Pressure Calculator

About Pressure Calculator

The Pressure Formula

Pressure equals force divided by area: P = F/A. The SI unit is the Pascal (Pa), defined as 1 Newton per square metre. Because 1 Pa is very small, most practical measurements use kPa, bar, or atm.

Solve For	Formula	Example
Pressure	P = F / A	500 N / 0.02 m² = 25,000 Pa (25 kPa)
Force	F = P x A	200,000 Pa x 0.05 m² = 10,000 N
Area	A = F / P	600 N / 150,000 Pa = 0.004 m² (40 cm²)

Worked example: a 70 kg person stands on one foot with a sole area of about 150 cm² (0.015 m²). Force = 70 x 9.81 = 686.7 N. Pressure = 686.7 / 0.015 = 45,780 Pa (about 6.6 psi). On high heels with a heel area of just 1 cm², pressure = 686.7 / 0.0001 = 6,867,000 Pa (about 68.7 bar) - enough to damage wooden floors.

Pressure Unit Conversions

Unit	Symbol	Equivalent in Pa	Common In
Pascal	Pa	1	SI standard, science
Kilopascal	kPa	1,000	Weather, tyre pressure (non-US)
Megapascal	MPa	1,000,000	Material strength, hydraulics
Bar	bar	100,000	Scuba diving, industrial
Atmosphere	atm	101,325	Chemistry, gas laws
Pounds per square inch	psi	6,894.76	US tyre pressure, hydraulics
Millimetres of mercury	mmHg	133.322	Blood pressure, barometers
Torr	torr	133.322	Vacuum systems
Inches of mercury	inHg	3,386.39	US weather, aviation

Quick conversions: 1 atm is roughly 1 bar, 14.7 psi, 760 mmHg, or 101.3 kPa.

Hydrostatic Pressure (P = rho x g x h)

The pressure at a depth h in a fluid of density rho is P = rho x g x h. This gives the gauge pressure (above atmospheric). Absolute pressure is atmospheric pressure plus gauge pressure.

Fluid	Density (kg/m³)	Gauge Pressure at 10 m	Absolute Pressure at 10 m
Fresh water	1,000	98,100 Pa (0.97 atm)	199,425 Pa (1.97 atm)
Seawater	1,025	100,553 Pa (0.99 atm)	201,878 Pa (1.99 atm)
Mercury	13,534	1,327,685 Pa (13.1 atm)	1,429,010 Pa (14.1 atm)
Crude oil	870	85,347 Pa (0.84 atm)	186,672 Pa (1.84 atm)

A useful rule of thumb: in water, pressure increases by about 1 atmosphere for every 10 metres of depth. At 100 m depth, absolute pressure is about 11 atm.

Common Pressures in Context

Scenario	Pressure	Unit
Perfect vacuum	0	Pa
Outer space (low Earth orbit)	~0.0001	Pa
Standard atmospheric pressure	101,325	Pa (1 atm)
Car tyre (recommended)	207 - 241	kPa (30-35 psi)
Bicycle tyre (road)	620 - 830	kPa (90-120 psi)
Normal blood pressure (systolic)	16	kPa (120 mmHg)
Scuba tank (full)	20,000	kPa (200 bar)
Deepest ocean (Mariana Trench, 10,935 m)	~109	MPa (~1,086 atm)
Car engine cylinder (combustion)	~7,000	kPa (~70 bar)
Diamond formation	~5,000	MPa (~50,000 atm)

Gauge Pressure vs Absolute Pressure

Most pressure gauges read zero at atmospheric pressure - this is gauge pressure. Absolute pressure is gauge pressure plus atmospheric pressure. A tyre gauge reading 35 psi means 35 psi above atmospheric pressure, so the absolute pressure inside the tyre is 35 + 14.7 = 49.7 psi. In physics and gas law calculations (like PV = nRT), always use absolute pressure. In everyday settings like tyre inflation or blood pressure, gauge pressure is standard.

Why Area Matters for Pressure

The same force spread over different areas produces vastly different pressures. This principle explains many real-world designs.

Example	Force	Area	Pressure	Design Rationale
Snowshoes	700 N	0.3 m²	2,333 Pa	Large area prevents sinking in snow
Normal shoe	700 N	0.03 m²	23,333 Pa	Moderate pressure for grip
Ice skate blade	700 N	0.001 m²	700,000 Pa	High pressure melts ice for gliding
Knife edge	50 N	0.000001 m²	50,000,000 Pa	Extreme pressure for cutting

How Is the Pascal Defined?

The pascal is the SI derived unit for pressure, defined as one newton per square metre (1 Pa = 1 N/m² = 1 kg/(m·s²)) per the BIPM SI Brochure (9th edition, 2019). It is named after French mathematician Blaise Pascal (1623-1662) whose work on fluid statics led to Pascal's Principle: pressure applied to an enclosed fluid transmits undiminished to every point in the fluid and to the walls of its container.

Because 1 Pa is a very small unit (roughly the pressure a dollar bill exerts flat on a table), practical measurements use kPa, MPa, or bar. The standard atmosphere (atm) was redefined in 1954 as exactly 101,325 Pa by the 10th General Conference on Weights and Measures (CGPM), anchoring conversion factors across all pressure units. The NIST SI Guide lists the conversion as exact to that value.

What Is a Safe Blood Pressure Reading?

The American Heart Association (AHA) 2017 guidelines, still current in 2026, classify blood pressure in five categories based on systolic and diastolic readings in mmHg. A systolic reading of 120 mmHg equals 15.999 kPa - pressure gauges measure in mmHg because Torricelli's 1643 mercury barometer set the historical precedent, and blood pressure cuffs still balance mercury columns in principle.

NHS England uses slightly different thresholds (140/90 for hypertension diagnosis in clinic). The World Heart Federation estimates over 1.28 billion adults aged 30-79 worldwide have hypertension as of the WHO 2023 global report.

How Deep Can Humans Dive Before Pressure Becomes Lethal?

Recreational scuba diving is limited to 40 m (131 ft) per PADI standards, where absolute pressure reaches 5 atm (506,625 Pa). At this depth, nitrogen narcosis risk rises and air consumption is five times surface rate. Technical divers using trimix gas blends routinely reach 100 m, where pressure is 11 atm.

The current open-circuit scuba depth record is 332.35 m, set by Ahmed Gabr in the Red Sea on 18 September 2014, where the absolute pressure was about 34.2 atm (3.47 MPa) - a dive requiring 12 minutes down and 14 hours of decompression. Submersibles routinely descend further: the DSV Limiting Factor (now Bakunawa) reached the Challenger Deep at 10,935 m on 28 April 2019, carrying Victor Vescovo through 109 MPa (1,086 atm) of pressure, enough to compress seawater by about 4.96% of its surface volume.

Free divers face a different limit. The static apnea world record (Budimir Šobat, 24 min 37.36 s, 2021) is set at the surface, but Alexey Molchanov's 2021 constant weight record of 131 m without fins exposed him to 14.1 atm of absolute pressure on his lungs and sinuses. Without pressure equalisation, tissues rupture.

What Is Gauge Pressure vs Absolute Pressure?

Gauge pressure is the pressure above atmospheric (sea-level atmospheric = 101,325 Pa = 14.696 psi). Absolute pressure is the pressure above perfect vacuum. Most consumer gauges (tyre gauges, blood pressure cuffs, bicycle pumps) read zero when exposed to atmosphere - they measure gauge pressure. Engineering and physics calculations almost always require absolute pressure, especially any gas law calculation that involves PV = nRT.

Worked example of the distinction: A tyre reading 35 psi on a standard gauge has absolute pressure of 35 + 14.7 = 49.7 psi (about 342.6 kPa). If the same tyre were taken to the summit of Mount Everest (atmospheric pressure ~33.7 kPa per NOAA standard atmosphere tables), the gauge would read 342.6 - 33.7 = 308.9 kPa (44.8 psi), making the tyre appear over-inflated even though nothing had changed inside.

The suffix "a" (absolute) or "g" (gauge) distinguishes the two in engineering: 100 psia means absolute, 100 psig means gauge. When a claim omits the suffix in everyday life, assume gauge. When it comes from a physics textbook or a gas law equation, assume absolute.

Common Pressure Calculation Mistakes

• Mixing gauge and absolute in gas laws: PV = nRT requires absolute pressure in kelvin temperature units. Plugging in gauge pressure of 0 (atmospheric) would predict zero volume, which is absurd.
• Using density in g/cm³ instead of kg/m³: Hydrostatic pressure P = ρgh needs SI units. Water density is 1,000 kg/m³, not 1 g/cm³, in SI calculations. A factor of 1,000 error cascades.
• Forgetting depth is vertical: Hydrostatic pressure depends on vertical depth h, not on the shape of the container or the diagonal distance along a sloped pipe. Pascal's barrel demonstration showed this in 1646: a tall thin tube full of water could burst a sealed barrel because what mattered was column height, not water volume.
• Confusing force and pressure: A 1,000 N force on a 1 m² plate is 1 kPa (low). The same force concentrated on a 1 mm² nail tip is 1 GPa (enough to dent steel). Pressure scales inversely with area.
• Pounds vs pounds-force: US pressure calculations use pounds-force (lbf), not pound-mass. 14.7 psi means 14.7 lbf/in². Many student errors trace to confusing lbf with lbm.

For gas pressure problems involving temperature and volume, the ideal gas law calculator solves PV = nRT. For the forces that produce pressure, the force calculator applies F = ma. For material density values used in hydrostatic calculations, the density calculator has a reference table of common materials. All calculations run in your browser with no data sent to any server.

Sources

• BIPM - SI Brochure (9th edition)
• NIST - SI Units and Conversion Factors
• American Heart Association - Understanding Blood Pressure Readings
• WHO - Hypertension Fact Sheet
• NOAA - Atmospheric Pressure Reference
• Guinness World Records - Deepest Scuba Dive
• OpenStax College Physics - Variation of Pressure with Depth