Pressure Converter — Pa, bar, psi, atm and torr

Background.

The sticker inside a car door says 2.2 bar; the air line at the filling station reads in psi. A weather app gives 1013 hPa while an American forecast says 29.92 inches. Blood pressure comes in millimetres of mercury, vacuum gauges in torr or millibar, hydraulic data sheets in megapascals, and an old boiler gauge may be marked in kgf/cm². All of them measure one physical quantity, force per unit area. The variety is a record of who was measuring, where, and in which century.

Every conversion here passes through the pascal, the SI unit, equal to one newton per square metre. It is a small unit — ordinary air pressure at sea level is around 100,000 Pa — which is why kilopascals, hectopascals and the bar are used in practice. Several units are fixed exactly in pascals: the bar is 100,000 Pa, the millibar 100 Pa, the standard atmosphere 101,325 Pa, the torr one 760th of an atmosphere, and the kilogram-force per square centimetre 98,066.5 Pa. The psi follows exactly from the definitions of the pound, the inch and standard gravity, at about 6,894.757 Pa. The mercury units are conventions: the pressure under a column of mercury of specified density in standard gravity.

The units that cause trouble are the near-twins. A bar is 1.3% smaller than an atmosphere, close enough to be confused and far enough apart to matter in a gas-law calculation. A kilogram-force per square centimetre is about 2% below a bar. A torr and a millimetre of mercury differ by about 0.14 parts per million, which is irrelevant at a doctor's surgery and occasionally relevant in a calibration laboratory. Each has its own selector.

What no unit conversion can tell you is the reference. A tyre gauge reads pressure above the surrounding air, while a barometer reads absolute pressure. Converting 32 psi to kilopascals gives 220.6 kPa above the outside air, not 220.6 kPa absolute. Keep the label — gauge, absolute or differential — attached to the number in both units.

What is pressure converter?

Pressure is the force a fluid or surface exerts per unit area, acting at right angles to that area. The BIPM's SI Brochure gives its unit, the pascal, as the newton per square metre. A pressure value also has a reference. Absolute pressure is measured from a perfect vacuum, so it can never be negative. Gauge pressure is measured from the local atmospheric pressure, so it is negative in a partial vacuum. Differential pressure is the difference between two points, such as across a filter. Converting units changes the scale of the number but never its reference: an absolute value stays absolute and a gauge value stays gauge. Engineers in the US often mark this on psi readings as psia for absolute and psig for gauge. Weather reports add one more convention: the pressure they publish is reduced to sea level, so that stations at different heights can be compared on one map. The absolute pressure actually present at altitude is much lower; in the International Standard Atmosphere it is about 84.6 kPa at 1,500 m and 79.5 kPa at 2,000 m, against 101.325 kPa at sea level.

How to use this calculator.

1. 01Type the pressure as it appears on the gauge, label or document, including a minus sign if it is a gauge reading below atmospheric.
2. 02Choose the unit it is in. Take care with near-twins: pick torr only if the source says torr, and conventional mmHg if it says millimetres of mercury; a bar is not an atmosphere.
3. 03Choose the unit you want for the headline result. Every other unit is listed underneath at the same time, so one entry covers a whole table.
4. 04Read the pascal or kilopascal line as a cross-check against any value you already know, such as 101.325 kPa for one standard atmosphere.
5. 05Record the result with the same reference label as the original reading and no more significant figures than the instrument justified.
6. 06If the value came from a weather report, it is a sea-level figure. For the absolute pressure at a site well above sea level — for a gas calculation or to correct a gauge reading — use a local station reading instead.

The formula.

A conversion is two steps. The value is multiplied by the number of pascals in the source unit, then divided by the number of pascals in the target unit: target = value × Pa per source unit ÷ Pa per target unit. Because every unit is anchored to the pascal, converting psi to torr is no different from converting psi to pascals and pascals to torr.

The factors come from definitions. The psi is one pound-force on one square inch: 0.45359237 kg × 9.80665 m/s² = 4.4482216152605 N, spread over 0.0254² = 0.00064516 m², giving 6,894.757 Pa. The kilogram-force per square centimetre is 9.80665 N on 0.0001 m², exactly 98,066.5 Pa; that is also the pressure under 10 m of water at 1,000 kg/m³ in standard gravity. The conventional millimetre of mercury takes mercury at 13,595.1 kg/m³ under 9.80665 m/s², so one millimetre of it presses with 133.322387415 Pa, exact by that convention. The torr is 101,325 ÷ 760 = 133.3224 Pa, fractionally smaller. The inch of mercury is taken as exactly 25.4 conventional millimetres, which is 3,386.3886 Pa (NIST lists the rounded 3,386.389 Pa), so an inch of mercury reads 25.4 mmHg at any precision shown.

A conventional mercury unit is not a real barometer column. A mercury barometer's reading depends on the mercury's temperature and the local strength of gravity, and needs corrections before it equals the conventional unit; the converter applies none.

Results are calculated to ten decimal places and displayed to four, or to four significant figures in scientific notation below 0.001. That is ample for everyday pressures, but it loses ultra-high vacuum: a value below about 10⁻¹⁰ of the target unit becomes zero, so convert such readings into pascals or millibar, where the numbers are larger.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST SP 811 Appendix B.6 supplies pressure factors for atmosphere, bar, psi, torr, mercury columns and kgf/cm².
2. [2]BIPM SI Brochure defines pascal as newton per square metre.
3. [3]NIST SP 330 independently lists the pascal SI derived unit.
4. [4]NIST Handbook 44 Appendix C provides customary/SI legal-metrology relationships.
5. [5]NOAA National Weather Service glossary provides atmospheric millibar/hectopascal context.