Pressure Calculator — P = F/A
Calculate pressure from force and area. Covers P = F/A, pressure units (Pa, psi, bar, atm), fluid pressure, and engineering applications including hydraulics.
Pressure is force spread over an area. The same force concentrated into a smaller area creates dramatically more pressure — that's why knife blades cut and needles pierce. Snowshoes work in reverse: spreading your weight over a larger area to reduce pressure on snow. The concept scales from atomic-level surface forces to atmospheric pressure to deep-ocean crushing forces.
The CalcHub pressure calculator handles pressure, force, and area with full unit conversion.
The Formula
P = F / A- P = pressure (Pascals, Pa)
- F = force (Newtons, N)
- A = area (m²)
Pressure Unit Conversions
| Unit | Equivalent in Pa |
|---|---|
| 1 atm | 101,325 Pa |
| 1 bar | 100,000 Pa |
| 1 psi | 6894.76 Pa |
| 1 kPa | 1000 Pa |
| 1 MPa | 1,000,000 Pa |
| 1 mmHg | 133.32 Pa |
Fluid Pressure with Depth
P = ρgh (pressure at depth in a fluid)Where ρ is fluid density, g is gravity, h is depth. Pressure increases linearly with depth. At 10 m underwater: P = 1000 × 9.81 × 10 = 98,100 Pa ≈ 1 atm. Every 10 m of water adds approximately 1 atm.
Worked Example
A 75 kg person stands on one foot, with foot area 0.015 m². What pressure do they exert on the floor?
F = mg = 75 × 9.81 = 735.75 N
P = F/A = 735.75 / 0.015 = 49,050 Pa ≈ 49 kPa
Now compare to high heels: tip area ≈ 1 cm² = 0.0001 m²
P = 735.75 / 0.0001 = 7,357,500 Pa ≈ 7.36 MPa
High heels exert over 150 times more pressure than bare feet — which is why they damage hardwood floors.
What is gauge pressure vs. absolute pressure?
Absolute pressure includes atmospheric pressure (14.7 psi / 101.3 kPa at sea level). Gauge pressure measures above atmospheric: tire pressure of "32 psi" is gauge pressure — the actual absolute pressure is 32 + 14.7 = 46.7 psi. Most practical measurements use gauge pressure.
What is Pascal's principle?
Pressure applied to a confined fluid transmits equally in all directions throughout the fluid. This is the basis of hydraulic systems: apply a small force over a small area, and the pressure appears at a large piston area as a large force. Hydraulic brakes and jacks operate this way.
How does atmospheric pressure change with altitude?
Pressure decreases approximately exponentially with altitude: P ≈ P₀ × e^(−h/8500), where h is in meters. At 5500 m (base of Everest's death zone), pressure is about half sea-level. At the summit (~8849 m), roughly 1/3 of sea-level pressure — which is why supplemental oxygen is needed.