Science
Mass and spring period
Find the oscillation period and frequency of a mass attached to an ideal spring; a heavier mass slows the oscillation while stiffness speeds it up.
Calculators / Science / Simple pendulum period
Simple pendulum period calculator
Estimate the period and frequency of a small-angle pendulum using its pivot-to-bob length and local gravity, without needing the bob mass.
On this page
Period2.01s
Frequency0.5Hz
Calculator controls
How to calculate
Estimate the period and frequency of a small-angle pendulum using its pivot-to-bob length and local gravity, without needing the bob mass.
Period = 2*pi*sqrt(l/g) s; Frequency = sqrt(g/l)/(2*pi) Hz
Worked example
Pendulum length (m): 1; Gravity (m/s²): 9.80665.
Period: 2.01 s; Frequency: 0.5 Hz.
Assumptions and limits
Estimate the period and frequency of a small-angle pendulum using its pivot-to-bob length and local gravity, without needing the bob mass. Small-angle approximation for a simple pendulum, with negligible damping and a massless string. Large angles need a different model.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Estimate the period and frequency of a small-angle pendulum using its pivot-to-bob length and local gravity, without needing the bob mass.
When this tool is useful
Period = 2*pi*sqrt(l/g) s; Frequency = sqrt(g/l)/(2*pi) Hz
Understanding your inputs
| Input | What to enter |
|---|---|
| Pendulum length (m) | Enter a number of at least 1e-12 and no more than 1000000000000. |
| Gravity (m/s²) | Enter a number of at least 1e-12 and no more than 1000000000000. |
Frequently asked questions
What assumptions does this calculation use?
Estimate the period and frequency of a small-angle pendulum using its pivot-to-bob length and local gravity, without needing the bob mass. Small-angle approximation for a simple pendulum, with negligible damping and a massless string. Large angles need a different model.
How is the result calculated?
Period = 2*pi*sqrt(l/g) s; Frequency = sqrt(g/l)/(2*pi) Hz