Pressure Formula
The pressure formula P = F/A calculates the force per unit area.
Understand pressure in pascals with practical worked examples.
The Formula
Pressure is the amount of force applied per unit area. The same force spread over a smaller area creates higher pressure.
Variables
| Symbol | Meaning |
|---|---|
| P | Pressure (measured in pascals, Pa, where 1 Pa = 1 N/m²) |
| F | Force applied perpendicular to the surface (measured in newtons, N) |
| A | Area over which the force is distributed (measured in square meters, m²) |
Example 1
A 600 N force is applied to a surface area of 0.03 m². What is the pressure?
Identify the values: F = 600 N, A = 0.03 m²
Apply the formula: P = F / A = 600 / 0.03
P = 20,000 Pa (or 20 kPa)
Example 2
A 70 kg person stands on one foot. The sole of the shoe has an area of 0.015 m². What pressure do they exert on the ground?
First find the force (weight): F = mg = 70 × 9.81 = 686.7 N
Apply: P = F / A = 686.7 / 0.015
P ≈ 45,780 Pa (approximately 45.8 kPa)
When to Use It
Use the pressure formula whenever force is distributed over an area.
- Calculating pressure exerted by objects on surfaces
- Hydraulic systems and fluid mechanics
- Understanding why sharp objects cut more easily (small area = high pressure)
- Tire pressure, atmospheric pressure, and engineering applications
Key Notes
- Formula: P = F/A: Pressure equals force divided by the area over which it acts. SI unit is Pascal (Pa = N/m²). One atmosphere ≈ 101,325 Pa ≈ 14.7 psi ≈ 1.013 bar — these conversions appear constantly in engineering.
- Pascal's law: In a static fluid, pressure acts equally in all directions and transmits without loss through the fluid. This is the operating principle of hydraulic jacks and car brakes — a small force over a small area creates a large force over a large area.
- Gauge vs absolute pressure: Absolute pressure = gauge pressure + atmospheric pressure. Tire gauges read gauge pressure (pressure above atmosphere). A "flat" tire at 0 psi gauge still contains air at ~14.7 psi absolute.
- Hydrostatic pressure: P = ρgh: Pressure increases linearly with depth. For every 10 m of water depth, pressure increases by ~1 atm (~100 kPa). At 100 m depth, total absolute pressure is ~11 atm.
- Applications: Pressure calculations govern hydraulic system design, HVAC ductwork, scuba diving safety limits, atmospheric science, and the design of pressure vessels and pipelines.