String Harmonic Frequencies Calculator

Estimate harmonics for any stretched string quickly here. Compare overtones across instruments and setups easily. Download tables, verify units, and tune with confidence today.

Enter Inputs

Use the vibrating portion, not the whole string.
Tension strongly affects pitch and harmonics.
Changes which mode numbers are allowed.
Linear density input
Choose μ directly, or compute μ from mass and length.
Typical strings range from 0.001 to 0.02 kg/m.
μ = m / length.
Up to 50 rows for detailed overtones.
Choose precision for table values.
Reset

Example Data Table

Input L (m) Input T (N) Input μ (kg/m) f1 (Hz) f2 (Hz) f3 (Hz) f4 (Hz) f5 (Hz)
0.65 80 0.004 108.79 217.57 326.36 435.14 543.93

These values assume fixed–fixed ends and uniform tension.

Formula Used

Wave speed

v = √(T / μ)

T is tension (N). μ is linear density (kg/m).

Resonant frequencies

Fixed–Fixed / Free–Free: fₙ = n·v / (2L)

Fixed–Free: fₙ = (2n−1)·v / (4L)

L is vibrating length (m). n = 1,2,3…

Related quantities

  • λ (wavelength): λₙ = 2L/n for fixed–fixed, or λₙ = 4L/(2n−1) for fixed–free.
  • ω (angular frequency): ωₙ = 2πfₙ.
  • P (period): Pₙ = 1/fₙ.

How to Use This Calculator

  1. Enter the vibrating length L of the string section.
  2. Enter the string tension T and select the unit.
  3. Provide linear density μ directly, or compute it from mass and length.
  4. Select the boundary condition that matches your setup.
  5. Choose how many modes to compute and the decimals.
  6. Press Calculate to see results above the form.
  7. Use the CSV or PDF buttons to export the mode table.

For best accuracy, keep units consistent and measure the vibrating length carefully.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.