The pendulum calculator uses T = 2π√(L/g) to find period, frequency, or length for any simple pendulum. Toggle between meters and feet. Includes Earth, Moon, and Mars gravity presets — ideal for physics homework and clock design.
Pendulum Calculator
How to Use the Pendulum Calculator
This pendulum calculator solves the simple pendulum formula T = 2π√(L/g) for period, length, or gravitational acceleration. It's valid for small angles (under ~15°).
Step 1: Select What to Solve For
Choose Period (T), Length (L), or Gravity (g). Enter the other two known values.
Step 2: Use Gravity Presets
Click Earth (9.81 m/s²), Moon (1.62 m/s²), or Mars (3.72 m/s²) to set gravity, or enter any custom value.
The Seconds Pendulum
A pendulum with a 2-second period (1 second per half-swing) has length L = g × T²/(4π²) = 9.81 × 4/(39.478) = 0.9937 m ≈ 1 meter. This is why grandfather clock pendulums are almost exactly 1 meter long.
Length-Period Relationship
Doubling the length multiplies the period by √2 ≈ 1.414. A pendulum 4× longer has double the period. Mass has no effect on period — only length and gravity matter.
FAQ
What is the pendulum period formula?
The period of a simple pendulum is T = 2π√(L/g), where T is the period in seconds, L is the pendulum length in meters, and g is gravitational acceleration (9.81 m/s² on Earth). This formula is valid for small angles (under ~15 degrees) where sin θ ≈ θ.
How long should a pendulum be to swing once per second?
For a 1-second period (half-swing), you need a pendulum about 0.248 m (9.76 inches) long. For a 2-second full swing (classic 'seconds pendulum'), L = 0.993 m ≈ 1 meter. This is why grandfather clocks are about 1 meter tall.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
Does mass affect pendulum period?
No — for a simple pendulum, the period depends only on length and gravity, not mass. Doubling the bob mass doesn't change the period. This was one of Galileo's key discoveries. However, the amplitude (swing angle) does matter slightly for large angles.