What is the pressure formula?

Pressure = Force / Area (P = F/A). Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m². Standard atmospheric pressure at sea level is 101,325 Pa (14.696 PSI). The force must be perpendicular to the area.

How do I convert between pressure units?

1 atm = 101,325 Pa = 14.696 PSI = 1.01325 bar = 760 mmHg = 760 torr ≈ 29.92 inHg. 1 PSI ≈ 6,895 Pa ≈ 6.895 kPa. 1 bar = 100 kPa = 14.5 PSI. Weather often in hPa or millibars (same thing).

What's the difference between gauge and absolute pressure?

Absolute is above perfect vacuum. Gauge is above local atmospheric pressure. A 32 PSI gauge tire is at 46.7 PSI absolute (32 + 14.7 atmospheric). Most tire gauges, blood pressure monitors, and tank gauges read gauge pressure. Engineering and meteorology often use absolute.

How does water pressure change with depth?

P = ρgh adds 9.81 kPa per meter of depth in fresh water (10.05 kPa/m in seawater). At 10 m: ~1 atm of additional pressure. At 100 m: ~10 atm. Mariana Trench at 11,000 m: ~1,100 atm. Why submarines need very strong hulls.

Why do my ears pop in airplanes?

Cabin pressure changes with altitude (cruise altitudes have lower pressure, equivalent to ~8,000 ft). The pressure difference between inner ear and outside causes discomfort. Eustachian tubes equalize pressure (popping). Chewing gum or yawning helps. Painful for people with colds because tubes are blocked.

How much pressure can a human withstand?

External pressure: humans tolerate ~3 atm internally (lungs equalize). Saturation divers work at 30+ atm with proper gas mixes and slow decompression. Sudden exposure to vacuum: lungs explode if held closed, but unprotected exposure for ~15 sec is survivable. Crushing pressure (> 700 atm) limits unprotected diving depth.

What causes low pressure in weather?

Warm air rises, lowering surface pressure. Low pressure brings clouds, precipitation, storms. Hurricanes have extreme low pressure (sub-960 hPa). High pressure brings clear, dry weather. Pressure drops faster than 6 hPa in 3 hours signals severe weather approaching.

How does Pascal's principle work in hydraulics?

Pressure in an enclosed fluid transmits unchanged. Small input piston × small force = same pressure that acts on large output piston × large area = large output force. Trade-off: input must move long distance, output moves shorter distance (conservation of energy). Basis of all hydraulics: brakes, jacks, presses.

Pressure Calculator

Find pressure, force, or area using the relationship Pressure = Force / Area. Results are shown in pascals, PSI, atmospheres, bar, and other common pressure units.

Pressure is force distributed over area: P = F/A. It explains why a sharp knife cuts effectively (small contact area = high pressure for the same force), why snowshoes prevent sinking (large area spreads weight), why submarines must withstand crushing depths (water pressure increases with depth), and why your tires hold up a multi-ton vehicle (high pressure × area = supporting force).

The SI unit is the pascal (Pa), defined as 1 N/m². Pascals are tiny — atmospheric pressure is 101,325 Pa, so kilopascals (kPa), megapascals (MPa), and various non-SI units (PSI, bar, atm, mmHg, inHg) appear in engineering practice. Atmospheric pressure on Earth equals about 10 tonnes per square meter — invisible to us because it presses equally from all directions and we evolved under it.

For fluids at rest, pressure follows hydrostatic law: P = ρgh, where ρ is fluid density, g is gravity, and h is depth. Water gains 1 atm of pressure every ~10 m of depth — divers feel chest tightness even at modest depths because of this. The Mariana Trench at 11,000 m has pressure ~1,100 atm — crushing for unprotected humans, manageable for specially designed deep-sea probes.

Pressure conversions matter daily. Tire gauges typically read PSI in the US, bar/kPa in Europe. Weather reports use millibars (mb) or hectopascals (hPa). Cooking pressure cookers reach ~15 PSI (~200 kPa) above atmospheric. Industrial systems may operate at thousands of PSI or under deep vacuum.

Common applications: tire inflation, hydraulics, plumbing design, vacuum systems, weather, scuba diving, blood pressure, packaging, and any analysis involving fluids or distributed forces.

Inputs

Solve For

Force (N)

Area (m²)

Pressure (Pa)

Results

Pressure

10,000 Pa

Pressure (PSI)

1.45 PSI

Pressure (atm)

0.0987 atm

Pressure Results

Parameter	Value
Pressure (Pa)	10,000 Pa
Pressure (kPa)	10.0000 kPa
Pressure (PSI)	1.4504 PSI
Pressure (atm)	0.098692 atm
Pressure (bar)	0.100000 bar
Pressure (mmHg)	75.0062 mmHg
Force	500 N
Area	0.050000 m²
Area (cm²)	500.00 cm²
Formula	P = F / A

Last updated: May 29, 2026

Formula

**Pressure:** P = F / A Where: - P = pressure (Pa = N/m²) - F = force perpendicular to area (N) - A = area force is applied over (m²) **Rearranged:** - Force: F = P × A - Area: A = F / P **Worked example: woman in stiletto heels** A 60 kg woman, weight 588 N. Stiletto heel contact area ~1 cm² (0.0001 m²). P = 588 / 0.0001 = 5,880,000 Pa = 5.88 MPa = ~853 PSI That's higher pressure than an elephant's foot (~16 PSI)! Stiletto heels damage floors, sink into soft ground, and exceed allowable pressures on many surfaces. **Hydrostatic pressure (fluid at depth):** P = ρ × g × h Where: - ρ = fluid density (1,000 kg/m³ for water) - g = 9.81 m/s² - h = depth (m) Water pressure increases by ~9.81 kPa per meter (~1.42 PSI/m). **Common pressure units:** | Unit | In pascals | |---|---| | 1 Pa | 1 | | 1 hPa | 100 (= 1 millibar) | | 1 kPa | 1,000 | | 1 MPa | 10⁶ | | 1 atm | 101,325 | | 1 bar | 100,000 | | 1 mbar | 100 | | 1 PSI | 6,894.76 | | 1 ksi | 6.895 × 10⁶ | | 1 mmHg (torr) | 133.32 | | 1 inHg | 3,386.39 | | 1 inH₂O | 248.84 | | 1 atm (technical) | 98,066.5 (=1 kgf/cm²) | **Common pressures:** | Where | Pressure | |---|---| | Best lab vacuum | ~10⁻¹⁰ Pa | | Outer space (ISS altitude) | ~10⁻⁵ Pa | | Ultra-high vacuum | 10⁻⁵ Pa | | Mars atmosphere (surface) | ~600 Pa | | Mt. Everest summit | ~33,700 Pa (33%) | | Atmospheric (sea level) | 101,325 Pa | | Tire pressure (typical) | ~220,000 Pa (32 PSI gauge) | | Pressure cooker | ~200,000 Pa above atm | | Espresso machine | ~900,000 Pa (9 bar) | | Hydraulic systems | 1-30 MPa | | Diesel engine cylinder | ~10 MPa peak | | Deepwater oil well | ~50-100 MPa | | Mariana Trench | ~110 MPa | | Diamond anvil cell | ~400 GPa | | Earth core | ~360 GPa | | Neutron star surface | ~10³³ Pa | **Gauge vs absolute pressure:** - **Absolute pressure**: above perfect vacuum. - **Gauge pressure**: above local atmosphere. - **Atmospheric**: ~101.3 kPa absolute, 0 gauge. Most tire and tank gauges read gauge pressure. 32 PSI tire = 46.7 PSI absolute (at sea level). **Force from pressure (hydraulics):** F = P × A A car hydraulic jack: 200 kPa × 0.01 m² (piston) = 2,000 N output. Larger piston multiplies force: F_out / F_in = A_out / A_in A small input force on small piston creates large output force on large piston. Distance trade-off (conservation of energy). **Pascal's principle:** Pressure applied to enclosed fluid transmits unchanged throughout. Basis of all hydraulics: - Car brakes. - Hydraulic jacks. - Hydraulic presses. - Excavator booms. **Bernoulli's equation (flowing fluid):** Pressure + ½ρv² + ρgh = constant along streamline. Faster moving fluid = lower pressure. Explains airplane lift, Venturi flow meters, atomizers. **Worked example: scuba diver** Diver at 30 m depth in seawater (ρ = 1,025 kg/m³). P_hydrostatic = 1025 × 9.81 × 30 = 301,654 Pa ≈ 3 atm Plus atmosphere on top: ~4 atm absolute. Lungs at sea level inflate to 1 atm. At depth, regulator delivers air at 4 atm to balance — that's why divers consume air ~4× faster at 30 m than at surface. **Weather pressure:** | Reading | Weather | |---|---| | > 1,030 hPa (30.42 inHg) | Very high — clear, cold | | 1,013 hPa (29.92 inHg) | Standard | | 1,000 hPa (29.53 inHg) | Average storm | | < 980 hPa (28.94 inHg) | Strong storm | | < 960 hPa (28.35 inHg) | Severe (Cat 3+ hurricane) | | ~870 hPa (25.69 inHg) | Cat 5 hurricane (record lows) | **Altitude effect on pressure:** Pressure roughly halves every 5,500 m of altitude. | Altitude | Pressure | |---|---| | Sea level | 101.3 kPa (100%) | | 1,000 m | 89.9 kPa (89%) | | 2,000 m | 79.5 kPa (78%) | | 3,000 m | 70.1 kPa (69%) | | 5,500 m | 50.5 kPa (50%) | | Everest summit (8,848 m) | 33.7 kPa (33%) | | 11,000 m (cruise altitude) | 22.6 kPa (22%) | | 20,000 m | 5.5 kPa (5%) | This is why airliner cabins are pressurized (to ~75 kPa or ~8,000 ft equivalent). **Stress (solid mechanics):** In solids, pressure-like quantities are called stress: - **Normal stress**: σ = F/A (same units as pressure). - **Shear stress**: τ = F_tangential/A. - **Hydrostatic stress**: pressure equivalent in solids. Steel yield strength: ~250 MPa. Concrete compressive: ~30-100 MPa. Diamond: ~9,000 MPa. **Tire pressure recommendations:** Posted on driver's door jamb. Typical cars: 30-35 PSI cold. Bicycles: 40-130 PSI depending on tire type. Trucks: 80-120 PSI for heavy loads. Under-inflation: more rolling resistance, faster wear, blowout risk. Over-inflation: harsh ride, center wear, less grip.

How to use this calculator

Choose what to solve for: pressure, force, or area.
Enter the two known values with consistent SI units.
Calculator returns the unknown.
Force in newtons, area in m², pressure in pascals.
For depth: P = ρgh (water adds ~9.81 kPa per meter depth).
Convert: 1 atm = 101,325 Pa = 14.7 PSI = 1.013 bar.

Worked examples

Stiletto heel vs elephant

**Scenario:** 60 kg woman, ~1 cm² stiletto contact area. Pressure? **Calculation:** F = 588 N, A = 0.0001 m². P = 5.88 MPa ≈ 853 PSI. Compare elephant: 5000 kg, 4 feet × ~400 cm² each ≈ 1600 cm². P = 49,050 / 0.16 = 307 kPa ≈ 44 PSI. **Result:** Stiletto ~19× more pressure per area than elephant! Stilettos damage hardwood, sink in soft ground, and even punch through some materials. Larger contact area (snowshoes, tank tracks) distributes weight.

Diving pressure

**Scenario:** Scuba diver at 30 m depth in seawater. Absolute pressure? **Calculation:** P_hydrostatic = 1025 × 9.81 × 30 = 301,654 Pa ≈ 3 atm. Add surface atmosphere: total ~4 atm absolute. **Result:** Diver experiences 4× sea-level pressure (~407 kPa abs). At this pressure, nitrogen narcosis can begin, and air consumption increases ~4× because gas density is 4× higher. Beyond 60 m: serious decompression concerns; needs gas mixes like trimix.

Hydraulic car jack

**Scenario:** Car jack has input piston 1 cm², output piston 10 cm². Force needed to lift 1,000 kg car? **Calculation:** Car weight: 9,810 N. Output pressure: 9810 / 0.001 = 9.81 MPa. Input force: 9.81 × 10⁶ × 0.0001 = 981 N. **Result:** Only ~100 kg of input force lifts 1,000 kg of car — 10× mechanical advantage from area ratio. Trade-off: input must move 10× the distance of the output. Conservation of energy (work in = work out).

When to use this calculator

**Use pressure calculations for:**

- **Tire inflation**: maintaining correct pressure. - **Plumbing design**: pipe pressure ratings, water hammer. - **Hydraulics**: jacks, brakes, presses, excavators. - **Pneumatics**: compressed air systems. - **Vacuum technology**: pumps, gauges. - **Diving and submarine engineering**: pressure ratings. - **Aviation**: cabin pressurization, atmospheric data. - **Weather forecasting**: barometric pressure analysis. - **Industrial process**: chemical reactors, steam systems. - **Medical**: blood pressure, ventilator settings.

**Pressure measurement techniques:**

- **Bourdon tube**: mechanical gauge (tire gauge, pressure cookers). - **Diaphragm gauge**: electronic sensors. - **Manometer**: U-tube of liquid (lab use). - **Piezoelectric**: dynamic pressure (engines, gunshots). - **MEMS**: smartphone barometers.

**Tire pressure check:**

- Always check cold (not after driving). - Use accurate gauge (cheap ones are ±2-3 PSI off). - Match vehicle placard, not max on tire sidewall. - Check monthly; pressure drops ~1 PSI/month from permeation. - Pressure drops 1 PSI per 10°F temperature drop.

**Pascal's principle in practice:**

Hydraulic systems work because fluid pressure transmits unchanged. Powerful applications: - **Car brakes**: ~100 N pedal force → 1,000+ N brake caliper. - **Hydraulic press**: tens of kN input → MN output. - **Excavator arm**: small piston → huge bucket force.

**Vacuum levels:**

| Range | Pressure | Application | |---|---|---| | Rough vacuum | 100 Pa - 100 kPa | shop vac, vacuum sealing | | Medium vacuum | 0.1 Pa - 100 Pa | mass spectrometry | | High vacuum | 10⁻⁵ Pa - 0.1 Pa | research, fusion | | Ultra-high vacuum | 10⁻⁹ Pa - 10⁻⁵ Pa | surface science | | Extreme high vacuum | < 10⁻⁹ Pa | particle accelerators |

**Common applications:**

- **Blood pressure**: 120/80 mmHg = ~16/11 kPa (systolic/diastolic). - **Brake fluid**: typically 1-10 MPa. - **Pressure cookers**: 100 kPa above atmospheric (sealed). - **Espresso**: 9 bar at puck. - **Fire hydrant**: 100-200 PSI typical. - **Water main**: 30-100 PSI residential. - **Compressed air shop**: 90-150 PSI typical. - **Hydraulic systems**: 1,000-5,000 PSI industrial. - **Diesel injector**: 200-2,500 bar peak.

**Weather and pressure:**

Barometric pressure changes indicate weather: - Rising → improving weather. - Falling → storms approaching. - Rapid drop → severe weather.

Hurricanes have very low central pressures (sub-960 hPa for Cat 3+).

**Pressure vs depth in different fluids:**

| Fluid | Density (kg/m³) | Pressure per m | |---|---|---| | Air (sea level) | 1.225 | 12 Pa | | Helium | 0.179 | 1.7 Pa | | Water (fresh) | 1,000 | 9.81 kPa | | Seawater | 1,025 | 10.05 kPa | | Mercury | 13,546 | 133 kPa | | Crude oil | 800-900 | 7.8-8.8 kPa |

**Software:**

- **Pipe flow simulators**: AFT Fathom, Pipe-Flo. - **HVAC tools**: Trane Trace, Carrier HAP. - **CFD**: ANSYS Fluent, OpenFOAM for complex flows. - **Weather services**: NWS, ECMWF for atmospheric models.

**Pitfalls:**

- **Confusing gauge and absolute**: tire 32 PSI gauge = 46.7 PSI absolute. - **Mixing units**: PSI vs kPa vs bar vs atm — easy to factor-of-10 error. - **Forgetting altitude**: pressure varies with location. - **Treating pressure as vector**: it's a scalar (acts equally in all directions in fluids). - **Ignoring temperature dependence**: tire pressure drops ~1 PSI per 10°F. - **Stress vs pressure terminology in solids**: stress includes shear; pressure is normal only. - **Using formula F=PA without checking perpendicularity**: F should be perpendicular component.

Common mistakes to avoid

Confusing gauge pressure with absolute pressure.
Mixing units (PSI vs kPa vs bar vs atm).
Forgetting that pressure in fluids increases with depth.
Treating pressure as a vector (it's scalar).
Using non-perpendicular force in F/A formula.
Ignoring temperature effects on gas pressure.
Using atmospheric pressure as zero without specifying.
Forgetting that pressure acts equally in all directions (hydrostatics).

Frequently Asked Questions

Sources & further reading

SponsoredShop Top Deals on AmazonSupport CalcMountain — browse top-rated products at no extra cost to you.