Note Frequency Calculator

Frequently Asked Questions

How is a note's frequency calculated?

In 12-tone equal temperament, f = A4 × 2^(n/12), where n is the number of semitones from A4. With A4 = 440 Hz, A5 = 880 Hz and A3 = 220 Hz (one octave doubles or halves frequency).

What is A4 = 440 Hz and can I change it?

A4 (the A above middle C) at 440 Hz is the modern concert pitch standard (ISO 16). Some orchestras tune to 442–443 Hz, and historical/Baroque tuning uses 415 Hz. The calculator lets you set this reference.

What is equal temperament?

12-TET divides the octave into 12 equal semitones, each a frequency ratio of 2^(1/12) ≈ 1.0595. It makes every key equally usable at the cost of slightly impure intervals compared to just intonation.

What frequency is middle C?

Middle C (C4) is about 261.63 Hz at A4 = 440 Hz. It sits 9 semitones below A4: 440 × 2^(−9/12) ≈ 261.63 Hz.

Provided by AllCalculators.io
Free online calculators for everyday. No registration required.

Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

JavaScript is required to use the interactive calculator above. The questions and answers below remain readable without JavaScript.

How This Calculator Works

Every pitch on a piano corresponds to a precise frequency in hertz. This calculator converts a note name and octave into that frequency using twelve-tone equal temperament (12-TET), the tuning system used by virtually all modern instruments. The reference is the concert pitch A above middle C - A4 - conventionally 440 Hz but adjustable here (orchestras sometimes use 442 or 443 Hz, and historically-informed ensembles use 415 Hz). From A4 the calculator counts how many semitones away your chosen note sits and applies the equal-temperament ratio. It also returns the MIDI note number (a single integer identifying the pitch in software and hardware), the waveform period in milliseconds, and the acoustic wavelength in air, which tells you how big a resonator or room mode for that note really is. This single conversion sits behind a huge range of practical tasks: tuning a synth oscillator to a known pitch, setting a notch filter on the exact frequency of a hum, building a test tone, or sanity-checking a tuner that seems off. Doing it from the equation rather than a lookup table also lets you instantly explore non-standard reference pitches, which a fixed chart cannot.

Formula / Method

In 12-TET each octave is split into twelve equal ratio steps, so one semitone multiplies frequency by the twelfth root of two, 2^1÷12 ≈ 1.059463. The frequency of a note n semitones from A4 is f = ref × 2^{(n ÷ 12)}. The MIDI number is computed as (octave + 1) × 12 + pitch-class index, where C has index 0 and B has index 11, giving middle C (C4) = 60 and A4 = 69. The semitone distance is simply MIDI − 69. Period in milliseconds is 1000 ÷ f, and wavelength is the speed of sound (about 343 m/s at 20°C) divided by f.

Worked Example

Take A4 with the default 440 Hz reference. It is 0 semitones from A4, so f = 440 × 2⁰ = 440 Hz exactly, MIDI 69, period 1000 ÷ 440 ≈ 2.27 ms, wavelength 343 ÷ 440 ≈ 0.78 m. Now C5: it is 3 semitones above A4, so f = 440 × 2^3÷12 = 440 × 1.1892 ≈ 523.25 Hz, MIDI 72. Lower the reference to 432 Hz and every note scales by 432÷440 ≈ 0.982, so A4 becomes 432 Hz and C5 about 513.7 Hz - the same intervals, shifted globally.

Common Mistakes

Mixing octave conventions: this tool uses the scientific standard where middle C is C4 (MIDI 60); some software calls middle C C3 or C5.

Assuming sharps and flats differ - in 12-TET C# and Db are the same frequency (enharmonic equivalents).

Forgetting that just intonation gives slightly different frequencies than equal temperament; a 12-TET major third is about 14 cents sharp of pure.

Treating the A4 reference as fixed at 440 - period instruments and some orchestras use other values.

Comparing this to an instrument that is not actually in tune - check the tuner first.

Tips & FAQ

Why does each octave double the frequency? Doubling frequency is a 2:1 ratio, the most consonant interval, which is why notes an octave apart share a name. What is the 432 Hz debate? Some people prefer a 432 Hz reference for tonal reasons; the math here lets you test it instantly - it is purely a global shift, not a different scale. Why report wavelength? A low E1 (about 41 Hz) has a wavelength over 8 metres, which is why bass frequencies excite room modes and are so hard to tame acoustically; high notes have wavelengths of centimetres. How accurate is the MIDI number? It is exact and integer for the twelve named pitches; pitch-bend or microtonal tuning adds a fractional offset on top.

Frequently Asked Questions

Related Music Calculators