How this instrument works
Pressure in pounds per square inch is unusual among surviving units because it still leans on gravity. A pound of force means the weight of one avoirdupois pound, and weight changes with where you stand, so this unit had to be frozen in size by picking a value for gravity and refusing to let it drift. That value, 9.80665 m/s², was settled in 1901; the pound itself was pinned at 0.45359237 kg by six standards bodies in 1959. Their product is 4.4482216152605 newtons, and spreading it over an inch square — an area of 0.00064516 m², because the inch is 25.4 mm to the letter — makes one psi equal 6894.757293168361 pascals.
The standard atmosphere arrived from the opposite direction: not force divided by area, but a mercury column standing 760 mm high at 0 °C. Evangelista Torricelli raised the first of them in 1643 and worked out that the surrounding air was holding it there. Compute that column honestly and it lands on 101325.0144 pascals, an untidy result that the 10th CGPM tidied by decree in 1954, defining a standard atmosphere as precisely 101325 Pa and leaving mercury behind as a historical curiosity.
Divide 6894.757293168361 by 101325 and this sheet's multiplier appears. Both endpoints were legislated rather than measured, so the quotient carries no experimental uncertainty whatever, yet it declines to terminate: 0.06804596390987773… trails off into a cycle that never closes on a final digit, so twelve significant places is where this sheet stops. Invert it and you get 14.6959487755 psi to the atmosphere — the source of every 14.7 you have seen in an engine-tuning thread or a diving manual. Those are exactly the two worlds this pair joins, since American cylinders, manifolds and regulators are marked in psi while dive tables, hyperbaric protocols and gas-law problems count in atmospheres absolute.
- Enter your gauge figure in the PSI (psi) box; it opens at 30, a number equally at home on a cold tyre or a boost log.
- The Atmospheres (atm) result follows every keystroke, with nothing to press.
- Settle first whether your source is gauge or absolute. Add 14.6959 before converting if you need atmospheres absolute.
- Running the calculation backwards? Multiply your atmospheres by 14.6959487755 to return to psi.
Worked example — 30 psi of turbo boost
A tuner logs 30 psi of boost on a built four-cylinder and wants the figure in atmospheres before estimating charge density from the gas laws. Put 30 into the PSI (psi) box and 2.0413789173 atm appears on the Atmospheres (atm) line, a shade over two atmospheres of boost on top of what that engine would draw unaided.
Here is where people slip. Boost is measured against ambient air, so the manifold is not sitting at 2.04 atm but at 2.04 plus one, or 3.0413789173 atm absolute. Adding 14.6959 to that gauge reading and converting 44.6959 gives an identical 3.0413789173, as it must. Call it three times the air an unassisted engine breathes, before any intercooler or temperature correction is applied.
Questions
Is 1 psi exactly 0.0680459639099 atm?
It is an exact ratio, displayed rounded. Both ends are defined rather than measured — 6894.757293168361 Pa against 101325 Pa — so the quotient is a plain fraction of whole numbers with no uncertainty in it. What that fraction will not do is terminate, because 127 squared and 193 sit in its denominator once reduced. Cutting the expansion at twelve significant digits shifts an answer only in the thirteenth, far below anything a dead-weight tester could reveal.
Does 30 psi on a gauge mean 30 psi of absolute pressure?
No, and this is the mistake that ruins most conversions in this direction. Workshop gauges rest at zero in open air, so they report excess over ambient rather than absolute pressure. Absolute pressure adds one atmosphere, 14.6959 psi at sea level, which is why 30 psi on a dial is 3.0414 atm absolute although only 2.0414 atm of gauge pressure. Gas-law work, diving depth and vacuum systems need the absolute value; inflation targets, hose ratings and boost figures are quoted as gauge.
Is 14.7 psi of boost one full atmosphere?
Near enough, yes. Sea-level pressure is 14.6959 psi, so a turbo holding 14.7 psi has doubled the absolute pressure in the manifold: one atmosphere of ambient air plus one atmosphere of boost. Two nearby numbers cause trouble, though. One bar of boost is 14.5038 psi, a little less, and the 14.7 to 1 that engine people quote for a stoichiometric air-fuel mixture is an unrelated coincidence with no pressure in it at all.
How do cylinder psi and atmospheres of depth relate for divers?
They are two uses of the same factor. An aluminium 80 filled to 3000 psi is holding 204.1 atm of gas, while depth is tallied in atmospheres absolute: roughly 33 feet of seawater adds one atmosphere, so a diver at 66 fsw sits at 3 ATA and empties a cylinder about three times as fast as at the surface. Hyperbaric medicine uses the same scale — the standard US Navy oxygen table runs at 2.8 ATA, an absolute pressure of 41.15 psi.
Why is one atmosphere 14.6959 psi rather than something rounder?
Because these two units were fixed independently and never negotiated with each other. The atmosphere was set to match a 760 mm mercury column; the psi fell out of a pound, a square inch and a legislated value of gravity. Nothing obliged them to line up, so the ratio came out at 14.6959487755. The everyday 14.7 is simply that trimmed to three figures, and the 14.5 you meet just as often belongs to the bar, a different unit again.
How many decimal places are worth keeping?
Two will usually flatter your instrument already. A workshop dial can be read to perhaps half a psi, which is 0.034 atm, so reporting 2.0413789173 atm from a needle sitting near 30 psi claims precision the gauge never had. Keep the long form when the value feeds a further calculation or a calibration record, and round to 2.04 atm for anything you intend to say out loud.