Help / About
Are you making a set of panpipes for a music lesson or your own project? The Panpipe Playground helps you design a custom set of panpipes and calculate the pipe lengths needed to produce specific musical notes.
How it works
Panpipes are stopped pipes — closed at one end, open at the other. The frequency a pipe produces depends on its length and internal diameter:
f
=
v
4(L + 0.82d)
or, to solve for length:
L
=
v
4f
−
0.82d
f = freq (Hz) ·
v = speed of sound (34,300 cm/s) ·
L = length (cm) ·
d = inner diameter (cm) ·
0.82 = end correction value
If you want to learn more about how this formula works or what the end correction means, click here to find out more.
Usage
- Enter any two of Length, Diameter, and Frequency / Note. Then press Solve to calculate the third.
- The Note field accepts note names like C4 or A#3 and will auto-fill the frequency. There's also a piano key input mode.
- Press Add to draw a pipe, then click any pipe to select it —
edit its values and press Update, or press Delete to remove it.
- The ↕ button shows the usable note range for the chosen diameter.
- Press Preview to hear your pipes played in sequence.
- Press Summary to see a cut list of all pipe lengths.
- Use Presets to save/recall pipes or work on a multi row instrument.
What do I need to make my own?
- Pipe material — bamboo or PVC tubing work well. Try this 15mm pipe which has an 11mm inner diameter.
- A pipe cutter or saw — pipe cutters can be safer for children, and make a neater cut with fewer rough edges that need sanding!
- String, tape, or wire — to bind the pipes together side by side.
- A wood or card strip — on each side to hold the pipes in line. Lollipop sticks work well. These jumbo ones will fit up to 10 pipes with 15mm pipe!
- A stopper — you can often find plastic counters like these that fit 15mm pipe! Glue or stick them on with double sided tape
End Correction
A panpipe tube is a stopped pipe — closed at the bottom and open at the top. When air vibrates inside, the sound wave does not stop exactly at the physical rim of the tube: it extends a short distance into the open air before reflecting back. This means the tube behaves acoustically as though it were slightly longer than its physical cut length. That extra effective length is called the end correction (ΔL).
The formula uses the effective acoustic length, not the cut length alone:
f
=
v
4(L + ΔL)
or, to solve for length:
L
=
v
4f
−
ΔL
A larger end correction means a shorter physical pipe reaches a given pitch; a smaller correction means the pipe must be cut longer. You can override the default by entering a value directly in the End Correction field, but unless you're being really particular you can safely ignore this if you just want to get building something which will work perfectly well enough!
Approaches to calculating end correction
1 — Pure acoustic, unflanged pipe
ΔL ≈ 0.61 × radius = 0.305 × diameter
This is the theoretically correct value for a cylindrical pipe whose open end radiates freely into open air — which is the physical situation for a panpipe tube. It originates from the exact mathematical derivation of Levine and Schwinger (1948) and is confirmed by both Olson (1967) and Fletcher and Rossing (1991). For a 15 mm inner diameter pipe this gives a correction of approximately 0.46 cm.
2 — Pure acoustic, flanged pipe
ΔL ≈ 0.82 × radius = 0.41 × diameter (Olson, 1967) or 0.85 × radius = 0.425 × diameter (Fletcher and Rossing, 1991)
This applies when the open end of a pipe terminates flush with a large flat baffle. A panpipe tube has no such baffle, so this value slightly overestimates the correction. For 15 mm it gives approximately 0.62–0.64 cm. Note that the figure 0.82 here refers to the radius, not the diameter.
3 — Empirical playing rule (used by this app)
ΔL ≈ 0.82 × diameter
This figure appears in the Wikipedia article on pan flute and in practical instrument-making guides. It is approximately 2.7 times larger than the pure acoustic unflanged value and is not a direct reading from any of the academic sources above. It appears to be a composite empirical value that bundles the acoustic end correction with the shortening effect of a player's lips partially covering the tube opening during playing (Wikipedia contributors, no date). For 15 mm it gives approximately 1.23 cm.
This app uses this value by default because in testing I've found it to give the most reliable result when working with improvised materials in the real world. If you want to model the pure acoustics of the tube alone or found an offset that works better with your specific materials, you can enter a custom end correction based on approach 1 or 2 in the End Correction field.
Bore-to-length ratio and tone quality
The ratio of a pipe's internal diameter to its length affects its tone colour. A ratio of 1:10 (diameter = one tenth of length) gives the characteristic panpipe sound. The strict acceptable range is 1:7 to 1:14 (length-to-diameter 7:1–14:1): pipes outside this range produce noticeably reedy results if too wide, or thin and flutey results if too narrow (Wikipedia contributors, no date; confirmed by Fletcher and Rossing, 1991).
This means that ideally tubes of a varying diameter should be used to achieve the best tone quality for each pipe (wider for deeper pitched pipes, and narrower for higher pitched pipes). In practice, hobbyist builders often work with a single pipe diameter across an entire set. This app therefore allows a 20% margin either side of the strict range before raising a warning, giving an effective tolerance of 5.6:1 to 16.8:1. Pipes within this looser range may show slight tonal character differences but will still function as panpipes. The warning highlight is removed automatically if you edit the pipe so that it falls back within the tolerated range.
Testing your pipes
When checking a pipe against a tuner, blow at a steady, gentle pressure. Overblowing drives the air column toward higher harmonics and sharpens the pitch, making a correctly-cut pipe appear out of tune.
References
- Fletcher, N.H. and Rossing, T.D. 1991. The Physics of Musical Instruments. New York: Springer-Verlag.
- Levine, H. and Schwinger, J. 1948. 'On the radiation of sound from an unflanged circular pipe'. Physical Review 73(4): 383–406.
- Olson, H.F. 1967. Music, Physics and Engineering. Second Edition. New York: Dover Publications.
- Wikipedia contributors. 'Pan flute', Wikipedia. https://en.wikipedia.org/wiki/Pan_flute (accessed 15 May 2026).
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