Pounds per Square Inch Calculator finds psi from a force on a rectangle, a circle or any known area, or from bar, kPa or kg/cm2, with full steps plus the absolute pressure in psia.
Enter the force and the two sides of the area it presses on.
Result Unit
Step-by-Step Working
- Known values: F = 900 lbf, L = 5 in, W = 6 in
- Area: A = L × W = 5 in × 6 in = 30 in²
- Pressure: P = F ÷ A = 900 lbf ÷ 30 in² = 30 psi
- Result: P = 30 psi
Same Force on Other Areas
| Area (in²) | psi | kPa |
|---|---|---|
| 7.5 | 120 | 827.4 |
| 15 | 60 | 413.7 |
| 30 | 30 | 206.8 |
| 60 | 15 | 103.4 |
| 120 | 7.5 | 51.71 |
Pounds per Square Inch Calculator for Force and Area
Pounds per square inch, or psi, is a unit of pressure. One psi is a force of one pound pressing evenly on an area of one square inch. It is the everyday pressure unit in the United States for tires, air compressors, water lines and hydraulic systems.
The Pounds per Square Inch Calculator works out psi from a force and the area it presses on. The Calculate From menu takes the area as a rectangle, a circle or a known figure. A fourth setting, Another pressure unit, converts bar, kPa, kg/cm² and other units into psi.
Force can be entered in pounds-force, newtons, kilonewtons or kilograms-force. Lengths can be in inches, feet, millimeters, centimeters or meters. Metric entries are converted first, so the tool also serves as a pounds per square inch calculator in metric units.
The starting entries are 900 lbf on a rectangle of 5 in by 6 in. The main result reads 30 psi on the Surface. The Result Unit option can switch that figure to kPa, MPa, bar, atmospheres, kg/cm², psf or pascals.
PSI Formula
The formula for calculating psi is pressure equals force divided by area. With the force in pounds and the area in square inches, the answer comes out in pounds per square inch with no conversion needed.
$$P = \frac{F}{A}$$
For a rectangle the area is length times width. The example gives 5 × 6 = 30 in², and 900 ÷ 30 = 30 psi. This is how to get pounds per square inch for any flat pad, plate or footing.
$$P = \frac{F}{L \times W}$$
For a round face such as a piston or a cylinder rod, the area comes from the diameter d. With the tool’s Force on a circle setting, 900 lbf on a 4 in diameter gives an area of 12.57 in² and a pressure of 71.62 psi.
$$P = \frac{4F}{\pi d^{2}}$$
The Step-by-Step Working panel in the Pounds per Square Inch Calculator shows the area line and the division. If the force or lengths were entered in metric units, it first lists them in pounds-force and inches.
How to Calculate lb to psi
Pounds cannot be converted to psi on their own, because psi also needs an area. A pounds to psi calculator divides the pounds by the square inches they rest on. A 180 lb person standing on shoes with 60 in² of sole puts 3 psi on the floor.
The same person balanced on two heel tips of 1 in² each puts 90 psi on it. That is why a narrow heel dents a wood floor and a flat shoe does not. The Same Force on Other Areas panel lists this effect for your own force.
| Area under 900 lbf (in²) | Pressure (psi) | Pressure (kPa) |
|---|---|---|
| 7.5 | 120 | 827.4 |
| 15 | 60 | 413.7 |
| 30 | 30 | 206.8 |
| 60 | 15 | 103.4 |
| 120 | 7.5 | 51.71 |
How to Calculate Pounds from psi
To go the other way, multiply the pressure by the area. A hydraulic cylinder with a 3 in bore has a piston area of 7.069 in². At 1,500 psi it pushes with 1,500 × 7.069 = 10,603 lbf.
$$F = P \times A$$
A tire works the same way. A 3,000 lb car on tires at 32 psi needs roughly 3,000 ÷ 32 = 93.75 in² of rubber on the road, or about 23 in² per tire. The Force Calculator solves pressure times area for any units. The Car Center of Mass Calculator gives the load on each axle.
What Is 1 Pound per Square Inch Equal To?
One psi equals 6,894.757 pascals, which is 6.895 kPa. That factor comes from the NIST Guide to the SI. The same guide defines the bar, the standard atmosphere and the kilogram-force per square centimeter as exact values in pascals.
| psi | kPa | bar | kg/cm² | atm | psf |
|---|---|---|---|---|---|
| 1 | 6.895 | 0.06895 | 0.07031 | 0.06805 | 144 |
| 14.696 | 101.3 | 1.013 | 1.033 | 1 | 2,116 |
| 25 | 172.4 | 1.724 | 1.758 | 1.701 | 3,600 |
| 30 | 206.8 | 2.068 | 2.109 | 2.041 | 4,320 |
| 100 | 689.5 | 6.895 | 7.031 | 6.805 | 14,400 |
| 2,000 | 13,790 | 137.9 | 140.6 | 136.1 | 288,000 |
So 25 psi in pressure is 172.4 kPa, or 1.724 bar. That is a little more than one and a half times the pressure of the air at sea level. The first two result cards of the Pounds per Square Inch Calculator show these units for whatever pressure you enter.
Pounds per Square Inch to Bar
To convert pounds per square inch to bar, divide by 14.504. One bar is exactly 100,000 Pa, which makes it 14.504 psi. The converter in the Pounds per Square Inch Calculator starts with 2 bar and returns 29.01 psi. To go from psi to bar, multiply by 0.06895.
Pounds per Square Inch in kg
Pounds per square inch in kg means kilograms-force per square centimeter. To convert lbs per square inch to kg/cm², multiply by 0.07031. One kg/cm² is 14.223 psi. For a larger figure, 2,000 pounds per square inch comes to 140.6 kg/cm².
The kilogram here is a force, the weight of one kilogram under standard gravity, so the unit is often written kgf/cm². The kg to Newtons Calculator covers that step, since 1 kgf is 9.80665 N.
Feet of Water and Inches of Mercury
Pressure can also be stated as the height of liquid it holds up. One psi supports a column of water 2.307 ft tall, or 2.036 inches of mercury. The third card shows 30 psi as 69.2 ft of Water Column and 61.08 inHg.
This is the figure plumbers use for water towers and well pumps. A tank 100 ft above a faucet delivers about 43 psi before any pipe losses. Sea-level air pressure, 14.696 psi, matches a water column of 33.9 ft.
Pounds per Square Inch Symbol: psi, psig, psia
The pound per square inch symbol is psi, also written lbf/in² or lb/in². There is no need to convert pounds per square inch to psi, because they are the same unit. The abbreviation just drops the words.
Two longer forms say what the pressure is measured against. A reading in psig is gauge pressure, the amount above the surrounding air. A reading in psia is absolute pressure, measured from a perfect vacuum. Absolute is gauge plus 14.696 psi at sea level.
The fourth card of the Pounds per Square Inch Calculator makes that step. It shows 30 psi as 44.7 psia if Read on a Gauge, along with 3.041 atm and 308.2 kPa absolute. Gas law calculations need the absolute figure.
A tire gauge reads psig. NHTSA says the recommended pressure for a car is on the Tire and Loading Information label on the driver’s door edge or post, in both kPa and psi. It should be checked with the tires cold.
Square Inches, Square Feet and psf
The area is half of every psi calculation, so it has to be right. To calculate square inches for a rectangle, multiply the length in inches by the width in inches. For a circle, multiply π by the radius squared.
A 1 inch square measures 25.4 mm on each side, about the size of a large postage stamp. One square inch equals 6.4516 cm². One square foot is 12 in by 12 in, which makes 144 square inches.
How to Calculate Pounds per Square Foot
Pounds per square foot, or psf, is the force in pounds divided by the area in square feet. Because a square foot holds 144 square inches, 1 psi equals 144 psf. To turn psf into psi, divide by 144.
Floor loads and wind loads are quoted in psf because the numbers are easier to read. A floor load of 50 psf is only 0.347 psi. The Pounds per Square Inch Calculator accepts the area in square feet under Force on a known area, and psf is one of its result units.
How to Calculate Pounds per Inch
Pounds per inch is a different quantity, with no area in it. It is a force divided by a length. The most common use is a spring rate, where a 200 lb/in spring needs 200 lb to compress it by one inch. The Hooke’s Law Calculator works with that unit.
Cost per Square Inch and per Pound
“Per square inch” is also used for prices. A square inch rate is the price divided by the area in square inches. An $18 pizza of 14 in diameter has 153.9 in², so it costs 11.7 cents per square inch. A $12 pizza of 12 in diameter costs 10.6 cents.
To find a rate per square foot, divide the price by the square feet. To change it to a square inch cost, divide again by 144. A countertop at $60 per square foot costs about 42 cents per square inch.
A price per pound is the total price divided by the weight in pounds. These rate sums share only the division with pressure. In the Pounds per Square Inch Calculator, the top line is always a force and never a price.
For the force itself, the Normal Force Calculator gives the push of an object on the surface under it. More force tools are listed under Dynamics and Statics Calculators.