Pressure units:
how atmosphere, bar, pascal and psi relate

What a pressure unit actually measures

Pressure is force spread over an area. The SI unit, the pascal (Pa), is one newton per square metre. It is a very small unit: the weight of a thin sheet of paper lying on a table is on the order of a pascal, so everyday pressures are given in thousands (kPa) or hundreds of thousands of pascals.

Other units grew up around particular jobs. The atmosphere began as the typical pressure of the air at sea level. The bar was defined to be a convenient round number near it, 100,000 Pa, and meteorologists work in hectopascals or millibars. The pound per square inch, psi, remains the everyday unit on tyre gauges in many places and in US engineering.

All of these are the same physical quantity expressed with different scale factors. Once you remember the pascal values of a few of them, every conversion goes through that one common unit.

The factors that connect the units

Other directions use the same table: psi = atm × 14.696, and mmHg = atm × 760. For quick estimates, treat 1 atm as 1 bar, but for engineering or lab work keep the 1.3% difference.

Worked example: 3.5 atmospheres

Now a check in the other direction. A car tyre recommended at 2.2 bar is 220,000 Pa, or 220 kPa. Divided by 101,325 that is 2.17 atm, and multiplied by 14.5038 psi per bar it is 31.9 psi, close to the 32 psi that appears on many placards.

Weather reports give a third flavour. A standard sea-level pressure of 1,013.25 hPa is the same as 1.01325 bar. A reading of 1,000 hPa is about 0.987 atm, which is a little below standard and often goes with unsettled weather.

Gauge pressure versus absolute pressure

Many gauges, including tyre and cylinder gauges, show pressure relative to the surrounding air. That is gauge pressure. Absolute pressure is measured from a perfect vacuum, so it equals gauge pressure plus atmospheric pressure.

A tyre showing 2.2 bar gauge has an absolute pressure of about 3.2 bar. When you apply gas-law formulas, absolute pressure is the one to use. Unit labels sometimes hide the difference: psig means gauge, psia means absolute, and a bare 'psi' is usually gauge in a tyre context.

Altitude, weather and high-pressure cylinders

The standard atmosphere is a sea-level reference. Air pressure falls steadily with height because there is less air above you. At around 5.5 km it has roughly halved, near 500 hPa, which is why mountaineers and aircraft cabins need special provisions. A city a few hundred metres above sea level, such as Hyderabad, sits near 950 hPa on a typical day rather than 1,013.

Weather services therefore adjust station readings to sea level before drawing a map, so that a low in the mountains and a low on the coast can be compared fairly. If a barometer app shows a figure far from 1,013 hPa, it may be showing station pressure rather than the sea-level value.

High-pressure equipment is commonly rated in bar or megapascals. A full industrial gas cylinder at 150 bar holds 15 MPa, which is 148.0 atm or about 2,176 psi. Always read the rating in the unit printed on the cylinder and its regulator rather than converting from memory, because a mistake of a factor of 10 between bar and MPa is easy to make.

Where each unit is used

• Pascal and kilopascal: engineering, building codes, scientific papers, air conditioning.
• Bar: tyres in many countries, diving cylinders, industrial hydraulics, steam and boiler systems.
• Atmosphere: chemistry textbooks, gas laws, high-pressure physics problems.
• hPa or millibar: weather maps and aviation altimeter settings.
• psi: tyres in some markets, compressors, US plumbing and hydraulics.
• mmHg: blood pressure and some vacuum measurements.

Underwater, pressure rises by roughly 1 bar for every 10 metres of depth, so a diver at 20 m experiences about 3 bar absolute, which is about 3 atm. This is a rule of thumb that helps you check whether a conversion seems plausible.

In medicine and meteorology the units also carry habit. Blood pressure of 120 over 80 is in mmHg, and a doctor would not convert it to kPa in conversation, even though that would be 16.0 over 10.7 kPa. When you read a number, always check the unit label before you decide what it means.

Mistakes to avoid

• Treating bar and atmosphere as identical in precise work. The factor of 1.01325 matters in gas-law calculations.
• Mixing gauge and absolute pressure in the same formula.
• Forgetting that kPa is 1,000 Pa and hPa is 100 Pa. A reading of 1,013 hPa is 101.3 kPa, not 1,013 kPa.
• Dividing by the wrong factor when reversing: pascals to atmospheres divide by 101,325, not multiply.
• Applying a tyre pressure from a different vehicle. The right figure is the one on the car's placard or manual, not a generic value.

A related slip is reading a unit prefix too quickly. A pressure of 0.5 MPa is 5 bar and 500 kPa, and a gauge printed in MPa next to one printed in bar can look nothing alike at a glance. Write the unit beside every number as you convert, and compare the final answer with a figure you know.