Pressure Unit Converter: Pa, kPa, bar, atm and psi

Pressure Unit Converter

Pressure is the amount of force pushing on each piece of a surface. A pressure unit converter rewrites a pressure from one unit into another, such as pounds per square inch into bars. This page converts between pascals, kilopascals, bars, standard atmospheres and psi, and shows all five values at the same time.

What the converter does

A visitor types one number and picks the unit that number is written in. The page returns the same pressure in all five units.

• Results are shown to eight significant figures. Only the display is rounded. The conversion runs on the number as typed.
• A result below 0.0001 in size, or of a billion or more, is shown in scientific notation. Zero is shown as a plain 0.
• Negative values are accepted, because a gauge reading can be negative.
• An empty box produces a prompt rather than a number. A link carrying a unit the page does not offer produces a message rather than a conversion.

The five units

The pascal is one newton of force spread over one square metre. The other four units are each a fixed number of pascals, and none of those numbers is a measurement, so none of them changes over time.

Pressure conversion formula

Because every unit here is a fixed multiple of the pascal, a conversion is one multiplication and then one division. The value is carried into pascals and then back out into the unit wanted:

$P_2 = \frac{P_1 \times k_1}{k_2}$

where $P_1$ is the pressure typed in, $k_1$ is the number of pascals in one unit of the chosen unit, $k_2$ is the number of pascals in one unit of the wanted unit, and $P_2$ is the answer.

Nothing is added or subtracted along the way. All five scales read zero at the same pressure, so only the size of the step changes. Temperature is the case where that is untrue: Celsius and Fahrenheit start counting at different points, so a converter that only multiplied would report 0 °C as 0 °F instead of 32 °F.

Where the psi factor comes from

The psi is one pound-force pressing on one square inch. The converter builds it from two exact definitions rather than copying a printed decimal:

$1\ \mathrm{psi} = \frac{F}{A} = \frac{4.4482216152605\ \mathrm{N}}{(0.0254\ \mathrm{m})^2}$

where $F$ is one pound-force in newtons and $A$ is one square inch in square metres.

Both inputs are definitions. The international inch has been exactly 0.0254 m since the International Yard and Pound Agreement of 1959. The pound-force is the 1959 international pound, exactly 0.45359237 kg, multiplied by standard gravity, which the 3rd General Conference on Weights and Measures fixed at exactly 9.80665 m/s² in 1901. That product is exactly 4.4482216152605 N, as tabulated in NIST Special Publication 811, Appendix B.

The division is exact too, as the fraction 8,896,443,230,521 / 1,290,320,000. Its decimal expansion never ends. It begins 6,894.757293168361336…, so every decimal ever printed for the psi is a rounded version of it, including the 6,894.757 Pa listed by NIST.

Example: a car tyre at 32 psi

A tyre inflated to 32 psi holds 32 pound-force on every square inch. Multiplying by the psi factor carries that into pascals:

$P = 32 \times 6\,894.757293168361\ldots = 220\,632.2333\ldots\ \mathrm{Pa}$

Dividing that result by each of the other factors gives the rest. To eight significant figures the page shows 220,632.23 Pa, 220.63223 kPa, 2.2063223 bar and 2.1774708 atm.

The middle step is worth reading twice. Bars come from dividing by 100,000, and atmospheres from dividing by 101,325, so the two answers differ by about 1.3 percent. They are close, and they are not the same.

Common pressure conversions

Each row below is the value one unit produces in the other four, at eight significant figures.

Which values are exact and which are rounded

Four of the five factors are exact whole numbers, so a conversion between them is limited only by the arithmetic, not by the constants.

• 1 kPa is exactly 1,000 Pa. The kilo prefix means one thousand.
• 1 bar is exactly 100,000 Pa. The bar is not an SI unit, but the International Bureau of Weights and Measures lists it in the SI Brochure among the units accepted for use with the SI, with that exact value.
• 1 atm is exactly 101,325 Pa. The 10th General Conference on Weights and Measures fixed it in 1954, in Resolution 4.
• 1 psi is exact as a fraction and unwritable as a decimal, for the reason given above.

The rounding a reader will actually see comes from the display, not from the constants. Eight significant figures is wide enough to show a defining value in full and narrow enough to hide the last digits of the computer's arithmetic, which carry rounding noise rather than information.

Gauge pressure and absolute pressure

A tyre gauge does not measure the whole pressure inside the tyre. It measures how much that pressure beats the air outside. A reading taken that way is a gauge pressure, and a reading counted from a complete vacuum is an absolute pressure. At sea level the two differ by roughly one atmosphere.

A tyre at 32 psi on the gauge therefore holds about 46.7 psi absolute. The converter does not know which kind of reading has been typed, so it converts the number as given and sets no lower limit. That is deliberate: an absolute pressure cannot fall below zero, but a gauge pressure below zero is an ordinary partial vacuum.

Frequently asked questions

How many psi is 1 bar? 1 bar is 100,000 Pa, and dividing that by the psi factor gives 14.503774 psi at eight significant figures. The everyday rounding is 14.5 psi.

Is a bar the same as an atmosphere? No. A bar is 100,000 Pa and a standard atmosphere is 101,325 Pa, so 1 atm is 1.01325 bar exactly. The atmosphere is about 1.3 percent larger. The two are often swapped in casual use, which is fine for a rough figure and wrong for a calculation.

How many kilopascals is 1 psi? 6.8947573 kPa at eight significant figures, usually quoted as 6.895 kPa.

Why does the psi factor carry so many digits? Because it is a division that never comes out even. The converter composes it from the exact inch and the exact pound-force, instead of storing a decimal that has already been cut short. A shortened factor would push a small error into every psi result.

Can a negative pressure be converted? Yes. Gauge readings go below zero whenever the pressure inside is lower than the air outside, so the page converts negative values instead of refusing them.

Which unit should be used? The pascal and kilopascal are the SI units and are standard in science and engineering. Bars are common in European industry and on diving equipment, psi is common in the United States and on tyre gauges, and atmospheres are mostly used for comparison against ordinary air pressure at sea level.