How to Convert Pressure Units

Pressure unit confusion has wrecked more gas-law problems than any other single error. The math itself is trivial — multiply by a factor — but chemistry has inherited about seven different pressure units from different historical traditions, and PV = nRT only gives you the right answer when your pressure unit matches the R you picked. Mix atm with R = 8.314 and you’ll be off by a factor of 101.325. The fix is to anchor everything to one reference: 1 atm = 101 325 Pa = 760 mmHg = 14.696 psi. Memorize that line and you can derive any other pair on demand.

Why so many pressure units?

Each one came from a different measurement technology or community.

• atm (atmosphere) — defined as average sea-level air pressure. Standard in general chemistry textbooks because it puts everyday conditions at “1”.
• Pa (pascal) — the SI unit, 1 N/m². Honest but small: standard atmosphere is 101 325 Pa, which is awkward to write.
• kPa — pascals scaled up by 1000. SI-friendly and the right size for chemistry. Used in IUPAC publications and most countries outside the US.
• mmHg — height of mercury a barometer or manometer would support. Survives because mercury manometers were the workhorse instrument for centuries.
• torr — defined as exactly 1/760 atm, originally to honor Torricelli. For all practical chemistry purposes, 1 torr = 1 mmHg.
• bar — exactly 100 000 Pa. Conveniently close to 1 atm (off by 1.3%) and adopted as the IUPAC standard pressure in 1982.
• psi — pounds per square inch. Imperial unit you’ll meet in tire gauges, gas cylinders, and anything from a US engineering shop.

The anchor line

Keep this one identity in your head:

1 atm = 101 325 Pa = 101.325 kPa = 760 mmHg = 760 torr = 1.01325 bar = 14.696 psi

Every other conversion is a pair of multiplications through this line.

The recipe

1. Identify what you have (value + unit) and what you want.
2. Pick the conversion factor from the anchor line.
3. Multiply, letting the original unit cancel.
4. Check magnitude against the anchor.

Worked example: atm to kPa

Convert 2.50 atm to kPa.

2.50 atm × (101.325 kPa / 1 atm) = 253.3 kPa

Sanity check: 2.5 × 100 ≈ 250. Lands where it should.

Worked example: barometric reading in mmHg to atm

A mercury barometer reads 742 mmHg.

742 mmHg × (1 atm / 760 mmHg) = 0.976 atm

Slightly below standard — typical for elevation or a passing low-pressure system.

Worked example: tire gauge to psi

A tire gauge reads 220 kPa. Convert to psi.

Two-step through atm:

• 220 kPa × (1 atm / 101.325 kPa) = 2.172 atm
• 2.172 atm × (14.696 psi / 1 atm) = 31.9 psi

Or directly: 220 × (14.696 / 101.325) = 31.9 psi.

(One catch: tire gauges read gauge pressure, not absolute. Add 1 atm to get the absolute pressure inside the tire, which is what PV = nRT cares about.)

Worked example: matching R in PV = nRT

You measure P = 745 mmHg, V = 2.50 L, T = 25.0 °C and want n.

You can’t use 745 mmHg directly with R = 0.08206 L·atm/(mol·K) — the units don’t cancel. Convert first:

• Path A: P = 745 mmHg × (1 atm / 760 mmHg) = 0.9803 atm. Use R = 0.08206.
• Path B: P = 745 mmHg × (101.325 kPa / 760 mmHg) = 99.3 kPa. Use R = 8.314.

Both paths land on the same n (within rounding). Pick whichever R you have memorized and convert P to match.

Worked example: bar to atm

A reaction runs at 1.50 bar. Express in atm.

1.50 bar × (1 atm / 1.01325 bar) = 1.48 atm

Bar and atm are within ~1.3% — close enough that you can do a back-of-envelope estimate by treating them as equal, but for any quantitative work, do the conversion.

Quick reference

From / To	atm	kPa	mmHg	bar	psi
1 atm	1	101.325	760	1.01325	14.696
1 kPa	0.00987	1	7.501	0.0100	0.14504
1 mmHg	0.00132	0.13332	1	0.00133	0.01934
1 bar	0.98692	100	750.06	1	14.504
1 psi	0.06805	6.8948	51.715	0.06895	1

Traps people fall into

• R-mismatch in PV = nRT. This is the killer. R = 0.08206 wants P in atm; R = 8.314 wants P in kPa (or Pa with V in m³). Always check that your units cancel symbolically before plugging in numbers.
• Gauge vs. absolute. Tire gauges, pressure cookers, and most lab pressure regulators report gauge pressure (above atmospheric). Gas-law math wants absolute. Add 1 atm (or your local atmospheric pressure).
• Confusing torr and mmHg. They’re defined slightly differently but agree to 7 significant figures. Treat them as equal in any normal chemistry context.
• Treating bar as exactly atm. They’re 1.3% apart. Fine for an estimate, not fine for a balanced reaction yield.

Practice

Try these against the Ideal Gas Law Calculator:

1. Convert 3.00 atm to mmHg, kPa, and bar.
2. A gas cylinder reads 2200 psi (gauge). Convert to absolute atm and kPa.
3. Express 1.000 atm in every unit on the anchor line.
4. A lab measures 98.7 kPa. What is this in mmHg and atm?
5. Calculate n for 800.0 mmHg, 5.00 L, 300 K. Show the pressure conversion step explicitly.