How this instrument works
The bar is a round number pretending to be a natural one. Vilhelm Bjerknes, a Norwegian meteorologist building the first mathematical weather forecasts around 1909, wanted a pressure unit close to what a barometer reads at sea level but painless to compute with, and settled on 100 000 pascals — ten newtons pressing on every square centimetre. Weather services adopted its thousandth part, the millibar, which is why a synoptic chart still reads 1013 rather than 101 325.
A standard atmosphere is an older idea, and it began as a column of mercury: 760 millimetres of it at 0 °C under gravity of 9.806 65 metres per second squared. Multiply density by height by gravity and 101 325 pascals drops out, a figure that the 10th General Conference on Weights and Measures adopted in 1954 as a defined value rather than a measured one. Since that resolution neither unit carries any uncertainty — one is 100 000 Pa by construction, its rival 101 325 Pa by decree.
Divide those two definitions and you get 100 000 ⁄ 101 325, which cancels to 4000⁄4053. That denominator factors into 3 × 7 × 193, and since none of those primes divides ten, 0.986923266716… repeats forever instead of stopping; this sheet carries twelve places of it. Run the arithmetic backwards and all awkwardness vanishes: 1 atm = 1.01325 bar, five decimals and done. Hydraulic gauges across European industry, scuba fills and espresso group heads are marked in bar; chemistry papers, gas-law homework and hyperbaric medicine still count in atmospheres.
- Type your reading into the Bar (bar) field — 2 bar is loaded as a starting point.
- Read the answer on the Atmospheres (atm) line, shown to six decimals and recalculated as you type.
- Working from millibars or hectopascals? Divide by 1000 first, then enter that figure as bar.
- Going the other direction, divide your atmospheres by 0.986923266716 — or simply multiply by 1.01325, which is the identical operation with tidier digits.
- Confirm whether your gauge reads absolute or gauge pressure before converting; the ratio is unchanged, but the zero point is not.
Worked example — a 2 bar reactor headspace
A bench-scale hydrogenation is held at 2 bar absolute, but the kinetics paper you are checking against quotes every rate in atmospheres. Put 2 into the Bar (bar) field and the Atmospheres (atm) line returns 1.973847, or 1.97384653343 at full precision, because 2 × 4000⁄4053 is simply 8000⁄4053.
Verification runs cleanly in reverse: 1.97384653343 × 1.01325 gives 2.000000000 bar back, digit for digit. Notice what that 2 is not. Had it come off a dial gauge reading zero against room air, absolute pressure inside would sit near 3.013 bar, and 3.013 — not 2 — is the number you would feed this sheet.
Questions
Is one bar the same as one atmosphere?
No, though they sit close enough that people swap them by mistake. One bar is 100 000 Pa; one standard atmosphere is 101 325 Pa, making a bar 1.3077% smaller. At kitchen-scale pressures that gap hides easily — 2 bar and 2 atm differ by about 26 millibar — but a scuba cylinder filled to 200 bar holds 197.38 atm, a shortfall of 2.6 atm, which is more than enough to spoil a gas-blending calculation.
Is 0.986923266716 exact or rounded?
It is a truncation of something perfectly exact. Both units are defined in pascals with zero uncertainty, so their ratio is a rational number: 100 000⁄101 325, or 4000⁄4053 in lowest terms. Because 4053 factors into 3, 7 and 193, that fraction has no finite decimal form and its digits repeat instead of stopping. Twelve places pin the result to better than one part in 10¹¹, far beyond what any pressure transducer can resolve.
Does this work for gauge pressure as well as absolute?
Yes for the multiplication, no for the meaning. Scaling by 0.986923266716 converts any pressure difference, so 5 barg becomes 4.934616 atm of gauge pressure. What multiplication cannot do is move between scales: gauge pressure counts up from ambient air, absolute counts up from vacuum, and they differ by roughly one atmosphere that drifts with weather and altitude. Tag your figure barg or bara before converting, and keep that tag afterwards.
What is a technical atmosphere, and does it belong here?
It does not. A technical atmosphere, symbol at, is one kilogram-force per square centimetre — 98 066.5 Pa exactly — and shows up on older German, Russian and Japanese machinery, sometimes written ata or atü. It sits 3.2% below a standard atmosphere and 1.9% below a bar. If a vintage compressor plate is stamped at rather than atm or bar, multiply by 0.967841 to reach standard atmospheres, not by this page's factor.
Why do forecasters use hectopascals instead of atmospheres?
Because air pressure moves too much for so large a unit to stay readable. Sea-level readings swing between roughly 950 and 1050 hPa in ordinary weather, and one hectopascal is exactly one millibar, so a forecaster gets a comfortable spread of whole numbers rather than four decimals of an atm. Standard sea-level pressure, 1013.25 hPa, equals one atmosphere by definition; Typhoon Tip bottomed out near 870 hPa in 1979, or 0.8586 atm.
Which unit should new work be written in?
Pascals, or bars where a friendlier magnitude helps. The pascal is the SI unit, and the bar survives beside it as a convenient multiple that most European pressure equipment already carries on its dial. IUPAC shifted its standard pressure from 1 atm to 100 kPa in 1982, so thermodynamic tables published since then tend to be bar-based. Atmospheres persist in teaching, high-pressure physics and diving, where one atm is close to what ten metres of seawater adds.