Note Frequency Calculator

Pitch, frequency, and what this calculator does

Every musical note corresponds to a frequency: how many times per second a sound wave repeats. Frequency is measured in Hertz (Hz). Higher notes have higher frequencies; lower notes have lower frequencies.

This note frequency calculator converts a note name (like C, F#, A#) and an octave number into an estimated frequency in Hz using the most common modern tuning system:

• 12-tone equal temperament (12‑TET): the octave is divided into 12 equal semitone steps.
• Reference pitch A4 = 440 Hz: the note A in octave 4 is defined as 440 Hz, and all other notes are derived from it.

Because the calculator follows a standard mathematical model, it’s useful for tuning instruments, programming synthesizers, mapping MIDI notes, or studying music theory.

Equal temperament: why the “twelfth root of 2” shows up

An octave means doubling the frequency. For example, A4 is 440 Hz and A5 is 880 Hz. In 12‑TET, an octave is divided into 12 equal steps, so each semitone multiplies the frequency by the same constant ratio:

Semitone ratio = 2^1/12 ≈ 1.059463.

So moving up by 1 semitone multiplies frequency by 2^1/12, and moving down by 1 semitone divides by the same amount.

Core formula (with MathML)

If a note is n semitones away from A4, then its frequency is:

Where:

• f is the frequency in Hz
• n is the number of semitone steps from A4 (positive = above A4, negative = below A4)

How we compute n from note name + octave

To turn a note like “C5” into a semitone distance from A4, we can assign each note a position within the octave. This calculator uses the common mapping below (sharps only):

In this indexing, A has index 9. That means the semitone distance from A within the same octave is:

• (noteIndex − 9)

Then we account for octave shifts. Each octave changes pitch by 12 semitones. Using A4 as the reference octave:

• n = (noteIndex − 9) + 12 × (octave − 4)

Interpreting the result

The output is the theoretical frequency for that note in 12‑TET with A4 set to 440 Hz. In practice:

• Instrument tuning varies (a piano may be stretched; a guitar may not be perfectly tempered across frets).
• Performance varies (vibrato, bends, intonation adjustments).
• Rounding: for display, results are typically rounded (for example to 2 decimals). If you need more precision (synthesis / DSP), use more decimal places.

Worked example (C5)

Let’s compute the frequency of C5 step by step.

1. Find the note index: C has index 0.
2. Compute semitone distance within the octave: noteIndex − 9 = 0 − 9 = −9.
3. Account for octave: octave − 4 = 5 − 4 = 1; so add 12 × 1 = 12.
4. Combine: n = −9 + 12 = 3.
5. Frequency: f = 440 × 2^(3/12) ≈ 523.25 Hz.

This matches the commonly cited value for C5 in standard tuning.

Quick reference comparison table (common notes)

The table below gives a small reference set (rounded to 2 decimals) for A4 = 440 Hz. Use it to sanity-check results or tune by ear.

Using the calculator (tips)

• Select a note (this tool lists sharps; flats are enharmonic equivalents—see limitations below).
• Choose an octave. With the common “scientific pitch notation,” middle C is C4.
• Press Calculate Frequency to see the result in Hz and optionally copy it.

Limitations and assumptions (important)

• Temperament: Assumes 12‑TET. Just intonation, meantone, Pythagorean tuning, etc. will produce different frequencies for many notes.
• Reference pitch: Assumes A4 = 440 Hz. Some ensembles use 415 Hz (Baroque), 432 Hz, 442 Hz, etc.
• Note naming: The selector uses sharps (C#, D#, F#, G#, A#). Enharmonic flats are equivalent in 12‑TET (e.g., D# = Eb), but are not shown as separate options.
• Octave convention: Assumes the common convention where C4 is middle C. Some software/synths label octaves differently.
• Real instruments: Actual produced pitch can differ due to intonation, stretch tuning, temperature, string stiffness, and playing technique.
• Displayed rounding: Results are rounded for readability; use higher precision if needed for DSP or scientific work.

Related tools

If you’re working with rhythm and time-based effects, you may also like the Metronome Tempo Progression Planner and the Tempo Delay Calculator.