Simple Pendulum Period Calculator
Find the period T=2π√(L/g) of a simple pendulum. L=1 m → T≈2.01 s; frequency f=1/T≈0.498 Hz. Valid for small angles (<15°).
Input Data
Results
At a glance:A simple pendulum is an ideal point mass m swinging on a massless, inextensible string of length L under gravity g. For small angular displacement (θ<~15°) the motion is simple harmonic with period T=2π√(L/g), independent of mass and amplitude. Frequency f=1/T and angular frequency ω=2πf=√(g/L). Properties: (1) period grows with √L — double the length → √2 longer period; (2) lower g (e.g. Moon) gives a longer period; (3) mass cancels out. Example: L=1 m, g=9.81 → T=2π√(1/9.81)≈2.006 s, f≈0.498 Hz. The small-angle approximation breaks down beyond ~15–20°; a seconds pendulum (T=2 s) has L≈0.994 m and was used in grandfather clocks. Applications: (1) pendulum clocks and metronomes; (2) seismometers; (3) estimating g from L and T; (4) playground swings; (5) DSE Physics oscillation questions.
Formula
Period: T = 2π√(L/g)
Frequency: f = 1/T
Angular frequency: ω = 2πf = √(g/L)
Valid for small angles (θ < ~15°)
$$T = 2\pi\sqrt{\frac{L}{g}}, \quad \omega = \sqrt{\frac{g}{L}}$$How to Use
- Enter length L (m) and gravity g (m/s²).
- The tool returns T, f and ω.
- Common: L=1 m → T≈2.01 s; L=0.25 m → T≈1.00 s.
Case Studies
One-metre pendulum
L=1 m, g=9.81 m/s².
T = 2π√(1/9.81) ≈ 2.006 s.
f = 1/T ≈ 0.498 Hz (about one swing every 2 seconds).
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.