Pounds Per Square Inch Calculator
Pounds per square inch is the pressure unit you meet on tire gauges, air compressor dials and hydraulic spec sheets. This calculator turns a force in pounds and an area, or a piston diameter, into PSI, then converts the result into kilopascals, bar, atmospheres, mmHg, inHg and pascals in one click.
The diameter field takes precedence: if you enter both an area and a diameter, the calculator uses the circular area from the diameter. Force here means pound-force; the conversions show the same force in newtons and kilograms-force.
Quick Answer
A 100-pound force spread over 10 square inches is 10.000000 PSI, which converts to 68.947600 kPa and 0.689476 bar. Enter your force and area, or a piston diameter instead, and the calculator returns the PSI, seven unit conversions, a force and area breakdown, and a pressure classification.
Key takeaways
- PSI is force divided by area. The same force on half the area doubles the pressure, which is why small pistons generate such high readings.
- When both area and diameter are filled in, the diameter wins: the tool computes the circular area from the diameter and ignores the Area field.
- Pounds here mean pound-force. The force readout also shows newtons and kilograms-force, so metric gauges stay comparable.
- Typical passenger-car tires sit at 30 to 35 PSI cold, which lands in this tool's Medium band, not the Low one.
- Quick Answer
- How to use the PSI calculator
- The PSI formula, and where the conversion factors come from
- Worked example: 100 pounds on 10 square inches
- Going the other way: one unit expressed in PSI
- PSI anchors: numbers worth memorizing
- Direct area or diameter: pick the mode that matches your part
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
How to use the PSI calculator
Three fields, one button. The worked example (100 pounds on 10 square inches) is pre-filled so you can press Calculate PSI immediately and see the full output; results stay hidden until you do.
- Enter the force in pounds. This is the total push on the surface. If your gauge reads in newtons, convert it first with the newtons-to-pounds calculator.
- Enter the area and pick its unit, or enter a diameter. Square inches, square feet, square centimeters and square meters are all accepted and converted internally. For round pistons and cylinders, skip the area and enter the diameter instead; the tool works out the circular area itself.
- Click Calculate PSI. Read the big PSI number first, then the classification badge, the seven unit conversions, and the force and area breakdowns underneath.
Two validation rules keep bad input out: a blank or negative force stops with an error, and you must supply either an area or a diameter (a zero or blank pair stops too). The Reset button restores the worked-example values and hides the results.
The PSI formula, and where the conversion factors come from
Pressure is force divided by the area it acts on: PSI = force (lb) ÷ area (in²). OpenStax defines pressure exactly this way, as the normal force per unit area, and notes that pounds per square inch survives mostly as a tire-pressure unit.
1 PSI = 6.89476 kPa = 0.0689476 bar = 0.068046 atm = 51.7149 mmHg = 2.03602 inHg = 6894.76 Pa
The conversion factors are exact consequences of the definitions of the inch (2.54 cm) and the avoirdupois pound (0.45359237 kg), which is why every calculator that gets them right agrees to all six decimals. The pascal itself is defined by the BIPM's SI brochure as one newton per square meter, and the fundamental constants behind the newton are maintained in the NIST CODATA set. One subtlety worth naming: the pounds in this formula are pound-force, a unit of force, not pound-mass. If that distinction is new, the pound-force to pound-mass calculator untangles the two.
Worked example: 100 pounds on 10 square inches
The pre-filled values run the simplest possible case. The area needs no conversion (10 sq in is already in square inches), so the arithmetic is one division: 100 ÷ 10 = 10 PSI. Everything else on the results panel follows from that single number.
Press Calculate PSI with the defaults and you will see exactly this: 10.000000 PSI, conversions of 68.947600 kPa, 0.689476 bar, 0.680460 atm, 517.149000 mmHg, 20.360200 inHg and 68947.60 Pa, a force readout of 444.8220 N and 45.3592 kg-f, and the area restated as 0.069444 sq ft and 64.516000 sq cm. Try the diameter mode next: 500 pounds on a 2-inch piston gives a circular area of 3.141593 sq in and 159.154943 PSI (1097.335135 kPa), which the badge rates Very High Pressure.
Going the other way: one unit expressed in PSI
The calculator converts PSI outward into six other units. The table below runs the same factors in reverse, so you can sanity-check a gauge that reads in metric before you ever touch the tool.
| One unit of… | …equals this many PSI |
|---|---|
| Kilopascal (kPa) | 0.145038 |
| Bar | 14.503774 |
| Atmosphere (atm) | 14.695949 |
| Millimeter of mercury (mmHg) | 0.019337 |
| Inch of mercury (inHg) | 0.491154 |
| Pascal (Pa) | 0.000145038 |
PSI anchors: numbers worth memorizing
Pressure numbers mean little without reference points. Three are worth keeping in your head, and each is independently checkable:
Direct area or diameter: pick the mode that matches your part
The two area inputs look redundant, but they serve different jobs. The rule is simple: fill in whichever one you actually measured, and if you fill in both, the diameter wins.
Direct area mode
- Use it for plates, pads, footings and any flat contact patch you measured directly.
- Four units accepted; everything is normalized to square inches before dividing.
- Example: 2,000 lbs on 50 sq cm → 7.75 sq in → 258.064516 PSI.
Diameter mode
- Use it for round pistons, cylinders and bore calculations where the diameter is what you know.
- Five units accepted; area comes from A = π(d/2)².
- Example: 500 lbs on a 2-inch bore → 3.141593 sq in → 159.154943 PSI.
What competing calculators miss
PSI tools fall into three camps, and each leaves something out:
- Thin formula pages (CalculatorUltra's PSI pages): the formula and one worked example, but no diameter mode, no force or area breakdown, no pressure classification, and nothing that shows its working beyond the headline number.
- Reverse-direction tools (calculatorshub's PSI-to-LBF): useful if you already know the PSI and want the total force, but they cannot derive PSI from a force and area in the first place, which is the job most people arrive with.
- Generic unit converters: convert PSI to kPa faithfully, yet have no notion of force over area, so a piston problem still needs a second tool and a hand calculation.
- The gap this page fills: force and area (or diameter) in, PSI out, with the full conversion set, the force restated in newtons and kilograms-force, the area restated in three units, and a classification badge that says what the number means at a glance.
Frequently asked questions
Divide the force in pounds by the area in square inches: PSI = F ÷ A. For a 100-pound force on 10 square inches, that is 100 ÷ 10 = 10 PSI. OpenStax defines pressure the same way, as the normal force per unit area.
First find the circular area with A = π × (d ÷ 2)², then divide the force by it. A 500-pound force on a 2-inch bore gives an area of 3.141593 square inches and 159.154943 PSI. Enter the diameter in this calculator's diameter field and it does both steps.
Most passenger cars specify 30 to 35 PSI measured cold, and the exact figure is printed on the driver's door-jamb placard or in the owner's manual, not on the tire sidewall (the sidewall shows the maximum). That range sits in this calculator's Medium band. Bicycle tires run much higher, which is why they get their own tool.
Exactly 6.89476 kPa per PSI, so 10 PSI is 68.947600 kPa. The factor comes from the definitions of the inch and the pound, which is why every correct converter agrees on it.
PSIG (gauge) reads zero at atmospheric pressure, while PSIA (absolute) counts from a perfect vacuum. At sea level, PSIA equals PSIG plus about 14.7. This calculator works with the pressure you give it either way; just know which one your gauge reports.
Zero is fine and means no force is applied; the calculator returns 0.000000 PSI. Negative force is rejected, because a negative push has no meaning here. Vacuum readings below atmospheric pressure are a separate gauge convention, usually reported in inches of mercury.
By design, for piston and cylinder work where the diameter is the measured quantity. If both fields contain positive values, the calculator builds the circular area from the diameter and ignores the area input, and the area breakdown says so explicitly.
Yes. They derive from the exact definitions of the inch (2.54 cm) and the avoirdupois pound (0.45359237 kg), with the pascal defined as one newton per square meter in the SI brochure. The square-centimeter factor is rounded to 0.155, which shifts results by about two parts per million.
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References
- OpenStax. College Physics for AP Courses, 11.3 Pressure: pressure defined as force per unit area; pounds per square inch noted as a tire-pressure unit. Accessed October 23, 2026.
- LibreTexts Chemistry. 9.1: Gas Pressure: atmospheric pressure about 101 kPa or 14.7 lb/in² at sea level; pressure unit definitions. Accessed October 23, 2026.
- Autoblog. What should your tire pressure be? Recommended PSI levels for your vehicle: typical passenger-car pressure 30–35 PSI; door-jamb placard versus sidewall maximum. Accessed October 23, 2026.
- National Institute of Standards and Technology. Fundamental Physical Constants (CODATA). Accessed October 23, 2026.
- Bureau International des Poids et Mesures (BIPM). The International System of Units (SI Brochure): the pascal defined as one newton per square meter. Accessed October 23, 2026.
- Workforce LibreTexts. 3.4.02: Force (Water Hydraulics): pressure as pounds per square inch; 0.433 psi per foot of water column. Accessed October 23, 2026.