Pendulum Frequency
Calculate pendulum oscillation frequency, period, and angular frequency using the simple pendulum formula. Free online physics tool with interactive charts and step-by-step breakdown.
About This Calculator
The Pendulum Frequency Calculator computes the oscillation frequency of a simple pendulum using the formula f = 1/(2π) × √(g/L), where g is the acceleration due to gravity and L is the pendulum length. This tool is designed for physics students, educators, and anyone studying harmonic motion.
A simple pendulum consists of a point mass (bob) suspended from a frictionless pivot by a massless string. For small angular displacements (less than 15°), the motion is approximately simple harmonic, and the frequency depends only on the pendulum length and local gravity — not on the mass of the bob or the amplitude of swing. The calculator applies the small-angle approximation to deliver accurate results for most practical pendulum scenarios.
The frequency output is the number of complete oscillations per second (hertz). From frequency, the calculator also derives the period (time per oscillation), angular frequency (rate of phase change in rad/s), and oscillations per minute for convenience.
Regional Notes
Earth: The default gravitational acceleration is 9.80665 m/s², which is the standard value at sea level on Earth. For precise local values, adjust gravity based on latitude and altitude (e.g., 9.81 m/s² in most locations, 9.78 m/s² at the equator, 9.83 m/s² at the poles).
Other Celestial Bodies: Use the gravity field to calculate pendulum frequency on other planets: Moon 1.62 m/s², Mars 3.71 m/s², Jupiter 24.79 m/s², Saturn 10.44 m/s². This is useful for physics problems involving pendulum experiments in different gravitational environments.
Frequently Asked Questions
What is the formula for pendulum frequency?
The frequency of a simple pendulum is calculated using f = 1/(2π) × √(g/L), where g is the acceleration due to gravity (9.80665 m/s² on Earth) and L is the length of the pendulum in meters. This formula applies for small amplitude oscillations (less than 15°).
How do I calculate pendulum frequency from length?
Enter the pendulum length in meters and the gravitational acceleration (default 9.80665 m/s² for Earth). The calculator applies f = 1/(2π) × √(g/L) to compute frequency in hertz, along with period, angular frequency, and oscillations per minute.
Does the mass of the pendulum bob affect frequency?
No, the frequency of a simple pendulum is independent of the mass of the bob. Only the length of the pendulum and the acceleration due to gravity determine the frequency. This is analogous to free-fall where all objects accelerate at the same rate regardless of mass.
What is the small angle approximation for pendulum frequency?
The formula f = 1/(2π) × √(g/L) assumes small oscillations where the angular displacement is less than about 15° (0.26 rad). For larger amplitudes, the period increases and the frequency decreases due to nonlinear effects. The error at 15° is about 0.5%.
How does gravity affect pendulum frequency?
Pendulum frequency is proportional to the square root of gravitational acceleration. On Earth (g = 9.81 m/s²), a 1 m pendulum has a frequency of about 0.5 Hz. On the Moon (g = 1.62 m/s²), the same pendulum would have a frequency of about 0.2 Hz. On Jupiter (g = 24.79 m/s²), it would be about 0.79 Hz.
What is the frequency of a 1 meter pendulum?
A 1 meter long pendulum on Earth has a frequency of approximately 0.498 Hz, meaning it completes about one full oscillation every 2.01 seconds. This is why many pendulum clocks use a 1 m pendulum — the period is very close to 2 seconds.
Can I use this calculator for physical pendulums?
This calculator uses the simple pendulum formula which assumes a point mass on a massless string. For physical pendulums with distributed mass, use the physical pendulum formula T = 2π√(I/mgD) where I is the moment of inertia and D is the distance from pivot to center of mass.
Is this calculator free to use?
Yes, it is completely free to use with no registration or hidden charges. You can bookmark or share your results via the URL which saves all your inputs.