How this calculation works
The Simple Pendulum Period & Frequency Calculator computes the oscillation period (T in seconds), frequency (Hz), and full swings per minute for simple harmonic oscillators and grandfather clocks.
Mathematical formula and logic
Period T = 2π × √(L / g). Frequency f = 1 / T. Swings per Minute = 60 / T.
Worked example
A 1.0 meter long pendulum on Earth (g = 9.80665 m/s²) has an oscillation period of T = 2π × √(1.0 / 9.80665) = 2.006 seconds (Frequency 0.498 Hz, approx 30 full swings per minute).
Calculation assumptions
- Small angle approximation (oscillation angle θ < 15°).
- Massless rod or string with point-mass bob and zero aerodynamic damping.
Frequently asked questions
Does the mass of the pendulum bob affect the period?
No! In a simple pendulum, the period is completely independent of the bob's mass. Only the length of the string and local gravity determine the period.
How long must a pendulum be to tick once every second (1-second half-period)?
A 'seconds pendulum' (Period T = 2.0 seconds) requires a length of approximately 0.994 meters (39.1 inches) on Earth.
What happens to a pendulum clock on the Moon?
Because lunar gravity is 1/6th of Earth (1.62 m/s²), the pendulum swings slower, increasing the period by √6 = 2.45 times (a clock would lose ~14 hours per day).
What is a Foucault Pendulum?
A Foucault pendulum is a tall, heavy pendulum that demonstrates the Earth's rotation on its axis as the plane of its swing gradually rotates relative to the floor below.
What is the small angle approximation?
At angles under 15°, sin(θ) ≈ θ in radians, allowing linear simple harmonic motion equations to predict the period with less than 0.5% error.