Dew point formula from air temperature and relative humidity
Start by finding saturation vapor pressure at air temperature T. Multiply by RH/100 to find actual vapor pressure e, then invert the same curve to find dew point Td.
e = es(T) × RH / 100; Td = 237.3log10(e/611) / (7.5 − log10(e/611))Magnus equation constants used by the dew point formula
This site expresses saturation vapor pressure as es(T) = 611 × 10^(7.5T / (237.3 + T)), with T in degrees Celsius and pressure in pascals. The 611 Pa reference pressure, coefficient 7.5, and 237.3°C temperature constant define the curve used by all three moisture calculations.
Other reputable calculators may use a natural-log form or a slightly different Magnus coefficient set. Those forms describe the same vapor-pressure relationship but can differ by a few tenths of a degree after rounding, especially near the edge of their intended temperature range.
Relative humidity formula from temperature and dew point
Dew point identifies the actual vapor pressure. Air temperature identifies the saturation vapor pressure. Their pressure ratio gives the relative humidity percentage.
RH = 100 × es(Td) / es(T)Air temperature formula from dew point and relative humidity
Divide the vapor pressure at dew point by RH/100 to recover saturation vapor pressure at air temperature, then invert the Magnus relationship.
es(T) = es(Td) / (RH / 100); T = f⁻¹(es)Worked dew point calculator example at 20°C and 65% humidity
At 20°C, the estimated saturation vapor pressure is about 2,339 Pa. Multiplying by 65% gives about 1,520 Pa of actual vapor pressure. Inverting the equation gives a dew point near 13.2°C, or 55.8°F.
Dew point formula accuracy, temperature range, and limitations
The Magnus equation is an approximation for common atmospheric calculations, not a universal equation of state. Accuracy depends on the selected constants, whether saturation is defined over liquid water or ice, the temperature range, and the quality of the source measurements.
Below freezing, dew point over liquid water and frost point over ice are related but not identical. For calibrated laboratory, aviation, industrial, or safety-critical work, use the required standard, pressure treatment, coefficient set, and instrument uncertainty rather than assuming every online calculator implements the same convention.
When to use the dew point formula instead of the quick approximation
A common mental estimate subtracts roughly (100 − RH) / 5 from the Celsius air temperature. It can be useful for a quick sense check near moderate humidity, but its error grows in dry or extreme conditions.
Use the full Magnus calculation when comparing observations, evaluating condensation, converting between temperature units, or reproducing a result. The online calculator applies the full equation automatically and exposes the supporting vapor-pressure values.