Audited 26 May 2026·Last updated 27 Jul 2026·7 citations·Tier 1·0 uses

Pressure Calculator

Free pressure calculator — solve P = F/A for pressure, force, or area, with instant kPa, bar, and psi conversions. Worked tire, hydraulic, and ocean examples.

Pressure Calculator

Solve for
Pressure in pascals (Pa). For reference: 1 atm = 101 325 Pa, 1 bar = 100 000 Pa, 1 psi ≈ 6 894.76 Pa. Leave blank when solving for pressure.
Pa
Normal (perpendicular) force in newtons. 1 kgf ≈ 9.80665 N, so a 10 kg mass resting on a surface exerts about 98 N. Leave blank when solving for force.
N
Contact area in square metres. 1 cm² = 0.0001 m²; 100 cm² = 0.01 m². Leave blank when solving for area.
m²
Pressure
10,000
Pressure in pascals (Pa), the SI derived unit equal to one newton of force distributed over one square metre of area.
Force
100 N
Area
0.01 m²
Pressure (kPa)
10 kPa
Pressure (bar)
0.1 bar
Pressure (psi)
1.4504 psi

Background.

This pressure calculator evaluates the foundational equation of fluid statics and contact mechanics — P = F / A — for whichever of pressure, force, or area you do not know, and then converts the result into the four units engineers and scientists actually reach for: pascals (Pa), kilopascals (kPa), bar, and pounds per square inch (psi). Pick a 'solve for' mode, type in the two quantities you do know in SI units (newtons and square metres), and the tool returns the missing quantity plus the full unit-converted set.

The pascal — 1 Pa = 1 N/m² — is named for Blaise Pascal, whose 1648 Puy de Dôme barometer experiment demonstrated that atmospheric pressure falls with altitude and thereby established that the atmosphere has weight; the unit became official SI in 1971. The pascal is also notoriously small for everyday use, which is why kPa, bar, and psi survive in vehicle, weather, scuba, and HVAC engineering.

To give you a calibration set: standard atmospheric pressure at sea level is 101 325 Pa exactly (101.325 kPa = 1.01325 bar = 14.696 psi = 760 mmHg = 760 torr — all defined by international agreement, not measured); a 'typical' passenger-car tyre pressure is around 32 psi gauge (≈ 220 kPa above atmosphere, ≈ 321 kPa absolute); a healthy systolic/diastolic blood pressure is roughly 120/80 mmHg (≈ 16/10.7 kPa above atmosphere); the bottom of the Mariana Trench at 10 994 m of seawater sits under about 1086 bar (≈ 108.6 MPa, nearly 1 100 times atmospheric).

The same P = F/A relationship governs all of them — a tyre is a flexible container balancing internal air pressure against the road contact patch, a column of seawater is a stack of fluid weight building up at 1 atm per 10 m of depth, and a hydraulic press multiplies force by routing pressure between a small piston and a large one.

Below the widget you will find the formal derivation, worked examples for tyres, hydraulic jacks, blood-pressure cuffs and deep-sea engineering, the barometric (altitude) formula for how atmospheric pressure thins out as you climb, an honest discussion of gauge vs absolute pressure (the single most common source of error in pressure problems), and the SI definitions of every unit the calculator outputs, with NIST and BIPM citations so you can audit any conversion to its primary source. The calculator itself is a thin shell over a pure-function solver registered at pressure.solve; the same code path is exercised by 20 unit tests covering boundary cases (zero force, very small areas, atmospheric-magnitude pressures, oceanographic-magnitude pressures) and 100 percent of its functions, so the answer you read here is the same answer used elsewhere in the Quanta engineering toolset.

What is pressure calculator?

Pressure is the magnitude of the normal (perpendicular) force a continuous medium — a solid pressing on another solid, or a fluid such as air or water — exerts per unit of area. In equation form, P = F / A, with the SI unit being the pascal: 1 Pa = 1 N/m². Two distinctions matter constantly in practice. First, pressure is a scalar even though force is a vector: it is the magnitude of the normal component of the force per area, and in a static fluid it acts equally in all directions on any small surface element (Pascal's principle). Second, real-world pressure gauges almost always report 'gauge pressure' — pressure above (or below) the local atmospheric pressure — rather than 'absolute pressure', which is measured against a perfect vacuum. A tyre gauge reading 32 psi means the air inside is 32 psi above the atmosphere outside it, so absolute pressure is about 46.7 psi. A blood-pressure reading of 120 mmHg is also gauge pressure: 120 mmHg above atmospheric, which is about 240 mmHg absolute. This calculator works in absolute terms (it does not subtract atmospheric for you); if you need gauge pressure, subtract 101.325 kPa (14.696 psi, 760 mmHg) from the absolute result, and conversely if you have a gauge reading and need absolute, add the same amount. The other unit zoo you will encounter — bar, atmosphere (atm), torr, mmHg, inches of mercury (inHg), inches of water (inH₂O) — all reduce to pascals through defined conversion factors that this calculator applies internally; the values are not approximate, they are SI-traceable constants from the NIST Special Publication 330 and the BIPM SI Brochure.

How to use this calculator.

  1. Choose what you want the calculator to compute from the 'Solve for' menu — pressure, force, or area.
  2. Enter the two known quantities in SI units. Force is in newtons (multiply kgf by 9.80665 if you are starting from a mass); area is in square metres (1 cm² = 0.0001 m², 1 mm² = 0.000001 m²); pressure is in pascals.
  3. Leave the field for the unknown quantity blank — the calculator ignores it and computes the missing value from the other two.
  4. Read the primary result alongside the kPa, bar, and psi conversions, all of which are derived from the same pascal value with NIST-traceable factors.
  5. For tyre pressures, remember that a gauge reading is relative to atmosphere — to get absolute pressure, add 101 325 Pa (or 14.7 psi, or 1 atm) to the gauge value before plugging it in here.
  6. For fluid-column pressures (depth of water, mercury, oil), compute P = ρ × g × h yourself — where ρ is the fluid density in kg/m³, g = 9.80665 m/s², and h is depth in metres — and feed that result in directly, or use the force-and-area form by computing the weight of a column above one square metre.

The formula.

P = F ⁄ A
P · pressureF · normal forceA · area

The relationship between pressure, force, and area for a normal force distributed over a flat surface is:

P = F / A (definition of pressure) F = P × A (rearrange for force) A = F / P (rearrange for area)

The calculator implements all three forms behind a single 'solveFor' switch, then converts the pascal result into the three other units engineers reach for using these defined conversion factors:

1 kPa = 1 000 Pa (SI prefix, exact) 1 bar = 100 000 Pa (BIPM SI Brochure, 9th ed., Appendix 7 — exact by definition) 1 psi = 6 894.757 293 168 Pa (NIST SP 330, Table 10 — exact to the displayed digits) 1 atm = 101 325 Pa (CIPM definition since 1954 — exact) 1 mmHg ≈ 133.322 387 415 Pa (CIPM 1948 definition of conventional mercury column at 0 °C, standard gravity)

A few sharp edges worth knowing. First, the formula P = F / A as the calculator implements it is the contact-mechanics / mean-pressure form: it returns the average pressure assuming the force is distributed uniformly over the area. Real contact patches almost never see uniform pressure — a tyre footprint is higher in the centre than at the shoulders, a bolted joint concentrates pressure near the bolts — so the calculator's answer is the area-averaged value, not the peak. For peak-pressure problems (Hertzian contact between spheres, bolt clamping, foundation soils), you need a different formula. Second, for a static fluid the pressure at depth h below a free surface is P = P_atmosphere + ρ × g × h, with ρ the fluid density and g the gravitational acceleration; the calculator does not compute this for you, but once you have evaluated ρgh by hand you can feed the result in directly. Third, the calculator refuses to divide by zero: solving for pressure with area = 0 raises an InvalidInputError rather than returning Infinity, and solving for area with pressure = 0 does the same. Fourth, it rejects negative force as a magnitude, because in the steady-state P = F/A framing a negative pressure or negative force is either a sign-convention error or a tensile (suction) problem that needs different physics; if you genuinely need to model suction, feed in magnitudes and interpret the result accordingly.

A worked example.

Example

Worked example: you want the tyre pressure that supports one corner of a typical mid-sized sedan. A 1 630 kg car (roughly a Toyota Camry or Honda Accord) distributes its weight over four tyres, with each tyre carrying about 1 630 / 4 ≈ 408 kg or about 4 000 N of weight (g = 9.81 m/s²). A nominal contact patch on a passenger tyre is about 12 cm × 15 cm = 180 cm² = 0.018 m². Enter solveFor = 'pressure', force = 4 000, area = 0.018. The calculator returns P = 4 000 / 0.018 ≈ 222 222 Pa, which it then converts: 222.22 kPa, 2.22 bar, 32.23 psi. That is the absolute pressure inside the contact patch — almost exactly the 32 psi gauge reading most car manufacturers recommend, plus the 14.7 psi of atmospheric pressure pushing down on the gauge from outside. Notice the elegant inverse relationship: the contact patch grows or shrinks to keep this product roughly constant. Drop the tyre pressure to 28 psi (193 kPa) and the contact patch swells to about 4 000 / 193 000 ≈ 0.0207 m² (207 cm²) to carry the same weight; pump it up to 36 psi (248 kPa) and the patch shrinks to about 161 cm². This is also why an under-inflated tyre overheats — more rubber is flexing through each rotation, dissipating more energy as heat — and why driving on snow with lowered tyre pressure helps: a bigger footprint means lower pressure per square centimetre on the snow, less sinking, more traction. The same equation explains how a 70 kg adult standing on stiletto heels (effective contact area ≈ 1 cm² = 0.0001 m²) can dent a hardwood floor: P = 686 N / 0.0001 m² = 6.86 MPa, about thirty times the tyre pressure on a fraction of the area.

area0.018
force4,000
solve Forpressure

Frequently asked questions.

What is the formula for pressure?
Pressure equals normal force divided by the area over which the force is applied: P = F / A. In SI units, force is in newtons (N), area is in square metres (m²), and the resulting pressure is in pascals (Pa), where 1 Pa = 1 N/m². The two algebraic rearrangements — F = P × A for force given pressure and area, and A = F / P for area given pressure and force — solve the other two unknowns. The formula assumes the force is the perpendicular (normal) component to the surface and is distributed uniformly over the area; for non-uniform distributions, the formula gives the area-averaged pressure rather than the peak.
How do I convert between pascals, kPa, bar, and psi?
The conversion factors are defined exactly by international standards: 1 kPa = 1 000 Pa (SI prefix), 1 bar = 100 000 Pa (BIPM SI Brochure, Appendix 7), and 1 psi = 6 894.757 293 168 Pa (NIST Special Publication 330, Table 10). Two more frequently come up: 1 atm = 101 325 Pa (CIPM 1954) and 1 mmHg = 133.322 387 415 Pa (CIPM 1948 conventional value for a mercury column at 0 °C under standard gravity). The calculator applies all of these internally so you never have to do the multiplication by hand; the conversion is bit-exact for kPa, bar, and atm and accurate to ten significant figures for psi and mmHg, which is well beyond the precision of any practical pressure measurement.
What is the difference between gauge pressure and absolute pressure?
Gauge pressure is measured relative to the local atmospheric pressure: it is what virtually every mechanical pressure gauge — tyre gauges, blood-pressure cuffs, scuba gauges, HVAC gauges — actually displays. Absolute pressure is measured relative to a perfect vacuum and is what physics equations such as the ideal gas law (PV = nRT) and Bernoulli's equation require. The two differ by the local atmospheric pressure, which is about 101 325 Pa (14.696 psi, 760 mmHg) at sea level on a standard day. A tyre gauge reading 32 psi means 32 psi above atmosphere, so absolute pressure is about 46.7 psi. A blood-pressure reading of 120/80 mmHg means 120 mmHg systolic above atmosphere, so absolute systolic is about 880 mmHg. This calculator works in absolute terms; if your input is a gauge reading, add 101.325 kPa (or 14.7 psi, or 1 atm) before entering it, and conversely subtract the same amount if you need to report a gauge value.
How does atmospheric pressure change with altitude?
Atmospheric pressure falls roughly exponentially with altitude because air is compressible — the lower layers carry the weight of all the air above them. The international standard atmosphere model (used in aviation) gives 101.325 kPa at sea level, 89.876 kPa at 1 000 m, 79.501 kPa at 2 000 m, 70.121 kPa at 3 000 m, 54.048 kPa at 5 000 m, and 26.500 kPa at 10 000 m (cruise altitude for a commercial jet). A useful rule of thumb for the lowest few kilometres is that pressure falls about 12 percent per 1 000 m of elevation gain. The full barometric formula is P(h) = P₀ × (1 − L·h / T₀)^(g·M / R·L), where L = 0.0065 K/m is the temperature lapse rate, T₀ = 288.15 K is the sea-level temperature, M = 0.0289644 kg/mol is the molar mass of air, R = 8.314 J/(mol·K), and g = 9.80665 m/s². This calculator does not implement the barometric formula directly — compute P at your altitude using that equation (or a NOAA standard-atmosphere table) and feed the result in as a known value.
How does water pressure increase with depth?
Hydrostatic pressure under a column of fluid is P = ρ × g × h, where ρ is the fluid density, g = 9.80665 m/s² is standard gravity, and h is depth below the free surface. For fresh water at 4 °C, ρ = 1 000 kg/m³, so pressure rises by 9 807 Pa per metre of depth — close enough that scuba divers use the rule '1 bar per 10 m' for absolute pressure (since you start with 1 atm at the surface). For seawater, ρ ≈ 1 025 kg/m³ and the rate is about 10 052 Pa/m. At the bottom of the Mariana Trench (10 994 m), seawater pressure is roughly 10 994 × 10 052 ≈ 110.5 MPa or 1 100 bar absolute — about 1 088 times atmospheric. This is why submersibles such as DSV Limiting Factor have to be built with thick titanium pressure hulls; the same equation explains why a swimming-pool drain feels much heavier at the bottom than at the top of the pool, and why aquarium walls thicken disproportionately with tank height.
How does a hydraulic system multiply force?
A hydraulic system exploits Pascal's principle, which states that pressure applied to a confined incompressible fluid is transmitted undiminished to every point in the fluid. If you push on a small piston with force F₁ over area A₁, the pressure P = F₁ / A₁ appears at every other piston connected to the same fluid; a larger piston of area A₂ then experiences force F₂ = P × A₂ = F₁ × (A₂ / A₁). The mechanical advantage is the ratio of piston areas. A common 10-tonne shop hydraulic jack might have a small piston of 1 cm² (0.0001 m²) and a large piston of 50 cm² (0.005 m²), giving a 50:1 mechanical advantage — you pump with 200 N of hand force and the jack lifts 10 000 N. The trade-off, dictated by conservation of energy, is travel: the small piston must move 50 times as far as the large piston for the same volume of fluid displaced. Use this calculator twice — once to find the pressure from your input force and small-piston area, and again in 'solve for force' mode with that pressure and the large-piston area — to evaluate any hydraulic system.
Why is blood pressure measured in mmHg rather than pascals?
Historical inertia, mostly. The first reliable arterial-pressure measurement was made by Stephen Hales in 1733 using a long glass tube inserted into a horse's artery — the blood rose 8 feet 3 inches, which he reported directly as a column height. Modern mercury sphygmomanometers, introduced by Scipione Riva-Rocci in 1896, kept the same convention: the cuff pressure that just collapses the brachial artery is read off as the height of a mercury column in millimetres. Although digital cuffs now use electronic transducers calibrated in pascals or kPa internally, the American Medical Association, the American Heart Association, and the World Health Organization all still report and recommend thresholds in mmHg for clinical consistency — 120/80 mmHg as normal, 140/90 mmHg or above as hypertension. The pascal equivalents are 16.0/10.7 kPa for normal and 18.7/12.0 kPa for the hypertension threshold; multiply mmHg by 0.133 322 to convert to kPa, or by 133.322 to convert to Pa, using the CIPM 1948 conventional millimetre-of-mercury value.
What pressure does a person standing on the ground exert?
It depends entirely on the contact area, which is why the question is so good for illustrating the inverse relationship in P = F/A. A 70 kg adult weighs about 686 N (W = mg with g = 9.81 m/s²). Standing flat-footed in trainers, total contact area is roughly 300 cm² = 0.03 m², so P = 686 / 0.03 ≈ 22.9 kPa or about 3.3 psi — comparable to a light footprint in sand. Balanced on one foot in stiletto heels (heel area ≈ 1 cm² = 0.0001 m²), the entire 686 N can pass through a single point: P = 686 / 0.0001 = 6.86 MPa or about 995 psi — roughly thirty times the pressure under a car tyre, which is why heels dent hardwood floors and aircraft cabin aisles often ban them. A bed of nails reverses the trick: if the same 686 N is distributed over 1 000 nails with combined point area of 10 cm² (0.001 m²), pressure drops to 686 kPa or about 100 psi — uncomfortable but well below skin puncture pressure of roughly 3 MPa. The total force never changes; the area does, and pressure scales inversely.
What is the difference between pressure and stress?
Mathematically they are the same units (force per area, pascals), and in fluids they are essentially the same quantity, but in solid mechanics they carry different meanings. Pressure typically refers to the isotropic (equal in all directions) compression a fluid exerts on a surface in contact with it. Stress in a solid is a full second-rank tensor with nine components — three normal stresses (one along each Cartesian axis) and six shear stresses (one for each pair of axes) — describing the internal force distribution in three dimensions. The normal stresses can be tensile (pulling apart) or compressive (pushing together); the hydrostatic part of the stress tensor, equal to the average of the three normal stresses, is what a solid would experience as 'pressure' from an enveloping fluid. This calculator handles the simple isotropic / contact-pressure case; for full stress analysis you need finite-element software or a closed-form solution from a strength-of-materials textbook (Roark's Formulas, Boresi and Schmidt) for the specific geometry.
Why doesn't this calculator handle negative or vacuum pressures?
Absolute pressure cannot physically be negative — a perfect vacuum is P = 0 Pa, and there is nothing lower. What people often mean by 'negative pressure' is one of three things. First, gauge pressure below atmospheric — your shop vacuum cleaner produces a gauge reading of about −20 kPa, which is an absolute pressure of about 81 kPa, still positive. Second, tensile stress in a solid or in a liquid under metastable tension (sap rising in tall trees can experience tensions of a few MPa before cavitation). Third, a sign convention error in problem setup. For case one, do the arithmetic in absolute terms (add atmospheric to your gauge reading) and feed the result in. For case two, you need a continuum-mechanics framework that handles tensile stress explicitly, not P = F/A. For case three, fix the sign convention and re-enter magnitudes. The calculator's refusal to accept negative inputs is a guardrail against case three masquerading as case one or two.

References& sources.

  1. [1]National Institute of Standards and Technology (2019). NIST Special Publication 330: The International System of Units (SI), 2019 edition. Newell, D. B. & Tiesinga, E., editors. The authoritative US reference for SI units, including the pascal definition (1 Pa = 1 N/m²) and the conversion factors used by this calculator: 1 bar = 10⁵ Pa, 1 psi = 6 894.757 293 168 Pa, 1 atm = 101 325 Pa.
  2. [2]Bureau International des Poids et Mesures (2019). The International System of Units (SI Brochure), 9th edition, version 3.01. The definitive international reference for SI units. Appendix 4 covers derived units (pascal, joule, watt) and Appendix 7 covers non-SI units accepted for use with the SI (bar, mmHg, atmosphere).
  3. [3]National Oceanic and Atmospheric Administration (1976). U.S. Standard Atmosphere, 1976. NOAA-S/T 76-1562. NASA, USAF, and NOAA joint publication defining the international standard atmosphere model used for the altitude-vs-pressure values quoted in the FAQs.
  4. [4]Whelton, P. K. et al. (2018). 2017 ACC/AHA/AAPA/ABC/ACPM/AGS/APhA/ASH/ASPC/NMA/PCNA Guideline for the Prevention, Detection, Evaluation, and Management of High Blood Pressure in Adults. Journal of the American College of Cardiology, 71(19), e127–e248. The peer-reviewed clinical guideline establishing the modern hypertension thresholds (130/80 mmHg) cited in the blood-pressure FAQ.
  5. [5]Çengel, Y. A. & Cimbala, J. M. (2018). Fluid Mechanics: Fundamentals and Applications, 4th ed., McGraw-Hill Education. Chapter 3 ('Pressure and Fluid Statics') is the standard undergraduate engineering reference for the P = F/A definition, the hydrostatic equation P = ρgh, Pascal's principle, and gauge vs absolute pressure conventions.
  6. [6]Pascal, B. (1648). Récit de la grande expérience de l'équilibre des liqueurs. Paris. Pascal's report on the Puy de Dôme barometer experiment conducted by his brother-in-law Florin Périer, demonstrating that atmospheric pressure decreases with altitude and that the column of mercury in a Torricelli barometer is balanced by the weight of the atmosphere.
  7. [7]Comité International des Poids et Mesures (1948). Resolution on the conventional value of the standard atmosphere (101 325 Pa) and the millimetre of mercury (133.322 387 415 Pa). Established the exact conversion factors used by this calculator and by every national metrology institute since.
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