Natural Frequency Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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When you need a quick natural frequency check, the best result is one you can explain, not just copy. Stress, strain, stiffness, and section properties are tightly tied to geometry, so a correct formula can still give the wrong engineering answer when the wrong dimension is entered. The calculator below uses a narrow equation set and shows the output in a form that is easy to sanity-check.

What this calculator does

This page focuses on natural frequency from Type, Spring constant (k), Mass (M). The calculation stays deliberately narrow: it uses the fields tied to this relationship and reports related quantities only when they follow from those same inputs.

How to use it

Enter Spring constant (k), Mass (M), Pendulum length (L), Gravitational acceleration from the same physical setup, keeping every unit consistent with the selector shown on the page. Choose Type so the calculation path matches your case. After the result appears, make one small input change as a sanity check rather than relying on the first number simply because it has several decimal places.

How the calculation works

Mass-spring mode uses ωn = √(k/m) and f = ωn/(2π). Pendulum mode instead uses ωn = √(g/L). The selected system type therefore changes which physical inputs drive the same frequency output.

Example

Using the default example on the page (Type = Mass-spring system; Spring constant (k) = 100 N/m; Mass (M) = 1 kg; Pendulum length (L) = 1 m), the calculator returns natural frequency of 1.591549 Hz. Try increasing one input while holding the others fixed; the response should match the dependence shown in the formula above.

How to interpret the result

The reported frequency is the fundamental result of the selected ideal model: mass-spring or simple pendulum. A higher stiffness raises the mass-spring frequency, while greater mass lowers it; in pendulum mode, a longer length lowers frequency. Real assemblies can have multiple coupled modes.

Limitations and notes

The page models either an ideal single-degree-of-freedom mass-spring system or a small-angle simple pendulum. Damping, nonlinear stiffness, distributed mass, multiple modes, support flexibility, and large-angle pendulum behavior are outside these equations, so a real structure can have several natural frequencies rather than one.