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Pressure & Pascal's Law Calculator

Four modes covering pressure basics, hydrostatic pressure at depth, Pascal's law hydraulics, and atmospheric pressure vs altitude. Full unit conversions between Pa, atm, psi, mmHg, and bar.

Area A = 0.0100 m²F = 1.0 kNP = 100000 Pa

Controls

Force F1000.0 N
Area A0.0100 m²

Results

P=FAP = \dfrac{F}{A}
Pressure (Pa)
100000.00Pa
Pressure (Pa)
100000.00Pa
Unit Conversions
Pa1.000e+5
kPa100.00
atm0.98692
psi14.504
mmHg750.06
bar1.0000
P=1000.0 N0.0100 m2=100000.00 PaP = \dfrac{1000.0 \text{ N}}{0.0100 \text{ m}^2} = 100000.00 \text{ Pa}

Reference Guide

Pressure

Pressure is force per unit area. It acts equally in all directions inside a fluid (Pascal's principle).

P=FAP = \dfrac{F}{A}

SI unit is the Pascal (Pa = N/m²). Common conversions: 1 atm = 101 325 Pa = 14.696 psi = 760 mmHg = 1.01325 bar.

1 atm101 325 Pa 1 psi6 894.76 Pa 1 bar100 000 Pa 1 mmHg133.322 Pa

Hydrostatic Pressure

In a static fluid, pressure increases with depth due to the weight of the fluid above. Absolute pressure at depth h is:

P=P0+ρghP = P_0 + \rho g h

where P₀ is surface pressure, ρ is fluid density, g is gravitational acceleration, and h is depth. At 10 m depth in fresh water the total pressure is approximately 2 atm.

Gauge pressure (relative to atmosphere) is just the ρgh term.

Pascal's Law & Hydraulics

Pascal's law states that a pressure change applied to an enclosed fluid is transmitted equally throughout. A hydraulic system exploits this to amplify force:

F1A1=F2A2\dfrac{F_1}{A_1} = \dfrac{F_2}{A_2}

Mechanical advantage MA = A₂ / A₁. A car lift with A₂ = 50 A₁ can lift 50x the input force. Work is conserved: the large piston moves a much shorter distance.

Atmospheric Pressure

The atmosphere is compressible, so pressure falls exponentially with altitude rather than linearly. The barometric formula (isothermal approximation) gives:

P=P0 e−Mgh/RTP = P_0 \, e^{-Mgh/RT}

where M = 0.0290 kg/mol (molar mass of air), R = 8.314 J/(mol K), T = 288.15 K (sea-level temperature). Pressure halves approximately every 5 500 m. At Everest (8 848 m) the pressure is roughly 33% of sea level.