What is the formula for the period of a simple pendulum?

For small angles, the period of a simple pendulum is T = 2π√(L/g), where L is pendulum length and g is gravitational acceleration.

Can this pendulum calculator solve for length?

Yes. This calculator can solve for pendulum length when gravity and period or gravity and frequency are known.

Does the simple pendulum formula work for large angles?

The standard formula T = 2π√(L/g) is accurate for small angles. At larger amplitudes the period becomes slightly longer.

AmesWeb

Simple Pendulum Calculator

Use this pendulum calculator to find period, frequency, pendulum length, or gravity with the simple pendulum formula T = 2π√(L/g). It works as a pendulum period calculator, pendulum frequency calculator, and pendulum length calculator.

Pendulum Period, Frequency and Length Calculator

Change any input and the calculator updates automatically without pressing Calculate.

Calculator Inputs

Solve for

Gravity [g]

Gravity unit

Pendulum Length [L]

Length unit

Period [T]

Frequency [f]

Use “.” as the decimal separator.

Results

T = 2π√(L/g)

Gravity [g]

—

Pendulum Length [L]

—

Period [T]

—

Frequency [f]

—

Meaning of the result

Change any input to calculate pendulum period, frequency, length, or gravity instantly.

Simple Pendulum Diagram

The simple pendulum period formula assumes small-angle motion. At larger amplitudes, the true period becomes slightly longer than the small-angle approximation. This follows the same concept already described on the current page.

Simple Pendulum Formula

T = 2π√(L/g)

f = 1 / T

T = pendulum period
f = pendulum frequency
L = pendulum length
g = acceleration due to gravity

This is the same small-angle pendulum relationship used by the current calculator and code-behind for solving period, frequency, length, and gravity.

How to Use the Pendulum Calculator

Select whether to solve for period, frequency, length, or gravity.
Enter the known values.
Select the correct gravity and length units.
The calculator updates automatically when you change an input.
You can also use the Calculate button for a manual refresh.

Examples

Example 1: Find period and frequency

A simple pendulum has a length of 1.5 m and gravity is 9.8 m/s².

T = 2π√(1.5 / 9.8) = 2.458 s

f = 1 / 2.458 = 0.407 Hz

Example 2: Find pendulum length

A pendulum has period 2 s under gravity 9.81 m/s².

L = g(T / 2π)² ≈ 0.994 m

What This Pendulum Calculator Helps You Find

This page is useful for searches such as period of pendulum calculator, period of a pendulum calculator, pendulum frequency calculator, pendulum length calculator, and period of oscillation calculator.

FAQ

What is the period formula for a simple pendulum?

For small oscillation angles, the period is T = 2π√(L/g).

How do you find pendulum frequency?

Pendulum frequency is the reciprocal of the period: f = 1/T.

Can this page calculate pendulum length?

Yes. If period and gravity are known, the calculator can solve for pendulum length.

Does amplitude affect pendulum period?

For small angles the effect is negligible, but for larger angles the true period is slightly longer.

Related Physics Calculators

Physics Calculators Simple Harmonic Motion Calculator Acceleration Calculator Circular Motion Calculator Free Fall Calculator

References

Giancoli, Douglas C. Physics: Principles with Applications. Pearson.
Young, Freedman, Ford, Sears. University Physics. Pearson.
The current page already includes the small-angle formula and large-angle note for pendulum motion.