Pressure Calculator
Pressure is force per unit area. This calculator computes pressure in Pascals from force and area, and converts to common pressure units including psi, bar, atm, and mmHg.
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Formula
P = F / A
Pressure (P) equals force (F) divided by area (A). In SI units: Pascals (Pa) = Newtons (N) ÷ square meters (m²). 1 atm = 101,325 Pa. 1 psi = 6,894.76 Pa. 1 bar = 100,000 Pa. 1 mmHg = 133.32 Pa.
How to use the Pressure Calculator
- 1
Enter your force
Value should be in N.
- 2
Enter your area
Value should be in m².
- 3
Read your results instantly
Results update in real time as you type.
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Why area matters as much as force
Pressure depends on both force and the area over which it acts. A sharp knife exerts enormous pressure at the cutting edge because all the force concentrates on a tiny area. Snowshoes distribute body weight over a large area, reducing pressure on snow and preventing sinking. High heels concentrate weight on a very small area — a 60 kg person in stilettos can exert pressure comparable to an elephant.
This principle is everywhere in engineering. Dam gates must withstand enormous water pressure; the pressure at depth d in water is P = ρgd. Hydraulic systems transmit pressure through fluid to multiply forces — a small piston pressing at high pressure drives a large piston to lift heavy loads (Pascal's Principle).
Atmospheric pressure and altitude
Standard atmospheric pressure at sea level is 101,325 Pa (1 atm = 14.7 psi). This is the weight of the entire air column above a 1 m² area. At higher altitudes, the air column is shorter and thinner: at 5,500 m (Mount Everest base camp), pressure is about 50,000 Pa — half of sea level. At the summit (8,849 m), it's about 33,700 Pa.
Low pressure at altitude means less oxygen per breath, causing altitude sickness. Airplane cabins are pressurized to about 75,000 Pa (equivalent to ~2,400 m altitude) to keep passengers comfortable without the weight and cost of full sea-level pressurization.
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Gauge pressure vs. absolute pressure
Absolute pressure is measured from true zero (vacuum). Gauge pressure is measured relative to atmospheric pressure — it's what tire pressure gauges show. A car tire at 32 psi gauge has absolute pressure of 32 + 14.7 = 46.7 psi. Blood pressure is also gauge pressure: 120/80 mmHg above atmospheric.
Vacuum pressure is negative gauge pressure — below atmospheric. A vacuum of −50 kPa gauge equals 51,325 Pa absolute (half an atmosphere). Perfect vacuum is 0 Pa absolute, or −101,325 Pa gauge.
Tips & Insights
Convert cm² to m²
1 cm² = 0.0001 m². If your area is in square centimeters, divide by 10,000 to convert to m² before calculating.
Water pressure with depth
Water pressure at depth d: P = ρgd = 1000 × 9.81 × d Pa. Every 10 m of water adds about 1 atm of pressure.
Tire pressure: gauge not absolute
Tire pressure gauges show gauge pressure (above atmospheric). If your gauge reads 35 psi, the absolute pressure inside is 35 + 14.7 ≈ 49.7 psi.
Worked Examples
Hydraulic press
P = 50,000 N ÷ 0.05 m² = 1,000,000 Pa = 1 MPa ≈ 145 psi.
Atmospheric pressure on a window
P = 101,325 Pa = 1 atm = 14.7 psi. This is the force of the atmosphere on every square meter of surface.
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Frequently Asked Questions
What is pressure?
Pressure is force per unit area: P = F/A. It measures how concentrated a force is on a surface. Unit: Pascals (Pa) = N/m².
How do I convert Pa to psi?
Divide Pa by 6,894.76 to get psi. 1 psi = 6,894.76 Pa. 1 atm = 14.696 psi = 101,325 Pa.
What is atmospheric pressure?
Standard atmospheric pressure at sea level is 101,325 Pa (1 atm = 14.696 psi = 1.01325 bar). It decreases with altitude.
What is Pascal's Principle?
Pressure applied to an enclosed fluid transmits equally in all directions. Hydraulic systems use this to multiply force: small force on small piston = large force on large piston.
What is the pressure at the bottom of the ocean?
At the Mariana Trench (~11 km deep), pressure is about 110 MPa — over 1,000 times atmospheric pressure (1,086 atm).
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