }
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