End Correction Length Calculator

Calculator

Use the fields below to estimate end correction, effective acoustic length, and resonance behavior for cylindrical tubes and air columns.

Measurement unit

Physical tube length

Inner diameter

End A type

End B type

Custom coefficient for End A

Custom coefficient for End B

Air temperature (°C)

Mode number

Measured frequency (Hz) Optional

Reset

Example Data Table

These examples show typical cylindrical air-column cases using standard end-correction coefficients.

Case	Physical Length (m)	Diameter (m)	End A	End B	Total Correction (m)	Effective Length (m)	Approx. Fundamental (Hz at 20°C)
Open lab tube	0.50	0.030	Open unflanged	Open unflanged	0.01830	0.51830	331.29
Flanged mouth pipe	0.50	0.030	Open flanged	Closed	0.01230	0.51230	167.59
Wide flanged tube	0.75	0.050	Open flanged	Open flanged	0.04100	0.79100	217.08

Formula Used

1) Radius from diameter
r = d / 2

2) End correction for each open end
ΔL = k × r
Here, k ≈ 0.61 for an unflanged open end and k ≈ 0.82 for a flanged open end.

3) Effective acoustic length
L_eff = L + ΔL_A + ΔL_B

4) Speed of sound in air
c = 331.3 + 0.606T
where T is temperature in °C.

5) Resonance frequency
For open–open or closed–closed tubes:
f_n = n c / (2L_eff)

For open–closed tubes:
f_n = (2n - 1)c / (4L_eff)

These equations are standard approximations for cylindrical tubes in air and are most accurate when losses and complex edge geometry are small.

How to Use This Calculator

Select the unit you want to work in.
Enter the physical tube length and inner diameter.
Choose the termination style for End A and End B.
Use custom coefficients if your setup was calibrated experimentally.
Enter air temperature to adjust the speed of sound.
Set the mode number you want to evaluate.
Optionally enter a measured frequency to infer an effective length.
Press Calculate to show results above the form, view the graph, and export CSV or PDF files.

FAQs

1) What is end correction length?

End correction is the extra acoustic length added beyond a tube’s physical opening. The vibrating air extends slightly outside an open end, so the standing wave behaves as if the tube were longer.

2) Why do open ends need correction?

At an open end, the displacement antinode does not sit exactly at the tube edge. The oscillating air mass just outside the pipe stores energy, shifting the effective boundary outward.

3) What values are commonly used for the coefficient?

A common approximation is 0.61 times the radius for an unflanged opening and 0.82 times the radius for a flanged opening. Real setups can vary slightly with geometry and frequency.

4) Does tube diameter change the correction?

Yes. End correction scales with radius, so larger diameters produce larger corrections. Two tubes with the same physical length can have different effective lengths if their diameters differ.

5) How do open–open and open–closed tubes differ?

Open–open tubes allow all integer modes. Open–closed tubes support only odd harmonics. That changes the resonance formula and shifts the frequency pattern for the same effective length.

6) Can I estimate correction from a measured frequency?

Yes. If you know the mode and boundary condition, the measured resonance can be inverted to estimate the effective length. Subtracting the physical length gives an inferred total correction.

7) Why does temperature matter?

The speed of sound in air increases with temperature. Since resonance frequency depends directly on sound speed, warmer air usually produces a higher frequency for the same tube.

8) When should I use a custom coefficient?

Use a custom coefficient when your opening geometry is unusual, when fittings alter the boundary, or when experimental calibration gives a better value than the standard unflanged or flanged approximation.