Pendulum Frequency Calculator

Simple Pendulum Frequency

A simple pendulum swings back and forth under gravity. For small angles, its motion is nearly sinusoidal. Frequency tells you how many complete oscillations occur each second.

Frequency Formula

$$f = \frac{1}{2\pi}\sqrt{\frac{g}{L}}$$

Here $g$ is gravitational acceleration and $L$ is pendulum length from pivot to bob center. Period is $T = 1/f = 2\pi\sqrt{L/g}$. Angular frequency is $\omega = 2\pi f = \sqrt{g/L}$.

What Affects Frequency?

Longer pendulums swing slower (lower frequency). Stronger gravity increases frequency. Mass does not affect the ideal simple pendulum period. This approximation works best for small release angles.

Frequently Asked Questions

Does mass change pendulum frequency?

For an ideal simple pendulum, mass does not affect frequency. Only length and gravity matter in the small-angle formula.

What is a small angle?

Angles below about 10 to 15 degrees keep error small. Larger angles need nonlinear corrections.

Why does a 1 m pendulum on Earth give about 0.5 Hz?

With $g \approx 9.81$ m/s$^2$ and $L = 1$ m, $f \approx 0.5$ Hz, so one full swing takes about 2 seconds.

What is angular frequency?

Angular frequency $\omega$ is $2\pi f$ and is measured in rad/s. It appears in equations of simple harmonic motion.

Can I use feet for length?

Yes. Select the length unit and the tool converts to meters before applying the formula.

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Pendulum Frequency Calculator

Simple Pendulum Frequency

Frequency Formula

What Affects Frequency?

Frequently Asked Questions

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