Example 1
L = 1 m, blank g → T ≈ 2.01 s.
Pendulum calculator
Enter the string length and, if you want, your own g. You get the small-angle pendulum period. L = 1 m at Earth 9.81 m/s² is T ≈ 2.01 s, about what a school-clock seconds pendulum does.
The school assumptions live on the simple pendulum page. From this T you get f on frequency from period and ω on angular velocity.
Result
Length L (m) and g (m/s², optional). The result shows up here.
How it works
At small angles the pendulum period is T = 2π√(L/g). It depends on length and gravitational acceleration, not on mass, and in this approximation not on amplitude. L = 1 m and g = 9.81 m/s² give T ≈ 2.01 s. L = 2 m stretches the period by √2, so you get about 2.84 s, not 4 s. L = 0.25 m shortens T to about 1.00 s.
L is the length from the support to the center of mass, in meters. g is optional: leave it blank and the calculator uses Earth 9.81 m/s². For the Moon, type 1.62. A comma and a period are the same, so 0.5 m can be 0,5.
The formula is a small-angle approximation, usually good to about 15°. At a large swing the real period grows a little, because sin θ is no longer equal to θ. A playground swing or a house clock still fits this model if the angle stays modest.
On the Moon the same 1 m string has T ≈ 4.94 s, because g is smaller and √(L/g) grows. Typed g must be positive. Length must be positive too. The hanging mass never enters the calculator: one kilogram and 100 g on the same L share the same T.
Type L, leave g blank or enter your own, then Calculate. The calculator example 1 m and blank g is ≈ 2.01 s. Then try 2 m and read 2.84 s. For f, open frequency from period and paste that T.
The version that spells out the assumptions (point mass, massless string, small angle) is the simple pendulum page. Same formula, different emphasis. ω = 2π/T lives on angular velocity, not here.
How to use
- Type length L in meters, from the hook to the center of mass. The calculator example is 1 m, like a seconds pendulum.
- You can leave g blank: the calculator uses 9.81 m/s². On the Moon type 1.62. A typed g must be positive.
- Click Calculate. 1 m and blank g give T ≈ 2.01 s. Two meters at the same g is about 2.84 s, because T grows like the square root of L.
- There is no mass field, because mass is not in the formula. A large angle (well past 15°) stretches the real period past this card.
- To get f, open frequency from period and type this T. The school assumptions sit on the simple pendulum page.
Formula
T = 2π √(L/g)
Default g = 9.81 m/s2. Small-angle approximation.
Letters in T = 2π√(L/g)
A practical small-angle pendulum: T = 2π√(L/g). L = 1 m at Earth 9.81 m/s² is T ≈ 2.01 s, a seconds pendulum.
- T
- Period in seconds. At L = 1 m and g = 9.81 you get ≈ 2.01 s; L = 2 m is about 2.84 s, not 4 s.
- L
- Length from the pivot to the center of mass, in meters. L = 0.25 m shortens T to about 1.00 s.
- g
- Acceleration in m/s². A blank field is 9.81; mass has no field, because in this approximation T does not use it.
Real-life examples
Example 2
L = 2 m.
Example 3
L = 0.25 m.
Example 4
L = 0.5 m.
Example 5
L = 1 m, g = 1.62.
Example 6
L = 0.8 m.
Example 7
L = 1.5 m.
Example 8
L = 1 m, g = 9.8.
Example 9
L = 0.1 m.
Example 10
L = 3 m.
Ways to use this calculator
- You estimate the period of a swing or a clock: 1 m on Earth is about 2.01 s.
- You compare Earth with the Moon at the same L: 1.62 m/s² stretches T to about 4.94 s.
- From T you go to f = 1/T or ω = 2π/T on the neighboring pages.
Frequently asked questions
What period does a 1 m pendulum have at Earth g?
T ≈ 2.01 s. L = 2 m is about 2.84 s, not 4 s. L = 0.25 m is about 1.00 s.
Does mass change T?
Not in this model. One kilogram and 200 g on the same length share the same period.
What if I leave g blank?
The calculator inserts 9.81 m/s². For another planet, type g yourself, for example 1.62 on the Moon.
What T on the Moon at L = 1 m?
At g = 1.62 m/s² you get about 4.94 s, almost 2.5 times longer than on Earth.
Does the formula work at large angles?
It is a small-angle approximation. At a large swing the real period grows a little.
How do I get frequency from this T?
f = 1/T on the frequency-from-period page. From 2.01 s you get about 0.50 Hz.
Can I type 0.5 m with a comma?
Yes. 0,5 and 0.5 are the same length. T ≈ 1.42 s at g = 9.81.
How is this different from the simple pendulum page?
Same formula. That page stresses the assumptions: point, string, small angle. Here the examples are a swing and a clock.
Do I have to type L in meters?
Yes, the field wants meters. 80 cm is 0.8 m and T ≈ 1.79 s at 9.81.
How does T grow when I lengthen the string?
Like the square root of L. Four meters is about 4.01 s, twice the 1 m period, not four times.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.