Applied Pressure Calculator
Pressure from force spread over area, in psi, Pa, kPa, and atm.
What it does
Pressure answers how concentrated a push is. Fifty pounds on ten square inches gives a mild 5 psi, while the same fifty pounds on one square inch gives a sharp 50. Force alone never tells the story; the area it spreads over sets the effect.
The tool above runs both unit systems. Imperial mode divides pounds by square inches for psi. Metric mode divides newtons by square centimeters (converted to square meters inside) for pascals or kilopascals. Both modes also print atmospheres for a sense of scale.
Standards pin every factor. NIST lists the psi as 6.894757 kPa, and its SI guide defines the pascal as one newton per square meter. Georgia State HyperPhysics states the base rule directly: pressure is force per unit area. OpenStax College Physics works the same form with a tank example.
Shop numbers follow at once. A 30 psi tire on a 10 in2 contact patch carries about 300 lbf per tire, and a hydraulic cylinder at 2,000 psi on a 3 in2 piston pushes 6,000 lbf. Keep gauge readings (above atmosphere) apart from absolute ones when the manual calls for it.
How to use
- Pick imperial (lbf, in2) or metric (N, cm2).
- Enter the force pressing on the surface.
- Enter the loaded area in the matching square unit.
- Read pressure first, then the converted unit and atmospheres.
- To size a cylinder, flip the form: force equals pressure times area.
- Keep gauge and absolute readings apart when it matters.
Formula
- F
- Force pressing on the surface: lbf or N.
- A
- Loaded area: square inches or square cm.
- 6894.76
- Exact-by-definition NIST factor between psi and pascal.
F must press perpendicular to the area A. Metric defaults mirror the imperial ones (222.4 N on 64.5 cm2 gives the same 5 psi class result).
Worked example
Example: 50 lbf on 10 in2
Imperial defaults: 50 lbf of force spread over 10 square inches.
- Inputs: 50 lbf pressing on 10 square inches.
- Pressure: 50 / 10 = 5.00 psi.
- SI check: 50 lbf is 222.41 N, 10 in2 is 0.0064516 m2.
- Pascals: 222.41 / 0.0064516 = 34,473.8 Pa = 34.47 kPa.
- Tool shows 5.00 psi, 34.47 kPa, 0.3402 atm.
Reference table
| Level | Pa | psi |
|---|---|---|
| 1 Pa | 1 | 0.000145 |
| 1 kPa | 1,000 | 0.1450 |
| 5 psi (example) | 34,474 | 5.00 |
| Car tire 32 psi | 220,632 | 32.00 |
| 1 atm | 101,325 | 14.6959 |
Limits
- Square-on loads only. Shear and point loads need other models.
- Static pressure only. Pulses and water hammer differ.
- Ignores temperature effects on gases and seals.
- Gauge versus absolute must be tracked by the user.
Common mistakes
- Mixing square inches with square feet, a factor of 144 error.
- Reading gauge pressure where absolute is required.
- Forgetting the force must press squarely, not slide.
- Rounding psi to kPa mid chain instead of at the end.
- Applying fluid pressure math to point contacts.
Try it yourself
Quick checks. Answers sit tucked under each question.
100 N on 5000 cm2?
A is 0.5 m2. 100 / 0.5 = 200.0 Pa, which is 0.0290 psi.
500 N on 2500 cm2?
A is 0.25 m2. 500 / 0.25 = 2000 Pa = 2.00 kPa, which is 0.2901 psi.
Questions
What is pressure?
Force spread over area. Pounds over square inches gives psi; newtons over square meters gives pascals.
How do I convert psi to kPa?
Multiply psi by 6.89476 to get kPa. So 5 psi is 34.47 kPa.
What is one atmosphere in Pa and psi?
101,325 Pa, which is 14.6959 psi. Tire gauges read a few psi; weather maps use fractions of an atmosphere.
Must the force press straight on?
Only when the force presses squarely on the surface. Shear forces sliding along it need different math.
How do force and area trade off?
Pressure stays the same while force scales with area. Ten psi on 2 in2 pushes 20 lbf; on 10 in2 it pushes 100 lbf.
What if I halve the force?
Same area with half the force gives half the pressure. The tool follows P = F / A directly.
Sources
- NIST Guide to the SI, Appendix B.9 (pressure factors)
- Georgia State HyperPhysics: Pressure
- OpenStax College Physics: Pressure (Rice University)