Use the inputs below, then press Calculate.
End correction adjusts the physical length to an effective length that better matches acoustic boundary conditions.
- ΔL_end = k · r
- ΔL_total = N_open · (k · r) + ΔL_inside
- L_eff = L + ΔL_total
- If frequency is enabled:
- f₁ = v / (2·L_eff) for open–open tubes
- f₁ = v / (4·L_eff) for open–closed tubes
Here, r is the tube radius or an equivalent radius for non-circular sections.
- Enter the tube physical length and choose the output unit.
- Select a geometry mode and provide the needed dimensions.
- Choose a termination type, or enter a custom coefficient.
- Select how many ends are open for radiation correction.
- Optionally add an inside-end correction for cavity necks.
- Enable frequency if you want a resonance estimate.
- Press Calculate to view results above the form.
| Case | Physical length (m) | Radius (m) | k | Open ends | Total correction (m) | Effective length (m) |
|---|---|---|---|---|---|---|
| A | 0.300 | 0.015 | 0.61 | 2 | 0.0183 | 0.3183 |
| B | 0.500 | 0.020 | 0.85 | 1 | 0.0170 | 0.5170 |
| C | 0.250 | 0.010 | 0.61 | 1 | 0.0061 | 0.2561 |
Values are illustrative and depend on termination details.
1) End correction length in acoustic design
When a tube is open to the surrounding air, the pressure node does not occur exactly at the physical rim. The oscillating air just outside the opening adds an effective “radiating” mass, so the tube behaves as if it is slightly longer. This extra length is called end correction and is essential in tuning pipes, ducts, and musical wind instruments.
2) Physical meaning and boundary behavior
At an open end, particle velocity is high and pressure is low, but the transition from confined flow to free radiation is gradual. The flow lines bulge outward, increasing the participating air volume. End correction models this non-ideal boundary so the predicted standing-wave pattern matches measured resonance.
3) Typical coefficients and common data
A widely used approximation for an unflanged circular opening is k ≈ 0.61, giving ΔL ≈ 0.61·r per open end. For a flanged termination, values near k ≈ 0.85 are often used. This tool includes alternate presets (0.60, 0.82) to cover different published conventions and edge details.
4) Geometry inputs and equivalent radius
The calculator accepts radius, diameter, area, or rectangular width×height. For non-circular sections, it computes an equivalent circular radius from equal area: r = √(A/π). This is practical for first-order modeling, especially when the acoustic field is close to uniform across the opening.
5) How correction changes effective length
Total correction scales with the number of open ends: ΔL_total = N_open·(k·r). For example, with r = 0.015 m and k = 0.61, each end adds 0.00915 m. With two open ends, the tube behaves roughly 0.0183 m longer, which is large enough to shift pitch noticeably.
6) Resonance frequency implications
Once the effective length L_eff is known, the fundamental resonance can be estimated. For an open–open tube, f₁ = v/(2·L_eff); for open–closed, f₁ = v/(4·L_eff). Using v = 343 m/s near room conditions, a small correction can move frequency by several percent for short tubes.
7) Inside-end corrections for cavity necks
Some setups include a neck that opens into a larger cavity (such as cavity resonators). In such cases, an additional inside-end correction is often applied once, modeled here as ΔL_inside = k_inside·r. Selecting this option helps you represent the extra inertial length at the junction without altering the number of external open ends.
8) Practical accuracy and best use
End correction depends on edge thickness, baffle size, flow losses, and frequency range. For best results, match the termination type, keep units consistent, and compare against a measured resonance when possible. Treat the coefficient as a tunable parameter if your geometry is unusual, and document the chosen k for reproducible design work.
1) What does “end correction” represent?
It represents extra acoustic length caused by air motion outside an opening. The tube behaves longer than its physical length because the oscillating air near the rim contributes inertia and shifts the pressure node outward.
2) Which coefficient should I choose for k?
Use about 0.61 for a typical unflanged circular opening and about 0.85 for a flanged opening. If you have reference data for your exact edge shape, select custom and enter that coefficient.
3) How many ends should be counted as “open”?
Count only the ends that radiate to open air. If one end is closed, choose 1 open end. If both ends are open, choose 2. Closed ends usually do not need the same correction.
4) Can I use this for rectangular ducts?
Yes. Enter width and height to compute an equivalent radius from equal area. This gives a practical first estimate. For high-accuracy duct acoustics, compare against measurements or use a specialized duct model.
5) Why does correction matter more for short tubes?
The correction is proportional to radius, but its impact is relative to length. When L is small, a few millimeters of correction can be a large fraction of L, shifting resonance frequency noticeably.
6) What speed of sound should I use for frequency?
A common value is 343 m/s near 20°C in dry air. Higher temperature increases speed of sound. If you know local conditions, enter a measured or computed value for better frequency estimates.
7) When should I add an inside-end correction?
Add it when a neck opens into a cavity or large volume, where the junction adds inertial length. It is applied once in this calculator, in addition to any external open-end corrections.