Pipe Organ Frequency Calculator
Convert between organ pipe physical length and pitch for both open and stopped pipes. Includes end-correction physics, harmonic content, nearest-note identification, and a rank context table (32′ / 16′ / 8′ / 4′ / 2′ / 1′).
Input
Result
Rank context (same diameter, transposed by foot pitch)
| Rank | Required length | Resulting pitch |
|---|
"Foot pitch" is the conventional organ-builder label. An 8′ rank's low C plays at unison pitch (C2 ≈ 65.4 Hz); a 16′ rank's low C plays one octave lower, a 4′ rank one octave higher, etc.
About Organ Pipe Acoustics
This pipe organ frequency calculator converts between organ pipe physical length and the pitch it produces — the same acoustic physics that governs flutes and clarinets, scaled up by 100×. Two main families dominate: open flue pipes (open at both ends, like the Diapason / Principal / Gemshorn) and stopped flue pipes (one closed end, like the Bourdon / Gedackt / Lieblich Gedact). Reed pipes — Trumpet, Tromba, Regal — use a separate physics where a vibrating brass tongue drives the air column, and aren't covered by this tool. To see how the general tube resonance formula applies across different media and boundary conditions, also explore the acoustic resonance frequency calculator.
Open pipes
Both ends are pressure nodes — the standing wave fits an integer number of half-wavelengths between the ends. Fundamental: f₁ = c / (2·L_eff). All integer harmonics are present (1f, 2f, 3f, …), giving the classic bright "open flute" timbre.
Stopped pipes
One open end (pressure node), one closed end (pressure antinode). The standing wave fits an odd number of quarter-wavelengths between them. Fundamental: f₁ = c / (4·L_eff) — exactly an octave below the equivalent open pipe of the same length. Only ODD harmonics exist (1f, 3f, 5f, …), giving the characteristic hollow, "stopped flute" timbre. This is why a 16′ stopped rank takes only 8 feet of pipe — a major space savings for the bass register.
End correction
Air doesn't stop exactly at an open end — it "bulges" outward slightly, creating an acoustic impedance mismatch that increases the effective resonating length. The effective acoustic length is longer than the physical organ pipe length by ~0.6·r per open end (Levine-Schwinger, unflanged). An 8′ open pipe at 2.44 m with 100 mm diameter has L_eff = 2.44 + 1.2·0.05 = 2.50 m, lowering the predicted pitch by about 4%. Without end correction, a 2.44 m open pipe predicts 70.3 Hz; with correction, 68.6 Hz — close to but not exactly C2 (65.4 Hz). Real organ pipes are tuned by sliding tuning sleeves or cutting slots; the calculator's prediction is a starting point. To visualise the standing wave mode shapes inside the pipe, see the standing wave calculator, which renders the pressure and displacement profiles for both open and stopped boundary conditions.
Rank conventions (foot pitch)
Organ builders label ranks by the physical length of the C below middle C. An 8′ rank has its low C at approximately 8 feet (its C2 plays at the keyboard's C2 pitch — "unison"). Other rank conventions:
- 32′: two octaves below 8′ (lowest pedal stops, only in large organs)
- 16′: one octave below 8′ (typical pedal voice)
- 8′: unison (most ranks)
- 4′: one octave above 8′
- 2′: two octaves above 8′
- 1′: three octaves above 8′
- 5⅓′, 2⅔′, 1⅗′: mutation stops at non-octave intervals (a fifth, twelfth, seventeenth)
Frequently Asked Questions
Why is a stopped 16′ rank only 8 feet long?
c / (4·L_eff) instead of c / (2·L_eff) — exactly half the frequency of an open pipe of the same length. So a stopped pipe sounds one octave lower than the open pipe twice its size. An 8-foot stopped pipe plays the same low C as a 16-foot open pipe. The trade-off: stopped ranks only produce odd harmonics, giving a hollower timbre. Space-saving for cathedral organs that need huge 32′ pedal stops.Why does temperature affect tuning so dramatically?
√T (Kelvin). A church warms from 15 °C in winter to 25 °C in summer: c goes from 340 to 346 m/s, a 1.8% change = 31 cents (~⅓ semitone). The organ goes flat as it cools. Modern installations include heating control to stabilize this; period organs were tuned to play at concert temperature.