Pressure units are all multiples of one another
Pressure is force divided by area, and every unit in common use is simply a different choice of which force and which area. The SI unit is the pascal, one newton per square metre, and it is inconveniently tiny — a car tyre sits at around 220,000 Pa. That is why practical work uses multiples: the bar is exactly 100,000 Pa, the kilopascal is 1,000 Pa, and psi is the force of one pound-force spread over one square inch.
Because these are all fixed multiples, converting between them involves no physics at all. You go into pascals and back out again. The only judgement calls are which definition of a unit you mean — there are two atmospheres in circulation and two mercury-column conventions — and whether your number is measured from atmospheric pressure or from vacuum.
The psi factor comes out of the exact definitions rather than a measurement. One pound-force is 4.4482216152605 N (the international avoirdupois pound of 0.45359237 kg times standard gravity of 9.80665 m/s²), and one square inch is 0.00064516 m². Divide and you get 6,894.757293 Pa, which is why every reputable table quotes 1 bar as 14.5037738 psi rather than the rounded 14.5 that appears on workshop charts.
The unit you meet depends almost entirely on where a document was written. European and Asian equipment specifies bar or MPa; American equipment specifies psi; scientific work uses kPa; older Japanese and continental machine plates still carry kgf/cm²; meteorology uses hPa or millibar, which are the same size; vacuum work uses torr and millibar; and North American HVAC still measures duct static in inches of water column.
The multiples are fixed by standard, not by custom. ISO 80000-4 (Quantities and units — Mechanics) defines pressure and its coherent SI unit, and NIST SP 811 publishes the exact conversion factors used here: 1 psi = 6,894.757293168 Pa and 1 bar = 100,000 Pa, both exact rather than measured. That is what makes every figure in the table below an identity, and it is why rounding is the only source of error in a pressure conversion.
Gauge, absolute and the difference that ruins calculations
A tyre gauge reading 32 psi is not telling you that the air inside is at 32 psi. It is telling you the air inside is 32 psi higher than the air outside. Deflate the tyre completely and the gauge reads zero while the tyre still contains air at roughly one atmosphere. That is a gauge reading, written psig or barg.
Absolute pressure counts from a perfect vacuum. Written psia or bara, it is what every gas law, every compressor ratio and every psychrometric chart requires, because those relationships all involve dividing one pressure by another and the division is only meaningful when zero means zero. Absolute is gauge plus the surrounding atmospheric pressure — conventionally one standard atmosphere, 101,325 Pa or 14.6959 psi, though the real local value falls with altitude and moves with weather.
The practical consequences are specific. A compressor delivering 100 psig has a compression ratio of 114.7/14.7 = 7.8, not 100/0. A tyre that reads 32 psi cold in a warm garage and 29 psi at a mountain trailhead has usually lost almost nothing; the gauge is subtracting a smaller atmosphere. Boyle's law applied to gauge pressures gives an answer that is wrong by whatever the atmosphere contributes, which our tire pressure temperature change calculator handles by working the gas law in absolute terms and reporting back in gauge, the same convention this converter follows.
Vacuum adds a third convention. A vacuum gauge reading "25 inHg of vacuum" means 25 inHg below atmosphere, so its absolute pressure is about 29.92 − 25 = 4.92 inHg absolute. Enter that as a negative gauge value here and the calculator reports the corresponding positive absolute figure rather than pretending the pressure is negative.
Worked example: 32 psi of tyre pressure in bar and kPa
A European tyre placard specifies 2.2 bar and your gauge reads in psi. Work the conversion by hand.
- Into pascals. 32 psi × 6,894.757293 Pa/psi = 220,632.23 Pa.
- Out to bar. 220,632.23 ÷ 100,000 = 2.2063 bar. The placard's 2.2 bar is 31.9 psi, so 32 psi is right.
- Out to kPa. 220,632.23 ÷ 1,000 = 220.63 kPa. Some placards give 220 kPa, which is the same specification written a third way.
- Absolute pressure, for a gas-law calculation. 220,632.23 + 101,325 = 321,957.23 Pa, which is 46.696 psia or 3.2196 bara.
- Sanity check. 32 ÷ 14.5037738 = 2.2063 bar, matching step 2. Dividing by 14.5 instead gives 2.2069 — close enough for a tyre, not close enough for a hydraulic test report.
Notice how much the absolute conversion changes things: the gauge number rose by 46% when the atmosphere was added. That is the size of the error you introduce by feeding gauge pressures into a compression-ratio or gas-law calculation.
Exact pressure unit equivalences
| One unit of | Pascals | psi | bar | kPa |
|---|---|---|---|---|
| psi (lbf/in²) | 6,894.757293 | 1 | 0.06894757 | 6.894757 |
| bar | 100,000 (exact) | 14.5037738 | 1 | 100 |
| kilopascal (kPa) | 1,000 (exact) | 0.14503774 | 0.01 | 1 |
| megapascal (MPa) | 1,000,000 (exact) | 145.037738 | 10 | 1,000 |
| standard atmosphere (atm) | 101,325 (exact) | 14.6959488 | 1.01325 | 101.325 |
| kgf/cm² (technical atm) | 98,066.5 (exact) | 14.2233433 | 0.980665 | 98.0665 |
| inch of mercury (0 °C) | 3,386.389 | 0.4911541 | 0.03386389 | 3.386389 |
| mmHg / torr | 133.3223874 | 0.01933678 | 0.001333224 | 0.1333224 |
| pascal (Pa) | 1 | 0.000145038 | 0.00001 | 0.001 |
The bar, kPa, MPa, atm and kgf/cm2 factors are exact by definition. The psi and mercury-column factors are exact in principle but irrational in decimal, so they are shown to nine or ten significant figures.
Why most of the outputs stay gauge even when you meant absolute
The Reading basis selector adds one standard atmosphere in exactly one place: the Absolute pressure output. Every other figure on this page — the converted value and the psi, bar, kPa and atm equivalents — is your entered number re-expressed in a different unit on whatever basis you entered it in. Set the basis to gauge and those fields stay gauge quantities; they do not become absolute just because the selector is showing.
Run the 32 psig tyre example through it. The atm output is 220,632.2334 ÷ 101,325 = 2.1775 atm — but that is 32 psi of gauge pressure expressed in atmosphere-sized units, not “how many atmospheres the air inside is really at.” The true absolute figure is 3.1775 atm, and the gap between the two is exactly one atmosphere: since absolute pressure is defined here as gauge pressure plus 101,325 Pa, and one atm is itself exactly 101,325 Pa by definition, absolute-atm always equals gauge-atm output plus 1, precisely, for every reading this page accepts — it is an identity, not an approximation that happens to hold in one example.
The same shift applies to the psi, bar and kPa outputs: each is one atmosphere's worth short of the absolute figure once you convert that atmosphere into the matching unit (14.6959 psi, 1.01325 bar, 101.325 kPa). If a calculation downstream needs an absolute value in a unit other than psi, take the Absolute pressure figure and convert it yourself, or read the right-hand “Absolute” column of the equivalence table below rather than the left-hand column, which always mirrors the basis you entered.
Two atmospheres, and they are not the same
The standard atmosphere (atm) is exactly 101,325 Pa. The technical atmosphere (at, or kgf/cm²) is exactly 98,066.5 Pa. They differ by 3.3%, which is enough to matter on a pressure-vessel rating or a hydraulic test certificate. Older German, Japanese and Eastern European machine plates commonly use kgf/cm² and abbreviate it "at" or even "atm", so read the plate and the manual together before assuming. If a plate gives both a kgf/cm² figure and a bar figure that differ by about 2%, you are looking at the technical atmosphere.
Errors that show up in real pressure work
- Using 14.5 psi per bar. The correct factor is 14.5037738. The 0.026% error is invisible on a tyre and material on a 700-bar hydraulic test.
- Feeding gauge pressure into a gas law. Boyle's and the combined gas law need absolute pressure. Using gauge understates the pressure ratio and can be off by a factor of several at low pressures.
- Confusing bar with barg. European equipment sheets frequently write plain ‘bar’ for a gauge figure. If the sheet also quotes an ambient condition, it is absolute; if it quotes a working pressure, it is almost always gauge.
- Treating kgf/cm² as equal to bar. One kgf/cm² is 0.980665 bar. Close, but a 2% error that compounds through a safety-factor calculation.
- Mixing mercury conventions. Barometric inHg is normally referenced to 0 °C; some aviation and industrial instruments use 60 °F. The two differ by about 0.3%.
- Ignoring altitude when converting a gauge reading to absolute. This calculator adds one standard atmosphere. At 1,500 m the real ambient is closer to 84 kPa, so the absolute figure is roughly 17 kPa lower than shown.
Choosing the right unit for the job
Use whatever unit the specification you are working to uses, and convert only at the boundary. Converting back and forth mid-calculation is how rounding errors accumulate and how gauge and absolute get mixed.
Automotive and cycling. Tyre placards use psi, bar and kPa interchangeably. Bicycle tyres run from about 2 bar on a wide gravel tyre to over 8 bar on a track tyre; car placards cluster in the 2.0–2.5 bar band. Always use the door-jamb placard figure, not the maximum moulded into the sidewall, which is a construction limit rather than a recommendation.
Hydraulics. Mobile hydraulics specify bar or MPa in Europe and psi in North America, with common working pressures around 200–350 bar. Because 1 MPa is exactly 10 bar, converting between those two is a decimal shift, which is why MPa is popular on Japanese equipment plates. The torque values on the fittings holding that system together convert with our torque unit converter.
Compressed air and gas. Compressor output is quoted in psig or barg, and the compression ratio that determines discharge temperature and stage count is an absolute ratio. Drive power for that compressor is usually quoted in kW or hp depending on origin, which the horsepower to kilowatts calculator reconciles.
Beverage and food. Draught beer and soft-drink carbonation is set by pressure and temperature together, so a psi figure only means something alongside the serving temperature — see the keg carbonation psi calculator and, for the temperature side, the Celsius to Fahrenheit calculator.
Meteorology and aviation. Surface pressure is reported in hectopascals almost everywhere and in inches of mercury in the United States. One hPa is one millibar exactly, so the two older units are numerically identical; a station reporting 1013.25 hPa is reporting one standard atmosphere.