The idea
A cent is one hundredth of an equal-tempered semitone. It expresses a frequency ratio, not a fixed number of hertz. The deviation formula is 1200 × log2(actual frequency / reference frequency). Positive means sharper and negative means flatter than the selected note.
Try it
Set A4 to 440 Hz and enter 442 Hz as the frequency to identify. The nearest note is A4 and the deviation is about +7.85 cents. Change the A4 reference itself to 442 Hz; the same entered frequency now gives zero cents.
What to watch for
The nearest-note calculation rounds to an equal-tempered semitone, so cents are reported relative to that nearest note. Exactly halfway between two notes is a rounding boundary. A reading near a boundary should be interpreted with the intended note in mind. This is a numeric reference, not an automatic tuner.
Next step
Use the A4 reference agreed by your ensemble. Write it down along with your calculation, or keep the JSON download. When comparing instruments, ensure the measurement method identifies the fundamental frequency.