Magnus formulae:At a temperature t (in °C), the saturation vapour pressure ew(t), in pascals, over liquid water, is

ln ew(t) = ln 611.2 + (17.62 t)/(243.12+t)

(ew(t), is in pascals (Pa): 100 Pa = 1 millibar (mbar))

For the range -45 °C to +60 °C, values given by this equation have an uncertainty of less than ±0.6 percent of value, at the 95% confidence level.

Over ice, ei(t) is

ln ei(t) = ln 611.2 + (22.46 t)/(272.62+t)

For the range -65 °C to +0.01 °C, values given by this equation have an uncertainty of less than ±1.0 percent of value, at the 95% confidence level.

A more accurate but complex alternative formula for vapour pressure (in pascals) from dew point (in kelvin) is as follows for water

ln ew(T) = -6096.9385 T-1 + 21.2409642 - 2.711193×10-2 T + 1.673952×10-5 T2 + 2.433502 ln T

and for ice

ln ei(T) = -6024.5282 T-1 + 29.32707 + 1.0613868×10-2 T - 1.3198825×10-5 T2 - 0.49382577 ln T

But who can be bothered with all of that?

I prefer to use established government sites for such things, try these two links:

Relative Humidity CalculatorMeasuring Humidity