Pendulum Calculator
Calculate pendulum period, frequency, and angular frequency from length and gravity. Covers simple, physical, and Foucault pendulums. Includes large-angle correction, damped oscillation, and energy.
m
m/s²
Period (T)
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Frequency (f) —
Angular Frequency ω —
Extended More scenarios, charts & detailed breakdown ▾
m
m/s²
Period (s)
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Frequency (Hz) —
Angular Freq (rad/s) —
Professional Full parameters & maximum detail ▾
m
m/s²
°
Period
Period (small angle) —
Period (large angle corrected) —
Energy & Damping
Max Potential Energy —
Amplitude Decay Time (1/e) —
How to Use This Calculator
- Enter pendulum length in meters and adjust gravity if needed.
- See period, frequency, and angular frequency instantly.
- Use Physical Pendulum tab for a rigid body with moment of inertia.
- Use Foucault tab to find the rotation rate at a given latitude.
- The Professional tab applies large-angle correction and damped oscillation decay.
Formula
T = 2π√(L/g) | f = 1/T | ω = 2π/T = √(g/L)
Physical: T = 2π√(I/(mgd))
Foucault rotation: Ω = 2π sin(φ)/24h
Example
L = 1 m, g = 9.81 m/s²: T = 2π√(1/9.81) = 2.006 s, f = 0.498 Hz.
Frequently Asked Questions
- For a simple pendulum (small angle): T = 2π√(L/g), where L is length in meters and g is gravitational acceleration (9.81 m/s² on Earth). The period is independent of mass and amplitude for small angles.
- On the Moon g ≈ 1.62 m/s². A 1-meter pendulum has period T = 2π√(1/1.62) ≈ 4.95 s, compared to 2.006 s on Earth. Pendulums swing slower on the Moon.
- A Foucault pendulum demonstrates Earth's rotation. Its plane of oscillation appears to rotate at a rate that depends on latitude. At the poles the period is 24 hours; at the equator there is no rotation.
- A physical (compound) pendulum is a rigid body swinging about a pivot. Its period is T = 2π√(I/(mgd)), where I is the moment of inertia, m is mass, and d is the distance from pivot to center of mass.
- For small angles (< 15°) the effect is negligible. For large angles θ₀, a correction factor is needed: T ≈ T₀ × (1 + (1/16)θ₀² + (11/3072)θ₀⁴...) where θ₀ is in radians.