Wind Instrument Length Calculator
The pitch of a wind instrument comes from a standing wave in a column of air, and the length of that column sets the note. A pipe open at both ends sounds a fundamental of the speed of sound divided by twice its length; a pipe stopped at one end sounds an octave lower, the speed of sound over four times its length. This calculator takes a target frequency, the speed of sound (editable for temperature), and an end factor (2 for open, 4 for closed) and returns the ideal air-column length in metres, centimetres, and inches, plus the resonant wavelength. Use it to size flutes, organ pipes, and other tubes.
Air column formula
Wavelength = speed of sound / frequency
Length = speed of sound / (end factor * frequency)
Open pipe end factor = 2; closed pipe end factor = 4
Centimetres = length * 100; inches = length / 0.0254
This gives the ideal acoustic length with no end correction. The speed of sound is editable so you can match the air temperature; warmer air raises the speed and the pitch.
Wind instrument context
- Speed of sound is about 343 m/s at 20 degrees C, rising roughly 0.6 m/s per degree.
- Open pipes (flute) sound an octave higher than closed pipes (clarinet) of the same length.
- Closed pipes emphasise odd harmonics, giving a distinct timbre.
- Real pipes need a small end correction; the bore is a little shorter than this acoustic length.
- Conical and flared bores deviate from the simple cylindrical pipe model.
Air column length: frequently asked questions
How does pipe length set the pitch?
A vibrating air column resonates at a wavelength fixed by its length and which ends are open. For a pipe open at both ends the fundamental wavelength is twice the length; for a pipe closed at one end it is four times the length. The frequency is the speed of sound divided by that wavelength.
What is the difference between an open and a closed pipe?
An open pipe, open at both ends like a flute, sounds a fundamental of speed of sound over twice the length. A closed pipe, stopped at one end like a clarinet, sounds an octave lower for the same length, speed of sound over four times the length, and produces mainly odd harmonics.
What speed of sound should I use?
The speed of sound in air is about 343 metres per second at 20 degrees Celsius, rising by roughly 0.6 metres per second per degree. It is a user-editable input here, so you can enter the value for your temperature, since a warm instrument plays slightly sharp.
Does this account for end correction?
No. Real pipes resonate as if slightly longer than their physical length because the air just outside an open end also moves. This end correction is small but matters for precise instrument making. The calculator gives the ideal acoustic length; subtract an end correction to get the bore length.
Can I use this for organ pipes and didgeridoos?
Yes, as a first approximation. Organ flue pipes come in open and stopped (closed) forms that follow these relations, and a didgeridoo behaves roughly as a closed pipe. Conical and flared bores differ from a simple cylinder, so treat the result as a cylindrical-pipe estimate.
Official sources
- UNSW School of Physics: Pipes and harmonics.
- UNSW School of Physics: Music acoustics.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.