Pressure Calculator finds pressure from a force and an area, the force a pressure puts on a surface, or the area a heavy load needs, in Pa, kPa, bar, psi or kg/cm2 with full steps.
Enter the force and the area it presses on.
Result Unit
Step-by-Step Working
- Known values: F = 1,000 N, A = 0.4 m²
- Pressure: P = F ÷ A = 1,000 N ÷ 0.4 m² = 2,500 Pa
Same Force on Other Areas
| Area (m²) | Pa | psi |
|---|---|---|
| 0.04 | 25,000 | 3.626 |
| 0.08 | 12,500 | 1.813 |
| 0.4 | 2,500 | 0.3626 |
| 2 | 500 | 0.07252 |
| 4 | 250 | 0.03626 |
Pressure Calculator for Force and Area
Pressure is how hard a force presses on each unit of surface. OpenStax University Physics defines it as the normal force per unit area over which the force is applied. A large force on a wide surface can give less pressure than a small force on a point.
The Pressure Calculator links three quantities, and the Solve For menu picks which one to find. It returns pressure from a force and an area, force from a pressure and an area, or the area needed for a force at a set pressure.
Force can be entered in newtons, kilonewtons, meganewtons, pounds-force or kilograms-force. Area takes square meters, square centimeters, square millimeters, square inches or square feet. Pressure comes out in Pa, kPa, MPa, bar, psi, atm, kg/cm², psf or mmHg.
The starting entries are 1,000 N on 0.4 m². The main result reads 2,500 Pa on the Surface. The four cards under it list the same pressure as 2.5 kPa, 0.3626 psi and 25.49 cm of water column, and show what happens on a smaller or larger area.
Pressure Formula
The basic formula for pressure is force divided by area. The force is the part that pushes straight into the surface, and the area is the patch it actually touches. A push at an angle counts only by its perpendicular part.
$$P = \frac{F}{A}$$
To calculate pressure, put the force in newtons and the area in square meters. The answer is in pascals. For the starting entries that is 1,000 ÷ 0.4 = 2,500 Pa. This is all a force to pressure calculator does, apart from converting units.
A 70 kg person shows why area matters. Their weight is 686.5 N. Standing on two shoes with 0.035 m² of sole in total, they press with 19.6 kPa. Balanced on a heel tip of 1 cm², the same weight gives 6,865 kPa, which is 350 times higher.
| Area under 1,000 N (m²) | Pressure (Pa) | Pressure (psi) |
|---|---|---|
| 0.04 | 25,000 | 3.626 |
| 0.08 | 12,500 | 1.813 |
| 0.4 | 2,500 | 0.3626 |
| 2 | 500 | 0.07252 |
| 4 | 250 | 0.03626 |
These rows are the Same Force on Other Areas panel for the starting entries. The fourth card gives the short version, with 5,000 Pa on half the area and 1,250 Pa on double the area.
Force from Pressure and Area
Rearranged, the formula gives the push that a pressure produces on a surface. This is how hydraulic cylinders, air cylinders and presses are rated, and how the load on a tank wall or a window is found.
$$F = P \times A$$
With Solve For set to Force, the Pressure Calculator starts at 250 kPa on 0.4 m². The force is 250,000 × 0.4 = 100,000 N, or 100 kN. The second card turns that into a load of 10,197 kg Held Against Gravity, and the fourth gives the matching piston diameter.
Area Needed for a Load
The third form finds how much surface a load needs so the pressure stays under a limit. It is used to size footings, jack pads and base plates, where the ground or floor can take only so much.
$$A = \frac{F}{P}$$
A force of 1,000 N at a limit of 250 kPa needs 0.004 m², which is 40 cm². The cards show that as a circle 71.36 mm across or a square 63.25 mm on a side. Split over four pads, each one needs 10 cm².
Pressure Units Compared
The SI unit of pressure is the pascal. One pascal is one newton on one square meter, which is a very small pressure. Everyday values are quoted in kilopascals, bar or psi for that reason.
| Unit | In pascals | In psi | In kg/cm² |
|---|---|---|---|
| 1 kPa | 1,000 | 0.145 | 0.0102 |
| 1 psi | 6,894.757 | 1 | 0.0703 |
| 1 kg/cm² | 98,066.5 | 14.223 | 1 |
| 1 bar | 100,000 | 14.504 | 1.0197 |
| 1 atm | 101,325 | 14.696 | 1.0332 |
| 1 mmHg | 133.322 | 0.01934 | 0.00136 |
The pascal values are from the NIST Guide to the SI, and the Pressure Calculator uses the same ones. So 1 bar of pressure is 100 kPa, or 14.504 psi. One kg/cm² is 14.223 psi, and 1 psi equals 6.895 kPa.
The full form of psi is pounds per square inch. The Pounds per Square Inch Calculator works in that unit from pounds and inches. This Pressure Calculator starts from newtons and square meters and reports psi on its second card.
How to Calculate Pressure in kg
Pressure in kg means kilograms-force per square centimeter. Divide the load in kilograms by the area in square centimeters. A 500 kg machine on feet with 200 cm² of contact presses with 2.5 kg/cm².
In kg versus psi, one kg/cm² is the larger unit by a factor of 14.223. To convert psi to kg/cm², multiply by 0.0703. To convert 1 bar to kg/cm², multiply by 1.0197. The kg to Newtons Calculator gives the force behind a kilogram of load.
Common Pressure Readings Converted
The same handful of gauge readings come up again and again on tires, compressors and water lines. Each row below is one pressure written four ways, so a reading in one unit can be matched to a gauge in another.
| Reading | kPa | bar | psi | kg/cm² |
|---|---|---|---|---|
| 25 psi | 172.4 | 1.724 | 25 | 1.758 |
| 30 psi | 206.8 | 2.068 | 30 | 2.109 |
| 32 psi | 220.6 | 2.206 | 32 | 2.25 |
| 240 kPa | 240 | 2.4 | 34.81 | 2.447 |
| 40 psi | 275.8 | 2.758 | 40 | 2.812 |
| 3 bar | 300 | 3 | 43.51 | 3.059 |
| 60 psi | 413.7 | 4.137 | 60 | 4.218 |
| 7 bar | 700 | 7 | 101.5 | 7.138 |
| 300 psi | 2,068 | 20.68 | 300 | 21.09 |
So 3 bars of pressure is 43.51 psi, and 40 psi is 2.758 bar. A 240 kPa tire reading is 34.81 psi. Seven bar is 101.5 psi, so it is close to 100 psi but not equal to it. And 32 psi works out to 2.25 kg/cm².
Water Pressure, Height and ρgh
A liquid presses by its own weight, so its pressure depends on depth and not on a separate force. A pressure calculator from height uses the density ρ, gravity g and the depth h.
$$P = \rho g h$$
For fresh water at 1,000 kg/m³, one meter of depth adds 9.807 kPa. That is how many psi 1 meter of water gives, which is 1.422 psi. Ten meters adds 98.07 kPa, close to one atmosphere.
The third result card of the Pressure Calculator works this in reverse. It shows any pressure as the water column it would hold up, along with mm of mercury and inches of water. For 2,500 Pa that is 25.49 cm of water column and 18.75 mmHg.
Water pressure of 300 psi is 2,068 kPa. It equals the pressure under 211 m of water, about 692 ft. Household water lines run far lower, and a 60 psi supply matches 42.2 m of head.
How to Convert mm to psi
A pressure in mm is the height of a liquid column, so the answer depends on the liquid. For mercury, multiply mmHg by 0.01934. For water, multiply mm of water by 0.001422.
A reading of 150 mm of mercury is 2.9 psi, or 20 kPa. A reading of 150 mm of water is only 0.213 psi, because water is much less dense than mercury. In the Pressure Calculator, mmHg is one of the pressure units for both entry and result.
How to Calculate Total Pressure
Total pressure at a depth is the pressure on the surface plus the liquid’s own. OpenStax writes it as p = p0 + ρgh, where p0 is the air pressure above. At 10 m in fresh water the total is 101.3 + 98.1 = 199.4 kPa.
$$p = p_{0} + \rho g h$$
A gauge reads only the second part, which is called gauge pressure. Adding the atmosphere gives absolute pressure. When you solve for force on a tank wall or piston with air on the other side, enter the gauge value.
Normal Air Pressure and Standard Pressure
Normal air pressure at sea level is about 101.3 kPa. The standard atmosphere is fixed at exactly 101,325 Pa, which is 1.01325 bar, 14.696 psi or 760 mmHg. Weather reports give the same quantity in hectopascals, as 1,013.25 hPa.
Standard pressure in chemistry is a slightly different number. The IUPAC Gold Book sets it at 100,000 Pa, which is exactly 1 bar. It replaced 101,325 Pa in IUPAC’s recommendations from 1982 onward.
Air pressure acts on everything, which is why it goes unnoticed. On a tabletop of 0.4 m² the atmosphere pushes down with about 40,500 N. The table does not collapse because the air under it pushes up just as hard.
Pipes, Flow Rate, Blood and Bike Tires
Several searches use the word pressure for cases that need more than force and area. The Pressure Calculator covers the force and area part of each one, and the notes below say where the rest comes from.
Pressure in a Pipe and from Flow Rate
Pressure cannot be found from a flow rate alone. The flow rate gives the speed of the fluid, and the pressure drop then depends on the pipe length, diameter and roughness. The Velocity Calculator has a Flow in a Pipe setting for the speed.
What force and area do give is the load on a pipe’s end cap or a valve. Water at 400 kPa pushing on a cap of 50 cm² presses with 400,000 × 0.005 = 2,000 N. Set Solve For to Force to get that number.
Blood Pressure
Blood pressure is a gauge pressure measured in mm of mercury. The American Heart Association lists normal as less than 120 over less than 80 mm Hg. In other units, 120 mmHg is 16 kPa or 2.32 psi, and 80 mmHg is 10.7 kPa.
Bike Tire Pressure
The right bike tire pressure depends on tire width and rider weight, and the tire maker prints the range on the sidewall. The physics is the same as for any tire. A rider and bike weighing 800 N on tires at 620 kPa, which is 90 psi, rest on about 13 cm² of rubber in total.
For a force that is not spread over an area, the Force Calculator and the Normal Force Calculator are the places to start. Related tools are listed under Dynamics and Statics Calculators.