Pendulum Period

T = 2\pi\sqrt{\frac{L}{g}}

Period of simple pendulum (small angles).

Variables

Period

Time for one swing

Allowed values: greater than 0

Length

Pendulum length

Allowed values: greater than 0

Gravitational acceleration

≈ 9.8 m/s²

Allowed values: greater than 0

m/s²

Derivation

For small θ: ω = √(g/L), T = 2π√(L/g).

Your notes

0/5000

Constants in this formula

Standard Gravity

9.806 65. Exact by definition.

m/s²

Check value

Round inputs run through this page's calculator, with each constant at its tabulated value. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.

L = 2 m (Length)
g = 9.806 65 m/s² (Gravitational acceleration)

Result: T = 2.8374912 s

Other waves formulas with the same quantities

Physical Pendulum Period (Simple Harmonic Motion) shares Period, Gravitational acceleration
Torsional Oscillation Period (Simple Harmonic Motion) shares Period
Period and Frequency (Wave Properties) shares Period
Angular Frequency (Wave Properties) shares Period

Where this formula is listed

Waves formulas, under Simple Harmonic Motion, alongside SHM Displacement, SHM Velocity, SHM Acceleration, SHM Maximum Velocity and SHM Total Energy.
In the waves list it comes after Spring Oscillation Period and before SHM Total Energy.
Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Pendulum Period formula?

Pendulum Period is written T = 2π√(L/g). Period of simple pendulum (small angles). It belongs to Waves, under Simple Harmonic Motion.

What are the units in T = 2π√(L/g)?

In SI units, T is period, measured in s; L is length, measured in m; g is gravitational acceleration, measured in m/s².

How is the Pendulum Period formula derived?

For small θ: ω = √(g/L), T = 2π√(L/g). The result is T = 2π√(L/g).