Pendulum Period Calculator

Enter pendulum length and gravitational acceleration to calculate period, frequency, and angular frequency under the small-angle simple-pendulum model.

Pendulum length

Gravitym/s²

Model

Simple pendulum · small-angle approximation

—T = 2π√(L/g)

—Frequency

—Angular frequency

—Cycles/min

—Length used

Valid for an ideal point mass, massless string, negligible damping, and small oscillation angle. Large amplitudes require a different model.

Physics model preflight

Check the governing model before trusting the number

simple pendulum, small angle

T = 2π√(L/g)

Reading the current native inputs…

Length and gravity must be positive. Large-angle, damping and distributed-mass effects are excluded. This is an idealized educational model: unit consistency and valid inputs do not guarantee that omitted effects are negligible in a real system.

State the model before trusting the number

Classical formulas are only as good as their assumptions and units. Air resistance, damping, deformation, non-constant forces and measurement uncertainty are not silently invented when the selected model does not include them.

Governing physics model

T = 2π√(L/g) — simple pendulum, small angle.

How to verify the result

Square the period ratio when comparing lengths: T² is proportional to L when g is unchanged. Lower gravity increases period.

Domain and assumption boundary

Length and gravity must be positive. Large-angle, damping and distributed-mass effects are excluded. The calculator does not silently add drag, damping, deformation, varying fields, relativistic effects, measurement uncertainty, or geometry that the selected model does not contain.