Saturation Vapour Pressure (Magnus / Alduchov–Eskridge)

Air does not "hold" water the way a sponge holds it, and the sponge picture is the source of most confusion about humidity. Water vapour is a gas sharing a container with nitrogen and oxygen, and it exerts its own partial pressure quite independently of them. What temperature sets is the maximum partial pressure that vapour can sustain before it starts condensing back to liquid faster than it evaporates. That ceiling is the saturation vapour pressure, and it is a property of WATER ALONE. The air is not involved. Water saturating into a vacuum at 24 °C reaches the same pressure it reaches into a room.

The relationship is violently non-linear. From 0 °C to 24 °C the saturation pressure climbs from 0.611 kPa to 2.978 kPa — nearly five times — and it roughly doubles for every 11 °C. That single curve explains an enormous amount: why tropical air carries so much more moisture than arctic air, why a small drop in surface temperature makes a window run with condensation, and why the latent load on a coil in Houston dwarfs the one in Calgary at the same relative humidity.

Clausius and Clapeyron give the exact shape thermodynamically, but their equation has no closed-form solution, so everyone uses a fitted approximation. This page implements Alduchov and Eskridge's 1996 refinement of the Magnus form, $p_{ws} = 610.94\exp(17.625t/(t+243.04))$, valid from −40 °C to +50 °C with a stated maximum error of 0.384 %.

Expect the third digit to disagree with your reference, and do not treat that as an error. At least four coefficient sets are in wide circulation: the original Magnus/Tetens (6.1078 hPa, 17.27, 237.3), Buck's 1981 set, the WMO/Sonntag set that this catalog's dew-point page uses, and the Alduchov–Eskridge set here. At 24 °C they give roughly 2978 to 2985 Pa. A psychrometric chart drawn from the IAPWS reference formulation will read 2.985 kPa where this page reads 2.978 — a gap of 0.23 %, which is far smaller than the error in reading a sling psychrometer and far smaller than the difference between two thermometers on the same wall. What matters is knowing which fit you are quoting, and this one says so.

One trap worth naming. Below 0 °C this curve is saturation over SUPERCOOLED LIQUID WATER, which is what psychrometric charts tabulate. Saturation over ice is lower — about 4 % lower at −10 °C — and that gap is exactly why frost grows on a cold surface while surrounding droplets stay liquid: the ice is a lower-pressure sink, so vapour migrates to it. If your problem is a freezer coil, a frost line or an outdoor coil in a defrost cycle, you want the sublimation curve and different coefficients, not this one.