Pressure explains why knives cut and why snowshoes work. Enter a force and the area it acts on to get the pressure in pascals, kPa, bar and atmospheres.
Enter the force in newtons.
Enter the area in square metres.
Read the pressure in each unit.
Pressure: P = F ÷ A
Pressure is how concentrated a force is. This calculator divides a force in newtons by the area it acts on in square metres to give pressure in pascals, and then converts the result into kilopascals, bar and standard atmospheres. It is useful whenever a question mixes these units, which happens often in physics, engineering and everyday tyre or cylinder ratings.
Class 8 science introduces pressure with examples like sharp knives and broad school bag straps, and Class 11 extends it to fluids. The same idea tells an engineer whether soil can carry a column footing, a doctor how a blood pressure cuff works, and a cyclist why narrow tyres need higher air pressure. It answers one question: for this force on this area, how hard is each square metre being pushed?
1. Find the force in newtons. For a weight, multiply mass in kg by 9.8.
2. Find the contact area in square metres. Convert cm² by dividing by 10,000 and mm² by dividing by 1,000,000.
3. Divide: P = F ÷ A. The result is in pascals, since 1 Pa = 1 N/m².
4. Convert to kilopascals by dividing by 1000, and to bar by dividing by 100,000.
5. Convert to atmospheres by dividing by 101,325.
6. Check that the force is perpendicular to the surface; if it is at an angle, use only its perpendicular part.
The same force can do very different things depending on the area. A 60 kg person standing on flat shoes presses on the floor with about 600 N over perhaps 0.03 m², around 20 kPa. On a stiletto heel of 1 cm², the same weight can give several megapascals under the heel. Knife edges, nails and needles concentrate force onto tiny areas to break material; tractor tyres, snow shoes and wide foundations spread force out to avoid sinking.
The pascal is small, so real pressures are usually quoted in kPa, bar or atm. One bar is exactly 100,000 Pa. One standard atmosphere is 101,325 Pa, which is the average air pressure at sea level. Tyre pressures in India are often given in psi, where 1 psi is about 6.895 kPa, so 32 psi is roughly 220 kPa or 2.2 bar. Engineers also use N/mm², which equals one megapascal.
P = F ÷ A is the definition of average pressure over a surface. In a fluid at rest, pressure also acts equally in all directions and increases with depth as P = ρgh, which is why dams are thicker at the bottom. Gauge pressure, shown by a tyre gauge, is measured above atmospheric pressure; absolute pressure adds the atmosphere back. The calculator gives the pressure caused by the force you enter and does not add atmospheric pressure.
Rohan's loaded water tank weighs 9,800 N and rests on a square concrete pad with a contact area of 0.64 m² on his terrace.
P = F ÷ A: = 9800 ÷ 0.64 = 15,312.5 Pa
Other units: = 15.3125 kPa = 0.153125 bar = 0.151123 atm
Answer: Pressure 15,312.5 Pa; Kilopascals 15.3125 kPa; Bar 0.153125 bar
Entering area in cm² as if it were m², which makes the pressure 10,000 times too small.
Using mass in kg as the force without multiplying by g.
Mixing up gauge pressure and absolute pressure.
Using the whole area of an object instead of the actual contact area.
Assuming 1 bar and 1 atm are identical; they differ by about 1.3%.
Class 8 to 11 problems on pressure, thrust and fluids.
Checking bearing pressure of tanks, machines and footings on floors and soil.
Converting tyre, gas cylinder and pump ratings between kPa, bar and atm.
Designing hydraulic presses, jacks and brakes.
Explaining everyday effects such as sharp knives and wide bag straps.
How do I convert cm² to m²?
Divide by 10,000.
What is 1 bar?
100,000 Pa, slightly less than 1 atmosphere.