Semitone to frequency
Equal temperament divides the octave into twelve equal ratios, each the twelfth root of two — about 1.05946. Twelve of them multiply to exactly two, which is the octave. It is a deliberate compromise: no interval except the octave is perfectly in tune, but every key sounds equally acceptable, which is what made modulation between keys practical.
Each semitone multiplies frequency by the twelfth root of two, about 1.05946. Three semitones above A440 is 523.25 Hz — middle C. Twelve semitones doubles the frequency exactly, giving the octave.
How to calculate note frequencies
The reference pitch itself is a convention that has moved considerably. A440 was only standardised internationally in 1955; baroque ensembles commonly play at 415, a full semitone lower, and some orchestras tune to 442 or 443 for a brighter sound. The 432 Hz tuning that circulates online has no historical or acoustic basis despite the claims made for it — but it is a valid reference like any other, and the field here accepts it.
Questions
f = reference × 2^(semitones ÷ 12). Twelve semitones doubles the frequency.