Cantilever Beam Natural Frequency Calculator

Calculate the first five natural frequencies of a uniform cantilever beam with embedded JavaScript, fast client-side updates, cleaner layout, and SEO-ready explanatory content.

Modes calculated

1 to 5

Calculation model

Uniform cantilever beam

Result units

Hz and rad/s

Calculator

Enter beam properties below. The page uses the same mode constants as your existing calculator and computes results instantly in JavaScript.

Modulus of Elasticity, E

Converted internally to N/mm².

Area Moment of Inertia, I

Use your section property for the bending axis of interest.

Beam Length, L

Longer beams generally have lower natural frequencies.

Uniform Load per Unit Length, w

Include beam self-weight and any uniformly distributed load contribution used by your model.

Results updated.

Tip: use a dot . as decimal separator. The calculator recalculates automatically when inputs change.

Mode	K_n	Angular Frequency, ω (rad/s)	Natural Frequency, f (Hz)
1	3.52	—	—
2	22.0	—	—
3	61.7	—	—
4	121	—	—
5	200	—	—

Formula

This calculator follows the same equation and modal constants already used on your current page.

f_n = (K_n / 2π) √( E I g / ( w L⁴ ) )

Parameter definitions

Symbol	Description
E	Modulus of elasticity of the beam material
I	Area moment of inertia of the beam cross section
L	Beam length
w	Uniform load per unit length
g	Gravitational acceleration, 9810 mm/s²
K_n	Mode constant for the selected vibration mode

FAQ

What does this cantilever beam natural frequency calculator compute?

It computes the first five natural frequencies for a uniform cantilever beam and also reports angular frequency for each mode.

Why does the natural frequency decrease when the beam gets longer?

Length appears to the fourth power in the denominator, so increasing beam length strongly lowers stiffness relative to dynamic response.

What inputs affect the natural frequency the most?

Beam length has a very strong effect. Elastic modulus and section inertia increase frequency, while larger distributed load per unit length reduces it.

Can I use inch and foot units?

Yes. This page supports GPa or psi × 10^6 for E, mm⁴ or imperial inertia units, metric or imperial length units, and N/mm or lbf/in for distributed load.

Cantilever beam diagram

Mode constants used

Mode 1: K₁ = 3.52
Mode 2: K₂ = 22.0
Mode 3: K₃ = 61.7
Mode 4: K₄ = 121
Mode 5: K₅ = 200

How to use this calculator

Enter the modulus of elasticity of the beam material.
Enter the section moment of inertia for the bending axis.
Enter the cantilever length.
Enter the distributed load per unit length used by the equation.
Review the first five natural frequencies in Hz.

Engineering notes

This page is intended for a uniform cantilever beam. For stepped beams, tip masses, non-uniform geometry, or more advanced boundary conditions, use a more detailed beam or FEA model.

For preliminary design, the calculator is useful for screening resonance risk and comparing how length, stiffness, and section properties affect the vibration response.

About cantilever beam natural frequency

The natural frequency of a cantilever beam is a key design parameter in machine structures, tools, brackets, supports, sensor mounts, and lightweight mechanical assemblies. A beam that operates near one of its natural frequencies may experience excessive vibration, noise, poor surface finish, fatigue problems, or dynamic instability.

In general, increasing the modulus of elasticity or increasing the area moment of inertia raises the beam stiffness and therefore increases the natural frequency. Increasing beam length or distributed load lowers the natural frequency. This makes the calculator a practical tool during concept design, sizing studies, and quick design iterations.

Engineers commonly use the first mode for preliminary resonance checks, but higher modes can also matter when the excitation source contains harmonics or broad-band dynamic input. That is why this page reports the first five modes.