Pressure Calculator
Calculate pressure, force or area, with conversion between pascals, bar, psi and atmospheres.
About
Pressure Calculator
Pressure is P = F ÷ A: force divided by the area it is spread over. Choose which quantity to solve for above and the calculator rearranges the equation and converts between pascals, kilopascals, bar, psi and atmospheres.
Why area matters as much as force
The same force produces wildly different pressures depending on how much surface carries it. This is the whole point of the equation, and it explains a great deal of everyday experience.
A 70 kg person exerts 686.5 N regardless of their footwear. Standing in flat shoes with 300 cm² of total contact, the pressure on the floor is 686.5 / 0.03 = 22,882 Pa. Standing on a single stiletto heel with 1 cm² of contact, the same person puts 686.5 / 0.0001 = 6,864,655 Pa through the floor, about 6.86 megapascals. That is roughly 300 times the pressure, from an identical weight, and it is why heels dent soft flooring that shoes do not.
The principle runs both ways. Snowshoes and tracked vehicles spread weight over a large area to reduce pressure below what the surface can bear, while a knife, a nail and a drawing pin concentrate a modest force into a tiny area to exceed what the material can resist.
A worked example
Take a force of 1000 N acting over 0.05 m².
- Divide force by area: 1000 / 0.05 = 20,000 Pa
- In kilopascals: 20 kPa
- In bar: 0.2 bar
- In psi: 2.9008 psi
The pascal is a small unit
One pascal is one newton over one square metre, which is tiny. A sheet of paper resting on a table exerts a few pascals. This is why practical work rarely uses pascals directly and reaches for kilopascals, bar or psi instead.
| Unit | In pascals | Where you meet it |
|---|---|---|
| pascal (Pa) | 1 | the SI unit |
| kilopascal (kPa) | 1000 | weather, tyre pressures in metric countries |
| bar | 100,000 | industry, diving, close to atmospheric |
| psi | 6894.76 | tyres and plumbing in the US and UK |
| atmosphere (atm) | 101,325 | chemistry, defined as sea level pressure |
Bar was chosen deliberately to sit close to atmospheric pressure without being defined by it, which makes it convenient for gauges. One bar is 0.9869 atmospheres.
Gauge pressure against absolute pressure
Most gauges read zero in open air, which means they are measuring the difference from atmospheric rather than the true total. That is gauge pressure. Absolute pressure adds the atmosphere back on.
A tyre inflated to 32 psi on the gauge is at 32 + 14.7 = 46.7 psi absolute. The distinction matters in any calculation involving gas laws, where absolute pressure is required, and it is a routine source of error. Units are sometimes marked psig and psia to keep them apart.
Pressure in a fluid
Below the surface of a liquid, pressure rises with depth according to P = ρgh, where ρ is density. It depends only on depth, not on the shape or width of the container, which is why a tall thin tube of water pushes as hard at its base as a wide tank of the same depth.
Water has a density near 1000 kg/m³, so every metre of depth adds 1000 × 9.80665 = 9807 Pa, close to 0.1 bar. A diver at 10 m is under roughly one extra atmosphere, which is where the rule that pressure doubles at 10 m comes from once the air above is counted.
How much force the atmosphere applies
Atmospheric pressure at sea level is 101,325 Pa, which means every square metre of surface carries 101,325 N, about 10.3 tonnes-force. You do not feel it because the pressure inside your body matches it.
The consequences appear whenever that balance is broken. A vacuum chamber has to resist the full atmospheric load pushing inward, a suction cup holds because the air outside pushes harder than the trapped air inside, and a drinking straw works because reducing the pressure in your mouth lets the atmosphere push the liquid up.
Where it gets used
Ground bearing. Foundations spread a building's weight until the pressure falls below what the soil can carry, which is why soft ground needs wider footings.
Hydraulics. A small force on a small piston creates a pressure that acts on a large piston to produce a large force. The pressure is shared; the forces are not.
Medicine. Blood pressure is quoted in millimetres of mercury, a pressure expressed as the height of a fluid column, which is the same P = ρgh relationship in reverse.
Weather. Barometric pressure drives wind, and a fall of a few hectopascals is enough to signal an approaching storm.
Hydraulics: multiplying force with pressure
Pressure applied to a confined fluid is transmitted undiminished throughout it, which is Pascal's principle. That gives a way of turning a small force into a large one.
Push on a small piston of 2 cm² with 100 N and the pressure is 100 / 0.0002 = 500,000 Pa. That pressure acts on every surface in the system, so a larger piston of 200 cm² feels 500,000 × 0.02 = 10,000 N. A hundredfold increase in area gives a hundredfold increase in force.
Nothing is created. The large piston moves a hundredth as far, so the work done is the same on both sides, which is the same bargain a lever offers. Car jacks, brakes and excavator arms all run on it.
Tyre pressure and contact area
A tyre supports a vehicle through the air inside it, and the contact patch adjusts until the pressure balances. Rearranging gives area = force divided by pressure.
A 1500 kg car has a weight of 14,710 N, or 3677 N per wheel. At a tyre pressure of 2.2 bar, which is 220,000 Pa, each contact patch is 3677 / 220,000 = 0.0167 m², about 167 cm². That is roughly the size of a postcard, and every bit of steering, braking and acceleration passes through four of them.
Underinflate the tyre and the patch grows, which increases rolling resistance and heat. Overinflate it and the patch shrinks, which reduces grip. The recommended pressure is the compromise between the two.
Vacuum, and what negative pressure means
Pressure cannot truly be negative, because it comes from molecules striking a surface and there is no such thing as fewer than none. What people call negative pressure is a pressure below atmospheric, and it is negative only on a gauge that reads zero in open air.
A perfect vacuum is 0 Pa absolute, which is −101,325 Pa on a gauge, and that is the limit. This is why a suction pump can lift water no more than about 10.3 metres: at that height the weight of the water column exactly equals what atmospheric pressure can support, and no better pump helps.
Common mistakes
Mixing gauge and absolute. Gas law calculations need absolute pressure. Add atmospheric to a gauge reading first.
Using the wrong area. Only the area actually carrying the force counts, not the total footprint of the object.
Forgetting to convert area units. Square centimetres to square metres is a factor of 10,000, not 100.
Assuming pressure depends on volume. In a liquid it depends on depth alone. A narrow pipe and a wide tank at the same depth exert the same pressure.
Common questions
Frequently asked questions
Pressure equals force divided by area. A force of 1000 N spread over 0.05 square metres gives 20,000 pascals, which is 20 kPa or 2.9 psi.
Pressure depends on contact area. A 70 kg person in flat shoes exerts about 22,900 Pa, but the same person on a 1 cm² heel exerts 6.86 million Pa, roughly 300 times more.
A gauge reads zero in open air, so it shows the difference from atmospheric. Absolute pressure adds atmospheric back on. A tyre at 32 psi gauge is 46.7 psi absolute.
6894.76. One bar is 100,000 pascals and one atmosphere is 101,325 pascals.
It rises by about 9807 pascals per metre, close to 0.1 bar. At 10 m a diver is under roughly one extra atmosphere.
About 101,325 newtons on every square metre, roughly 10.3 tonnes-force. You do not feel it because the pressure inside your body matches it.
No. Pressure in a fluid depends only on depth and density, so a narrow tube and a wide tank of the same depth push equally hard at the base.
Divide by 10,000. Area conversions square the linear factor, so 100 centimetres per metre becomes 10,000 square centimetres per square metre.