Need to figure out how many psi is in a bar? Calculate the pressure at the bottom of a swimming pool? Or convert your tire's specification from kPa to psi? This free pressure calculator does all three: classic P = F/A from force and area, hydrostatic pressure (ρgh) at any depth in any fluid, and instant conversion between 15 pressure units — Pa, kPa, MPa, bar, mbar, atm, psi, ksi, torr, mmHg, inHg, cmH2O, inH2O, kgf/cm², and more. Exact conversion factors from NIST and BIPM.
Pressure is force spread over an area — the same total push concentrated into a small contact patch creates much higher pressure than the same push spread wide. The formal definition is P = F / A, with force in newtons and area in square meters giving pressure in pascals (Pa). The pascal honors Blaise Pascal, who in the 1640s showed experimentally that fluid pressure transmits equally in every direction and depends only on depth, not on the shape of the container — Pascal's principle. Today, pressure is everywhere in physics, engineering, meteorology, and medicine: tire psi, blood pressure mmHg, atmospheric hPa on the weather report, MPa in concrete strength specs, GPa in materials science. This calculator handles all three of the questions you'll actually ask: pressure from force and area, fluid pressure at depth, and conversion between 15 units.
Pressure feels intuitive — push harder, get more pressure — but the formal definition has a couple of subtleties worth knowing before plugging numbers into formulas.
Pressure is force divided by area. Double the force, double the pressure. Halve the area, double the pressure. This is why a sharp knife cuts and a blunt one doesn't, even with the same hand force — the sharp edge has tiny contact area, so local pressure is enormous.
Unlike force, pressure has no direction — it's a scalar. At any point in a fluid at rest, the pressure pushes equally on a surface no matter how you orient it. This is Pascal's principle, and it's why hydraulic brakes work: pressure applied at the pedal transmits in every direction inside the brake line.
In a liquid, the deeper you go the more weight of fluid sits above you. Hydrostatic pressure: P = ρgh. At 10 m fresh-water depth, that's about 1 extra atmosphere (≈101 kPa). At the Mariana Trench's 11 km, it's about 1100 atm. The container's shape doesn't matter — only the vertical depth.
Absolute pressure is measured from a perfect vacuum (zero). Gauge pressure is measured from current atmospheric pressure (so the 'zero' shifts with the weather). Tire gauges, blood-pressure cuffs, and pressure cookers report gauge. Vacuum systems, weather forecasts, and physics problems usually use absolute. Mixing them up is the #1 cause of pressure-related errors.
A magnitude map for pressures you actually meet — from the soft press of a finger to crushing depths and atomic stresses. Use it to sanity-check whatever number the calculator gives you.
| Source / situation | Pascals (Pa) | psi | bar / atm | mmHg |
|---|---|---|---|---|
| Hearing threshold (silence) | 2×10⁻⁵ Pa | 3×10⁻⁹ psi | 2×10⁻¹⁰ bar | 1.5×10⁻⁷ mmHg |
| Normal speech at 1 m | 0.02 Pa | 3×10⁻⁶ psi | 2×10⁻⁷ bar | 1.5×10⁻⁴ mmHg |
| Pain threshold (sound) | 20 Pa | 0.003 psi | 0.0002 bar | 0.15 mmHg |
| Standing on one foot (60 kg) | ~30 kPa | ~4.5 psi | 0.3 bar | ~225 mmHg |
| Atmospheric pressure at sea level | 101,325 Pa | 14.696 psi | 1.01325 bar / 1 atm | 760 mmHg |
| Car tire (typical) | ~220 kPa | 32 psi | 2.2 bar | ~1650 mmHg |
| Bicycle tire (road) | ~830 kPa | 120 psi | 8.3 bar | ~6230 mmHg |
| Espresso machine extraction | ~900 kPa | 130 psi | 9 bar | ~6750 mmHg |
| Mariana Trench (~11 km deep) | ~110 MPa | 16,000 psi | ~1100 bar | ~825,000 mmHg |
| Earth's core (~6000 km deep) | ~360 GPa | 52 million psi | 3.6 million bar | — |
| Diamond synthesis (HPHT) | ~5 GPa | 725,000 psi | 50,000 bar | — |
Pressure problems boil down to a small set of formulas. Here are the four that cover ~95% of everyday physics and engineering questions, exactly as they're written in textbooks.
The fundamental definition. F in newtons, A in m² → P in pascals. The whole reason pascal is a derived SI unit: 1 Pa = 1 N/m². Engineers also see this written as σ (stress) when describing internal forces in solids — same units, same idea, different naming convention.
A 200 N force on a piston with area 0.02 m²: P = 200 / 0.02 = 10,000 Pa = 10 kPa = 1.45 psi.
Pressure at depth h in a fluid of density ρ, under gravity g. Result is gauge pressure (above the surface). On Earth, g = 9.80665 m/s². Water density at room temperature ≈ 1000 kg/m³; mercury ≈ 13,534 kg/m³ at 20°C. The container shape doesn't matter, only the vertical depth — that's Pascal's hydrostatic paradox.
10 m deep in fresh water: P = 1000 × 9.80665 × 10 = 98,067 Pa ≈ 98 kPa ≈ 14.2 psi. Add atmospheric (101,325 Pa) for absolute pressure: about 2 atm total.
Always check what reference frame a pressure value is in. A scuba diving computer reads gauge depth pressure; a vacuum chamber reads absolute. Standard atmospheric is 101,325 Pa = 14.696 psi = 1 atm. Modern barometric pressure varies by ~3% around sea level depending on weather and ~50% if you climb to 5500 m altitude.
Tire spec 32 psi (gauge) at sea level: P_abs = 32 + 14.7 = 46.7 psia. At Denver (P_atm ≈ 12.2 psi), the same gauge reading is P_abs = 32 + 12.2 = 44.2 psia — the tire is actually 'softer' in absolute terms.
A pressure applied anywhere in a closed incompressible fluid transmits undiminished to every point. This is how hydraulic jacks, brake systems, and excavator arms multiply force: small input piston, big output piston, same pressure throughout. The force multiplication ratio equals the area ratio.
A hydraulic jack with input piston 1 cm² and output piston 100 cm² gives a 100× force multiplier. Push 100 N on the small piston → 10,000 N output. Catch: the small piston must travel 100× the distance of the large one — no free energy.
Most pressure errors don't come from arithmetic — they come from mixing up gauge and absolute pressure. The numbers look the same; only the implicit zero point differs. Here's how to keep them straight.
Measured relative to current atmospheric pressure. A reading of 'zero' means 'same as the air outside.' This is what tire gauges, blood-pressure cuffs, pressure cookers, and most everyday instruments display.
Measured from a perfect vacuum (true zero). Always ≥ 0. The pressure that matters in physics formulas, vacuum systems, and weather reports.
| Reading | Gauge interpretation | Absolute interpretation |
|---|---|---|
| 0 psi | Atmospheric (open to air) | Perfect vacuum |
| 14.7 psi | About 1 atm above atmospheric | Sea-level atmospheric pressure |
| 32 psi | Typical car tire (above atmospheric) | About 2.2 atm absolute |
| −5 psi | 5 psi vacuum below atmospheric | Doesn't exist (would be negative) |
| 29.92 inHg | About 1 atm above atmospheric | Standard sea-level pressure (aviation altimeter zero) |
Memorize the first three rows and you'll handle 90% of real-world pressure conversions to within 1%. Use the full calculator for precise work, but these rules of thumb are great for sanity-checking results.
| From | To | Rule of thumb | Exact factor |
|---|---|---|---|
| bar | psi | Multiply by 14.5 | × 14.5038 |
| psi | kPa | Multiply by 7 (rough), 6.9 (better) | × 6.89476 |
| atm | psi | About 14.7 | × 14.6959 |
| bar | atm | About 0.987 (≈ 1) | × 0.98692 |
| kPa | psi | Divide by 7 (rough) | ÷ 6.89476 |
| mmHg | kPa | Divide by 7.5 (mmHg = ⅛ kPa) | × 0.13332 |
| torr | mmHg | Treat as identical (off by 7 ppm) | × 1.00000003 |
| inHg | hPa | Multiply by 34 (rough), 33.9 (better) | × 33.864 |
| kPa | atm | Divide by 100 (= bar approximation) | ÷ 101.325 |
| 10 m water | atm | About 1 atm per 10 m of water depth | × 0.0968 |
People often confuse pressure with force. A heavier object doesn't necessarily exert more pressure — it depends on its contact area. This is why an elephant doesn't sink into mud as much as a stiletto heel, and why ice skates work the way they do.
How hard something pushes — total push. Scales with mass and gravity. Doesn't care about the shape of contact.
How concentrated the force is — push per unit area. Depends BOTH on force AND on the area it's spread over. What materials actually 'feel' when something presses on them.
| Object | Mass / weight | Contact area | Pressure on the floor |
|---|---|---|---|
| African elephant | 5,000 kg (49 kN) | ~3000 cm² (all 4 feet) | ~163 kPa (≈ 24 psi) |
| Adult on flat shoes | 75 kg (735 N) | ~360 cm² (both soles) | ~20 kPa (≈ 3 psi) |
| Adult on one stiletto heel | 75 kg (735 N) | ~1 cm² (one heel point) | ~7.4 MPa (≈ 1070 psi) |
| Ice skater | 60 kg (588 N) | ~12 cm² (blade contact) | ~490 kPa (≈ 71 psi) |
Both a party balloon and a car tire contain gas at higher pressure than the surrounding atmosphere. The physics is identical (PV = nRT, plus elastic skin tension), but the numbers — and the consequences of failure — are very different.
Latex skin, ~25 cm diameter
Reinforced rubber, ~16 inch wheel
Pressure isn't an abstract physics-class quantity. It's central to several practical fields — and getting it wrong has real costs.
Under-inflated tires roll with more flex, generate heat, wear out faster, and burn 1–3% more fuel. Over-inflated tires give a harsh ride and reduce contact patch (and grip). Most car specs are in psi (US/UK) or kPa/bar (EU). Cold inflation matters — tire pressure rises ~1 psi per 10°F (~12 kPa per 10°C) as the tire warms up.
Reported in mmHg as systolic/diastolic (e.g. 120/80). Normal adult resting blood pressure is gauge pressure relative to atmospheric. Hypertension (>130/80) and hypotension (<90/60) both have specific clinical thresholds. The mmHg unit dates to 19th-century mercury manometers and is universal in medical practice worldwide.
Barometric pressure (typically 950–1050 hPa at sea level) drives weather: low pressure = storms, high pressure = clear. Pressure drops about 12 hPa per 100 m of altitude in the lower atmosphere. This is how aircraft altimeters work — they read absolute pressure and convert to altitude. Pilots set 'QNH' to the local sea-level pressure so altimeters read true height above sea level.
Scuba divers gain about 1 atm of pressure per 10 m of saltwater descent. At 30 m, they're at 4 absolute atmospheres — air is 4× denser, dive time on a tank is ~¼ what it would be at the surface. Hydraulic systems use Pascal's principle to multiply force — excavator arms can output 250+ bar (3,600+ psi) at the actuator from compact pumps.
Write 'psig' or 'psia' (not just 'psi') in any document where the distinction matters. The same 30 psi tire reading is either 30 psig (~44 psia) or 30 psia (~15 psi above true vacuum) — wildly different physical states. Use 'g' or 'a' suffixes on any non-Pa unit.
Even if your final answer needs to be in psi, do the math in pascals: F in N, A in m², ρ in kg/m³, h in m, g in m/s². Convert the final number at the end. Mixing units mid-calculation (e.g. psi with cm²) is where most pressure errors hide.
Tire pressure spec is always 'cold' — measured before driving, before sun heating. Pressure rises ~1 psi per 10°F (≈12 kPa per 10°C) as the tire warms. If you check pressure on a hot tire and add air to reach spec, the tire will be 3–5 psi under-inflated when cold next morning.
Every 10 m of fresh-water depth adds about 1 atmosphere (≈101 kPa, ≈14.7 psi) of gauge pressure. This rule is exact to within 2% for typical conditions. For seawater (1025 kg/m³), use 9.75 m per atm. For mercury, it's just 76 cm per atm — which is why mercury barometers are so much shorter than water ones.
Pascal is the SI base, all formulas reduce cleanly with N/m²/kg, and you avoid the bear-trap of mixed units (mmHg with psi with kPa). Build the answer in Pa, then convert to whatever unit your audience wants. Engineers who internalize this make far fewer pressure errors.
A common slip: 100 N on a 5 cm² piston gives... not 20 N/cm². Convert area to SI first: 5 cm² = 0.0005 m². Then P = 100 / 0.0005 = 200,000 Pa = 200 kPa = 29 psi. Mixing N with cm² gives nonsense numbers off by 10,000×.
Ideal gas law (PV = nRT) requires absolute pressure. Throwing in 32 psi (gauge) instead of 46.7 psia gives temperatures or moles off by ~30%. Always add atmospheric to gauge before plugging into physics formulas.
1 torr is defined as 1/760 of a standard atmosphere = 133.322 368… Pa. 1 mmHg (conventional) = 133.322 387 415 Pa. The difference is about 7 parts per million — completely irrelevant for tire pressure, but in precision vacuum work it matters. Use 'mmHg' for medical and meteorological work; 'torr' for vacuum engineering.
Water density varies from 1000 kg/m³ at 4°C down to 958 kg/m³ at 100°C — about 4% range. Mercury changes ~0.5% over typical lab temperatures. For most engineering work, 1000 kg/m³ for water is fine; for precision lab work, use the actual temperature-corrected density.
1 bar = 100,000 Pa exactly; 1 atm = 101,325 Pa exactly. They differ by ~1.3%. For sloppy weather conversation, the difference doesn't matter; for engineering specs, regulatory documents, or scientific papers, it absolutely does.
The pascal (Pa), equal to 1 newton per square meter (1 N/m²). The pascal is a derived SI unit named after Blaise Pascal, the 17th-century French physicist who demonstrated that fluid pressure transmits equally in all directions. One pascal is a tiny pressure — about what a sheet of paper exerts on the table. Real-world pressures usually use prefixes (kPa, MPa, GPa) or non-SI units like bar, atm, psi, and mmHg.
Air pressure decreases roughly exponentially with altitude. Sea-level standard is 101.325 kPa. At 1500 m it drops to ~85 kPa; at 5500 m (where the air is half as dense) it's ~54 kPa; at the cruising altitude of an airliner (~11 km) it's ~22 kPa. The exact pressure-altitude relation is the 'barometric formula,' derived from hydrostatic equilibrium plus an assumed temperature profile.
Your middle ear is sealed by the eardrum, with pressurized air inside. Climbing reduces outside pressure faster than the Eustachian tube can equalize inside. The eardrum bulges outward until a 'pop' releases pressure through the tube. Same effect in reverse when diving or descending in an aircraft — the outside pressure increases and the eardrum bulges inward.
By exploiting Pascal's principle: pressure applied to a confined fluid transmits undiminished everywhere. With a small-area input piston and a large-area output piston, the SAME pressure produces proportionally MORE force on the larger piston. F_output / F_input = A_output / A_input. A car's hydraulic brake system multiplies pedal force by ~10×; an excavator arm by 50–100×. There's no free energy: the output piston moves a proportionally smaller distance.
Because 1 atm is defined as the average atmospheric pressure at Earth's sea level (101.325 kPa, exact since 1954). At 5500 m altitude, atmospheric pressure is about 0.5 atm. On Mars, the surface atmospheric pressure is about 0.006 atm (~600 Pa). On Venus, it's about 92 atm at the surface. The atmosphere unit is purely terrestrial — it's an Earth-shaped reference value, not a fundamental constant.
Static pressures around 1000 GPa (10 million atm) have been reached in diamond anvil cells, used in materials science to study how matter behaves at planetary-core conditions. Transient (dynamic) pressures from laser-driven shockwaves and nuclear tests reach much higher — around 10,000 GPa (100 million atm). These pressures crush most known materials into states that look nothing like their room-temperature forms — solid hydrogen becomes metallic, for instance.
The fundamental formula is P = F / A — pressure equals force divided by area. With force in newtons (N) and area in square meters (m²), the result is in pascals (Pa). For fluid columns, hydrostatic pressure is P = ρ × g × h, where ρ is the fluid density, g is gravitational acceleration (9.80665 m/s² on Earth), and h is the depth below the surface. Both formulas describe the same physical quantity — force per unit area — and give the same units when computed correctly.
1 bar = 14.5038 psi. The conversion factor 1 bar = 100,000 Pa is exact by definition (ISO 80000-4), and 1 psi = 6,894.757293... Pa is also exact (derived from the international pound at 0.45359237 kg, standard gravity at 9.80665 m/s², and 1 inch² = 6.4516 cm²). So 1 bar / (6,894.757293 Pa/psi) = 14.5038 psi. Engineers often use the round approximation 1 bar ≈ 14.5 psi for quick mental math — accurate to 4 parts in 10,000.
Absolute pressure is measured relative to a perfect vacuum (zero). Gauge pressure is measured relative to the current atmospheric pressure. So P_absolute = P_gauge + P_atmospheric. A tire gauge reading 32 psi means 32 psi ABOVE atmospheric — the absolute pressure inside the tire is about 32 + 14.7 = 46.7 psi. Conversely, a barometer reading 1013 hPa is showing absolute pressure. Engineers use suffixes: 'psig' for gauge, 'psia' for absolute. When a spec just says 'psi,' check whether your application assumes gauge or absolute.
Use P = ρ × g × h. For fresh water: ρ = 1000 kg/m³, g = 9.80665 m/s². So at 10 m depth: P = 1000 × 9.80665 × 10 = 98,067 Pa ≈ 98 kPa ≈ 0.98 bar ≈ 14.2 psi. A useful rule of thumb: every 10 meters of fresh water depth adds approximately 1 atmosphere (about 14.5 psi) of pressure. Seawater is denser (~1025 kg/m³), so the pressure builds slightly faster — about 1 atm per 9.75 m. This is also why scuba divers double their absolute pressure roughly every 10 m of descent.
Almost — but not exactly. 1 atm = 101,325 Pa (exact, defined by the 10th CGPM in 1954). 1 bar = 100,000 Pa (exact, defined by ISO 80000-4). They differ by ~1.3%. The atmosphere is based on average atmospheric pressure at sea level; the bar is a 'nice round number' SI-derived unit. Meteorologists report air pressure in hectopascals (hPa), where 1013.25 hPa = 1 atm. For most engineering work the 1.3% difference is small enough to ignore in early sketches, but you absolutely cannot substitute one for the other in precise specifications.
Because pressure is force divided by AREA, not just force. A 60 kg person's weight (588 N) spread across a flat shoe (~190 cm²) gives ~31 kPa — about 4.5 psi. The same 588 N concentrated on a 1 cm² heel point gives ~5.9 MPa — 850 psi, almost 200 times higher. That's why high heels indent hardwood floors, while a much heavier elephant (with its broad, flat foot) does not. Pressure tells you the local stress on a surface, not the total weight being supported. Snowshoes, tank treads, and surgical-instrument tips all exploit this geometry to either reduce or concentrate pressure on purpose.
Millimeters of mercury (mmHg), worldwide. A normal reading like 120/80 means a systolic pressure of 120 mmHg and diastolic of 80 mmHg — gauge pressure, relative to atmospheric. In SI units, 120 mmHg ≈ 16.0 kPa and 80 mmHg ≈ 10.7 kPa, but no clinician uses kPa for blood pressure in practice. The mmHg unit dates to 19th-century mercury manometers and persists because the entire medical literature, training, and equipment ecosystem standardized on it. Pilots use a similar legacy unit, inHg, for barometric altimeters.
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All conversion factors in this calculator are exact values from international standards bodies. The pascal is defined by the SI: 1 Pa = 1 N/m². Standard atmosphere (101,325 Pa) was fixed by the 10th CGPM in 1954. The bar (100,000 Pa) and the SI prefixes (hPa, kPa, MPa, GPa) are defined in ISO 80000-4. Psi derives from the international pound (0.45359237 kg, exact since 1959) and standard gravity (9.80665 m/s², exact since 1901), giving 1 psi = 6,894.757293 Pa exactly. Conventional mmHg uses ρ = 13,595.1 kg/m³ and g = 9.80665 m/s² (ISO definition); torr is 1/760 atm. We do not modify, average, or approximate the standard factors. Round-trip conversion preserves precision in IEEE 754 doubles.