What Are the Units of Pressure?

I remember being in high school and having to convert between all those different units of pressure. I think there are more units of pressure than any other measurable phenomenon! In this article, I’ll list all the units of pressure, and include conversion rates!

The SI unit for pressure is pascals (Pa). Other units of pressure include torr, barr, atm, at, ba, psi, and manometric units like mm Hg and fsw.

The Pa is defined as 1 newton per square meter. Or

   

If you want help remembering this, here is a fun joke!

Blaise Pascal, Isaac Newton, and Albert Einstein played a game of hide-and-seek. Einstein closed his eyes and counted to ten, while Newton ducked behind a wall. Pascal grabbed a piece of chalk and sketched a square with 1-meter sides.

When Einstein opened his eyes, he explained “Pascal, I’ve found you!”

But Pascal replied, “No, you’ve found one Pascal per square meter. You’ve found Newton!”

What is Pressure?

Pressure is the force per unit area. You probably first encountered pressure when learning about the gas laws in high school chemistry. There are many cool demonstrations you can do with pressure, such as placing a napkin in an upside-down cup underwater or boiling water with a vacuum chamber.

Pressure allows metal boats to float, airplanes to fly, straws to suck water, balloons to hold their shape, and even describes the interaction of all materials with any force!

More specifically, when we are talking about solid objects, we use the term stress. However, stress is still a force per area, so it’s identical to pressure.

Stress is extremely important in materials science, because it describes a material any time the material experiences a force (which is always, at least because of gravity, friction, and air pressure!).

Air pressure comes from the random motion of gas particles. As you may know, gas particles are often modeled as tiny spheres moving really fast and bouncing off of walls. A container of gas might have waaaay more than billions of gas molecules bouncing off the walls every second. Each molecule bounce imparts an imperceptible force, but if you add them all up, you get air pressure!

Although the Pa is the Si unit of air pressure, atmospheres (atm) are also commonly used for convenience, because 1 atm is the atmospheric pressure. Telling you that a container has 500 atm (which is 500 times the air pressure you feel right now) is probably a lot more meaningful to the average person than saying the container has 7000 psi.

All Reasonable Units of Pressure (and quite a few unreasonable ones)

Let’s talk about each unit of air pressure, and give the context where it might be used. In the next section, I’ll make a big conversion chart.

Pascals (Pa)

The standard SI unit of pressure is Pa, named after scientist Blaise Pascal.

The atmospheric pressure in pascals is 101,325 Pa, or about 100 = kPa.

Pa is exclusively used for stress, so materials scientists are quite familiar with this unit. Materials scientists may be more likely to read air pressure in terms of Pa because we are used to using Pa to describe stress, strength, elastic modulus, and hardness

However, since these values are so high, usually thousands or millions of Pa, they are expressed in MPa or GPa.

kPa = 1000 Pa (10^-3 Pa)

MPa = 1,000,000 Pa (10^-6 Pa) or 1,000 kPa

GPa = 1,000,000,000 Pa (10^-9 Pa) or 1,000,000 kPa or 1,000 MPa

Standard Atmospheres (atm)

The unit atmosphere (atm) is convenient because it is about equal to the atmospheric pressure. 

Technically, the atm is defined as 101,325 Pa, but it was originally designated as the air pressure at sea level and 0 ºC.

Atmospheres are most commonly used when the precise air pressure is unimportant. For example, I might say that I heated my sample in dry air at 1 atm. In this case I mean that I didn’t measure the air pressure, but I assumed it was basically the pressure of the room, which is more or less 1 atm.

Atmospheres might also be used in scientific fields where the reference to the real atmosphere is important, or when trying to communicate to the general public. Atmospheres are an intuitive, coarse unit of pressure.

There is also a unit “total atmospheres” (ata) which is used specifically when dealing with the pressure from multiple fluids. For example, under water you have water pressure and air pressure; a maverick scientist who decries the SI system may want to write the water pressure in terms of ata to include the air pressure above. In this case, 4 ata means that the water has a pressure of 3 atm (because there is 1 atm from the air above).

torr (Torr)

The unit torr is almost equal to 1 mm of Hg, which you can read about in the section of manometric units. In terms of the atmospheric pressure, 1 atm = 760 Torr (exactly).

The torr is useful for measuring very small pressures, like in a vacuum chamber. If you’re using torr, you may be more interested in 1/1000 of a torr, or a militorr (mTorr). 

The torr is named after Evangelista Torricelli, who laid the foundation for the barometer (a device that measures air pressure).

Fun (but confusing) fact: the unit torr is written with a lowercase letter, but the symbol Torr is written with a capital T. So you might say “The pressure in torr is 760 Torr.”

bar (bar)

The unit bar is super pointless. The bar is a metric unit that is the same as 100,000 Pa, or 100 kPa, or 0.1 MPa. More commonly, people use mbar (1 mbar = 0.001 bar, or 100 Pa).

No, there is no reason to use bar instead of Pa. Although many committees in charge of measurement want to get rid of the unit bar, it is still used, especially in meteorology (weather forecasting). I have personally operated vacuum equipment that read the pressure in mbar.

With the prefix “hecto-” which means 100, Pa can be easily converted to bar. 1 hectopascal (hPa) is equivalent to 1 mbar. Forward-thinking weathermen now do measurements in hPa instead of mbar.

The bar’s origin is the Greek word for weight, baros.

Pounds per Square Inch (psi or lb/in²)

Oh, right. American units (yes I’m American, it’s called self-deprecating humor).

Pounds per square inch means the pound-force per square inch. In other words, the weight of a pound times the force of gravity, per square inch. For those of you from countries that haven’t visited the moon, a pound is roughly half a kilogram, and a square inch is about 6 square centimeters.

The only time I’ve used psi is checking my tire pressure.

If you’re an American engineer, you may be used to working with ksi, which stands for kilopound-force per square inch. In other words, 1 ksi is 1000 psi.

There is also the ounce-force per square inch (ozf/in²) which is 1/16 of a psi.

The atmospheric pressure is about 15 psi.

Technical Atmosphere (at or kgf/cm²)

The technical atmosphere (at) is the metric equivalent of psi, and is measured in kilogram-force per square centimeter.

If you followed by back-of-the-envelope approximations from psi, you’d guess that the atmospheric pressure in technical atmospheres is about 1 kgf/cm². Actually, 1 at is 0.97 atm.

Technical atmospheres is an outdated measurement system and is not SI. If you see pressure gauges that still use this unit, I recommend upgrading your system 🙂

Barad (Ba)

The barad (Ba) is a cgs unit that is so unstandardized, it has many names. You may also see the barad called: baryd, baryed, barye, barrie, barie, or bary.

The barad is defined as 1 dyne per square centimeter (dyn/cm²). Alternatively, 1 Ba = 0.1 Pa.

Pièze (pz)

If you see this unit, you’re in trouble. The pièze is the standard unit of pressure in the mts measurement system which was used in the Soviet Union or perhaps 18th-century France.

The pièze is defined as 1 sthène per square meter (sn/m²). Alternatively, 1 pz = 1kPa.

Manometric Units (including mmHg, mmH₂O, fsw, and msw)

Manometric units are units that refer to a liquid influenced by air pressure. An early way to measure pressure involved a tube filled with mercury. The mercury would rise or fall depending on the pressure difference, so you would literally be measuring millimeters of mercury (mmHg).

In the past, mmHg was just one torr, but due to more rigorous definitions and redefinitions, the standard mmHg is now 1.00000014247 Torr. But yeah, if you have an application that uses such an outdated pressure gauge, the approximation will be fine.

Manometric units are imprecise because they can vary from location to location, depending on the density and temperature of the liquid. Even the local gravity may affect the measurement slightly (this is more problematic than you’d think because both gravity and air pressure are affected by altitude).

In addition to the most-popular manometric unit millimeters of mercury (mmHg), other manometric units include centimeters of mercury (cmHg), inches of mercury (inHg or “Hg), millimeters of water (mmH₂O), centimeters of water (cmH₂O), and inches of water (inH₂O, “H₂O, or iwc). Each of these units changes depending on the temperature.

Divers may use meters of sea water (msw) or feet of sea water (fsw). Meters of sea water is defined as 1/10 bar (or 10 kPa, for civilized folks) and feet of sea water is 0.445psi. These values are calculated by assuming an average density of sea water and gravity.

Here is a chart comparing each of these manometric units to atm and Pa.

Unit	Pa	atm
mmHg	133.3	1.316*10-3
mmH2O	9.807	9.678*10-5
msw	9807	9.678*10-2
fsw	2989	2.950*10-2

Converting Units of Pressure

The table below will help you convert different units of pressure.

Unit	Pa	atm	Torr	bar	psi	at	Ba	pz	mmHg
Pa	1	9.869*10-6	7.5*10-3	10-5	1.45*10-4	1.02*10-5	10	0.001	7.5*10-3
atm	101,325	1	760	1.013	14.69	1.033	1,013,250	0.1	760
Torr	133.3	1.316*10-3	1	1.333*10-3	0.0194	1.36*10-3	1333	0.133	1
bar	100,000	0.987	750.06	1	14.50	1.02	1,000,000	100	750.06
psi	6,893	0.068	51.71	0.0689	1	0.070	68,930	0.007	51.71
at	98,070	0.968	735.56	0.981	14.22	1	980,700	0.098	735.56
Ba	0.1	9.869*10-7	7.5*10-4	10-6	1.45*10-5	1.02*10-6	1	0.0001	7.5*10-4
pz	1000	9.869*10-3	7.5	10-2	0.145	1.02*10-2	10,000	1	7.5
mmHg	133.3	1.316*10-3	1	1.333*10-3	0.0194	1.36*10-3	1333	0.133	1

Final Thoughts

See, pressure isn’t so tricky after all! There are a lot of different units because pressure is used in many different contexts (and our ways of measuring pressure have changed a lot over history). 

But if you can remember these conversion rates (or bookmark this page) you’ll have no trouble at all!

Finally, here is a quick reference sheet in terms of the atmospheric pressure.

References and Further Reading

This is a paper on how to measure pressure properly.

Click here to check a pressure converter tool.