Everything in psychrometrics is measured against one curve: how much water vapour air can hold before it starts giving it back. That ceiling is the saturation vapour pressure, and it depends on temperature and on nothing else — not on how much air there is, not on the barometer, not on the wind.

This page uses the Alduchov–Eskridge Magnus fit: $p_{ws} = 610.94\exp\!\left(\dfrac{17.625\,t}{t + 243.04}\right)$, with $p_{ws}$ the saturation vapour pressure in pascals and $t$ the temperature in °C. The 610.94 is the saturation pressure at 0 °C — set $t = 0$ and the exponential becomes 1, which is a satisfying way to check you have typed it correctly. It is published for −40 °C to +50 °C and is good to about 0.4 % across that band.

An honest warning you will meet on a real job. Several coefficient sets are in circulation — Magnus/Tetens, Buck, the WMO's Sonntag set — and they disagree in the THIRD significant figure. At 24 °C they give roughly 2 978 to 2 985 Pa. A chart that disagrees with your calculator in the third digit is not wrong and neither are you; you are quoting different fits to the same physics, and the gap is far smaller than the error in reading a sling psychrometer.

The one thing to feel in your bones is the SHAPE. This is an exponential, not a line. Saturation pressure roughly doubles every 10 or 11 degrees — about 1.2 kPa at 10 °C, 2.3 kPa at 20 °C, 4.2 kPa at 30 °C. Warm air holds dramatically more water than cool air, and every sweating pipe, every dry January and every cooling coil in the world is a consequence of that one curve.