Instrument Tuning Frequency Calculator

Work out instrument tuning frequency instantly with clear inputs, formula shown and shareable results.

About Instrument Tuning Frequency Calculator

Equal temperament sets frequency as the reference pitch times two to the power of total cents over twelve hundred, where each semitone is exactly one hundred cents. A five cent offset is about the smallest most listeners notice on a sustained note, which is why tuners are calibrated in cents rather than hertz.

Formulas

Frequency

f = A4 x 2 ^ ((semitones x 100 + cents) / 1200)

Wavelength

wavelength = speed of sound / frequency, taking 343 m/s at 20 C

Worked example

With the default values below, Instrument Tuning Frequency Calculator returns Frequency of 524.7645. Change any input above and every figure here is recalculated in your browser.

Inputs used

Semitones from A4accepts -60–60: 3
Reference pitch for A4accepts 300–500 Hz: 440 Hz
Cents offsetaccepts -100–100: 5

Results

Frequency: 524.7645 Hz
Wavelength in air at 20 C: 0.6536 m
Period: 1.9056 ms
Frequency ignoring the cents offset: 523.2511 Hz

Step by step

1Values used
2Frequency
3Wavelength
4Frequency= 524.7645 Hz
5Wavelength in air at 20 C= 0.6536 m
6Period= 1.9056 ms
7Frequency ignoring the cents offset= 523.2511 Hz

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Instrument Tuning Frequency figure worked out?

f = A4 x 2 ^ ((semitones x 100 + cents) / 1200). Equal temperament sets frequency as the reference pitch times two to the power of total cents over twelve hundred, where each semitone is exactly one hundred cents.

Why does this matter?

A five cent offset is about the smallest most listeners notice on a sustained note, which is why tuners are calibrated in cents rather than hertz.

What do I need to enter?

Enter semitones from a4, reference pitch for a4, cents offset. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.