Note Frequency Calculator: Convert Notes to Hertz

A note frequency calculator converts a musical pitch—usually a note name and octave, or a frequency in hertz—into its equivalent frequency or nearest note. Enter the note’s equal-tempered semitone position or its frequency; the calculator returns the corresponding frequency in hertz.

Formula

The calculator uses the standard equal-tempered tuning formula, with A4 set to 440 Hz:

f = 440 × 2^n/12

• f is the note frequency in hertz (Hz), or cycles per second.
• n is the number of semitones above A4. A positive value is higher; a negative value is lower.

The additional outputs are useful for understanding the sound wave. Wavelength is estimated as λ = c/f, using a sound speed of 343 metres per second in air near room temperature. Period is T = 1/f, converted from seconds to milliseconds. The air wavelength is an estimate, not a universal value: sound speed changes with the medium and conditions.

Worked Example

With the default input, n = 0 semitones, the calculator evaluates A4:

1. Frequency: 440 × 2^0/12 = 440 × 1 = 440.00 Hz.
2. Wavelength in air: 343 ÷ 440 = 0.780 m.
3. Cycle period: 1000 ÷ 440 = 2.273 ms.

These are the results for the default values, rounded to the displayed precision.

How Note Frequency Is Calculated

In equal temperament, an octave contains 12 equal frequency steps called semitones. Each semitone multiplies frequency by the twelfth root of 2, approximately 1.05946. After 12 steps, the frequency doubles: 440 Hz becomes 880 Hz. Moving down 12 semitones halves it to 220 Hz.

A note name and octave can be converted into the calculator’s input by counting semitones from A4. For example, A5 is 12 semitones above A4, so its frequency is 880 Hz. A3 is 12 semitones below A4, giving 220 Hz. Middle C, commonly written C4 in scientific pitch notation, is nine semitones below A4: 440 × 2^−9/12, about 261.63 Hz.

Frequency is measured in hertz. A frequency of 440 Hz means that the sound wave completes 440 cycles each second. Musical pitch is related to frequency, but a sound’s timbre and loudness are separate properties. A pure tone and a complex instrument tone can share a fundamental frequency while sounding very different.

Using the Calculator and Reading Results

Enter a semitone offset from A4. Use zero for A4, 12 for A5, and −12 for A3. Fractional semitone values are valid for pitches between the standard equal-tempered notes; for instance, 0.5 represents a pitch halfway between A4 and the next semitone in equal-tempered pitch space.

• Use the frequency output when tuning, comparing pitches, or setting a synthesizer tone.
• Use wavelength to relate a frequency to the physical distance of one wave cycle in air. It is not the distance a sound travels in one second.
• Use period to see how long one complete cycle takes. Higher frequencies have shorter periods.

For US customary units, convert the wavelength in metres to feet by multiplying by 3.28084, or to inches by multiplying by 39.3701. The frequency remains in hertz in either unit system. The period output is in milliseconds; 1 millisecond is 0.001 second.

Tuning Standards and Detuning

The calculator assumes A4 = 440 Hz, a widely used reference for modern equal-tempered tuning. It does not imply that every performance or instrument uses that reference. A musician or ensemble may tune to a different A4 value, and historical or alternative tuning systems may use different pitch relationships.

To calculate a note against another reference frequency, use the generalized formula f = f_ref × 2^n/12, where f_ref is the chosen reference pitch and n is the semitone distance from it. This page’s calculator fixes the reference at 440 Hz, so its output will differ from a setup using another reference.

Small deviations from equal-tempered pitches are often expressed in cents. One semitone equals 100 cents, so a difference of 25 cents is one quarter of a semitone. A frequency ratio r corresponds to 1200 × log₂(r) cents. This is useful when comparing a measured instrument pitch with a target note; the calculator itself reports the exact equal-tempered frequency rather than a measured deviation.

Common Mistakes and Limitations

• Confusing note labels: Octave numbering conventions can differ between software and instruments. Check what a tuner means by labels such as C4 or C5 before entering an offset.
• Mixing semitones and cents: Enter semitones, not cents. Divide a cents offset by 100 to express it in semitones.
• Assuming every tuning is equal temperament: The formula gives equal-tempered pitches. It does not calculate just intonation or other systems unless their specific ratios are supplied.
• Treating rounded results as exact: Displayed decimals are rounded. Calculations and audio equipment may use greater precision.
• Taking wavelength as fixed: The wavelength output assumes a sound speed of 343 m/s. Temperature, humidity, and the propagation medium affect sound speed.

The formula describes the ideal frequency associated with a pitch position. A real instrument can be sharp or flat, and a recorded or noisy sound may not have one stable frequency. For an actual sound, a frequency analyzer or tuner measures the signal; this calculator provides a target or mathematical conversion.

Frequently Asked Questions

What frequency is A4?
A4 is 440 Hz when using the reference assumed by this calculator. It is the standard starting point for the semitone-offset formula shown here.

What is the frequency of middle C?
In scientific pitch notation, C4 is nine semitones below A4. At A4 = 440 Hz in equal temperament, C4 is approximately 261.63 Hz.

How do I convert hertz to a note?
For a frequency f referenced to A4 = 440 Hz, calculate n = 12 × log₂(f/440). The nearest whole semitone identifies the closest equal-tempered pitch; the remainder describes how far it is from that pitch.

Does changing the octave double the frequency?
Yes, in equal temperament an octave up doubles frequency, and an octave down halves it. For example, A4 at 440 Hz and A5 at 880 Hz are one octave apart.

Why might my tuner show a different frequency?
The instrument may be detuned, the tuning reference may not be 440 Hz, or the sound may contain noise and harmonics that affect measurement. Confirm the tuner’s reference setting and compare the fundamental pitch.

Related

• Convert Nanoseconds to Hertz: The Reciprocal Formula
• Gaussian Beam Focus Calculator in Python
• Seconds to Hz Converter: Formula and Examples

in n | Semitones from A4 | semitones | 0 | - | 
out frequency | Note frequency | Hz | 440 * 2^(n / 12) | 2
out wavelength | Wavelength in air | m | 343 / frequency | 3
out period | Cycle period | ms | 1000 / frequency | 3