The idea
In 12-tone equal temperament, each semitone multiplies frequency by the twelfth root of two. An octave doubles frequency. With A4 at 440 Hz, A5 is 880 Hz and A3 is 220 Hz. These relationships do not depend on the loudness of the sound.
Try it
Choose MIDI 69, a 440 Hz A4 reference and an input of 440 Hz. The calculation gives A4 with zero cents deviation. MIDI 60 corresponds to C4, around 261.626 Hz. MIDI note naming uses this convention; some software labels the octave differently.
What to watch for
This calculator takes a frequency you enter; it does not analyze a microphone or recording. A complex instrument tone contains many partials, and an entered overtone may identify a different note from the fundamental. Other tuning systems can give different frequencies for the same note name.
Next step
Download the CSV table to inspect MIDI 12–119 and the selected reference frequency. Compare a few values with a synthesizer that uses equal temperament and the same A4 reference.