Pressure Calculator

Calculate pressure using multiple methods and convert between 20+ pressure units. Essential physics tool for students, engineers, and scientists.

Force & Area
Fluid Pressure
Gas Pressure
Unit Conversion

Pressure Formula: P = F / A

P = F ÷ A

Where: P = Pressure, F = Force, A = Area

The perpendicular force applied to the surface
The surface area over which the force is distributed
Human Standing (500N on 0.5m²)
Car Tire (10kN on 0.01m²)
Needle Point (0.01N on 1mm²)

Hydrostatic Pressure Formula: P = ρ·g·h

P = ρ × g × h

Where: P = Pressure, ρ = Fluid density, g = Gravity, h = Depth/Height

Density of the fluid
Depth below the fluid surface or height of fluid column
Acceleration due to gravity
Water at 10m depth
Seawater at 100m
Mercury in barometer

Ideal Gas Law: PV = nRT

P = nRT / V

Where: P = Pressure, n = Moles, R = Gas constant, T = Temperature, V = Volume

Amount of gas in moles
Absolute temperature of the gas
Volume occupied by the gas
1 mole at STP (0°C, 22.4L)
2 moles at room temp
0.5 moles at 400K in 5L

Pressure Unit Conversion: Convert between Pascals, atmospheres, bars, psi, Torr, and more

Hold Ctrl/Cmd to select multiple units
Standard atmospheric pressure
100 kPa (≈1 bar)
14.7 psi (1 atm)
760 Torr (1 atm)

Understanding Pressure

Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed. It is a scalar quantity with SI units of Pascals (Pa).

Mathematical Definition:

P = F / A

where P is pressure, F is the normal force, and A is the area of the surface.

Pressure Formulas in Different Contexts

Context Formula Variables
Hydrostatic Pressure P = ρ·g·h ρ = density, g = gravity, h = height/depth
Ideal Gas Law P = nRT / V n = moles, R = gas constant, T = temperature, V = volume
Manometric Pressure P = P₀ + ρ·g·h P₀ = reference pressure, ρ = density, g = gravity, h = height
Pressure in a Fluid P₂ = P₁ + ρ·g·Δh Δh = height difference between two points
Gauge Pressure P_gauge = P_absolute - P_atmospheric Difference between absolute and atmospheric pressure

Common Pressure Units

Pa
Pascal
SI unit: 1 N/m²
bar
Bar
100,000 Pa (≈ atmospheric)
atm
Atmosphere
101,325 Pa (standard)
psi
Pounds/sq in
6,894.76 Pa
Torr
Torr
133.322 Pa (1 mmHg)
inHg
Inches of Hg
3,386.39 Pa

Practical Applications

1

Engineering: Pressure calculations are essential in mechanical, civil, and aerospace engineering for designing structures, hydraulic systems, and pressure vessels.

2

Meteorology: Atmospheric pressure measurements are crucial for weather forecasting and climate studies.

3

Medicine: Blood pressure monitoring and respiratory therapy rely on precise pressure measurements.

4

Chemistry: Pressure affects reaction rates, equilibrium states, and gas behavior in chemical processes.

Reference Pressure Values

  • Standard atmospheric pressure: 101,325 Pa (101.325 kPa, 1.01325 bar, 14.696 psi, 760 Torr)
  • Blood pressure (normal): ~120/80 mmHg (systolic/diastolic)
  • Tire pressure (car): 30-35 psi (207-241 kPa)
  • Deep ocean pressure (Mariana Trench): ~1,100 bar (110 MPa, 16,000 psi)
  • Vacuum (space): ~1.3×10⁻¹¹ Pa

Calculator Features:

  • Four calculation modes: Force/Area, Fluid Pressure, Gas Pressure, and Unit Conversion
  • Converts between 20+ pressure units with high precision
  • Includes common fluid presets and gas constant values
  • Visual pressure scale and unit comparison visualization
  • Real-time calculation with example presets for common scenarios

Frequently Asked Questions

Absolute pressure is measured relative to a perfect vacuum (zero pressure). Gauge pressure is measured relative to atmospheric pressure. Therefore: Absolute pressure = Gauge pressure + Atmospheric pressure. Most pressure gauges measure gauge pressure, while scientific calculations typically use absolute pressure.

Pressure increases with depth in fluids due to the weight of the fluid above. The hydrostatic pressure formula P = ρ·g·h shows that pressure is directly proportional to depth (h), fluid density (ρ), and gravitational acceleration (g). Each additional meter of depth adds the weight of that fluid column to the total pressure.

The ideal gas law (PV = nRT) assumes gas molecules have no volume and experience no intermolecular forces. It works well for gases at high temperatures and low pressures. For more accurate calculations with real gases at high pressures or low temperatures, use modified equations like the Van der Waals equation: (P + a(n/V)²)(V - nb) = nRT, where a and b are constants specific to each gas.

The SI unit of pressure is the Pascal (Pa), named after French mathematician and physicist Blaise Pascal. One Pascal is defined as one Newton of force applied over an area of one square meter: 1 Pa = 1 N/m². Because this is a relatively small unit, kilopascals (kPa, 10³ Pa) and megapascals (MPa, 10⁶ Pa) are commonly used in practice.

Atmospheric pressure decreases with altitude because there is less air above weighing down. The relationship is approximately exponential: P = P₀·e^(-Mgh/RT), where P₀ is sea level pressure, M is molar mass of air, g is gravity, h is height, R is gas constant, and T is temperature. Roughly, pressure decreases by about 12% per 1000 meters (1 kPa per 100 m) near sea level.