Pressure Converter

How the pressure units are defined

Pressure is force per unit area. The SI unit is the pascal, one newton on one square meter, which is a very small pressure: the air around you at sea level presses with about a hundred thousand of them. The other units fall into three families.

• Metric multiples. A hectopascal is 100 Pa and equals a millibar, which is why weather maps can use either. A bar is exactly 100,000 Pa (100 kPa), and a megapascal is 10 bar.
• Force on an area. A psi is one pound-force on one square inch. Both halves are defined exactly (the pound is 0.45359237 kg, standard gravity is 9.80665 m/s², the inch is 0.0254 m), so a psi is exactly 4.4482216152605 N ÷ 0.00064516 m², which works out to 6,894.757293… Pa. The kgf/cm², also called the technical atmosphere, is the weight of one kilogram under standard gravity on a square centimeter: exactly 98,066.5 Pa.
• Atmospheres and columns of liquid. The standard atmosphere was fixed in 1954 at exactly 101,325 Pa. The torr is 1/760 of it. Millimeters and inches of mercury and inches of water describe the height of a liquid column the pressure would hold up. Because real mercury and water change density with temperature, the modern units are conventional: they assume a fixed density (13,595.1 kg/m³ for mercury, roughly its density at 0 °C, and 1,000 kg/m³ for water) and standard gravity.

Two consequences are worth knowing. First, a torr and a millimeter of mercury differ by about one part in seven million (133.322368… Pa against 133.322387415 Pa), which only matters for calibration work. Second, older tables list inches of mercury “at 32 °F” or “at 60 °F” and inches of water “at 39.2 °F” or “at 60 °F”; those differ slightly from the conventional values this converter uses.

The conversion formula

Every unit here is a fixed number of pascals, so a conversion is one multiplication or division:

value

the pressure you enter

pascals in a unit

e.g. 100,000 for the bar, 101,325 for the atmosphere, 6,894.757293… for the psi

The definitions used, in pascals:

Worked examples

1 bar to psi. 100,000 Pa ÷ 6,894.757293 Pa = 14.50377377 psi. So a bar is a little under 14.5 psi, and a psi is about 0.069 bar.

A 32 psi tire in bar and kPa. 32 × 6,894.757293 Pa = 220,632.2 Pa, which is 2.206322334 bar or 220.6322334 kPa. Both are gauge readings, like the 32 psi you started with.

One standard atmosphere. 101,325 Pa is exactly 1.01325 bar, 101.325 kPa and 760 Torr, and about 14.69594878 psi, 29.92125558 inHg and 759.9998917 mmHg.

A barometer reading of 29.92 inHg in hectopascals. 29.92 × 33.86388640341 = 1,013.207481 hPa. It is not quite 1,013.25 hPa because 29.92 is the standard atmosphere (29.92125558 inHg) rounded to two decimals.

Gauge pressure or absolute pressure?

Most gauges read gauge pressure: how far the pressure is above the air around them. A tire gauge reads 0 on an empty tire even though the air inside is at about one atmosphere. Absolute pressure is measured from a perfect vacuum.

In US units the difference is often written into the unit: psig for gauge, psia for absolute. A tire at 32 psig at sea level holds air at about 32 + 14.7 = 46.7 psia. Barometric pressure, the pressures in gas-law problems and the pressure in a vacuum chamber are absolute.

Air pressure at altitude in the standard atmosphere

The U.S. Standard Atmosphere, 1976 (the same model as the ICAO standard atmosphere up to 32 km) gives the pressure of an idealized, average atmosphere. Real air pressure on a given day differs with the weather.

Altitudes are geopotential meters, which differ from height above sea level by less than 0.2% in this range. Temperature falls with height in the same model; for converting it, use the temperature converter.

Mistakes to avoid

• Mixing gauge and absolute pressure. Adding 14.7 psi, or not, changes the answer by a whole atmosphere. Check which one a formula needs; the ideal gas law always needs absolute pressure (and absolute temperature).
• Treating 1 bar and 1 atm as equal. They are 1.3% apart: 1 atm = 1.01325 bar. A kgf/cm² is another 2% lower, 0.980665 bar.
• Confusing hPa and kPa. Weather reports use hectopascals (about 1,013 at sea level); tire and engineering figures use kilopascals (about 101). They differ by a factor of ten.
• Reading inHg or inH₂O without the reference. Older instruments may be calibrated at a stated temperature rather than the conventional density, which shifts the reading slightly.