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Time period of a simple pendulum calculator

A-level Oscillations

The time for one swing of a simple pendulum, for small angles. It does not depend on the mass.

T = 2π√(l / g)

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

2.01 s

Working

  1. Write the equation
    T = 2π√(l / g)
  2. Constants used
    g = 9.8 N/kg
  3. Substitute the values
    T = 2π × √(1 ÷ 9.8)
  4. Calculate
    T = 2.00709 s
  5. Give the answer to 3 significant figures
    T = 2.01 s

Worked example

Find T, the time period. Given: length of the pendulum l = 1.00 m; gravitational field strength g = 9.8 N/kg.

  1. Write the equation
    T = 2π√(l / g)
  2. Constants used
    g = 9.8 N/kg
  3. Substitute the values
    T = 2π × √(1 ÷ 9.8)
  4. Calculate
    T = 2.00709 s
  5. Give the answer to 3 significant figures
    T = 2.01 s

Symbols and units

SymbolQuantitySI unit
TTime periods
lLength of the pendulumm
gGravitational field strength (constant)N/kg

Time period of a simple pendulum: rearranged

  • To find time period: T = 2π√(l / g)
  • To find length of the pendulum: l = g T2 / (4π2)

Exam tip

Length is measured from the pivot to the centre of the bob. The equation is only accurate for small angles.

Common questions

What is the formula for time period of a simple pendulum?

The equation is T = 2π√(l / g), where T is the time period (s); l is the length of the pendulum (m); g is the gravitational field strength (N/kg).

What units should I use for time period of a simple pendulum?

In SI units: time period in s, length of the pendulum in m, gravitational field strength in N/kg. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange T = 2π√(l / g)?

Rearranging gives these forms: to find time period: T = 2π√(l / g). to find length of the pendulum: l = g T² / (4π²).

Practise time period of a simple pendulum questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

Read the full explanation on the Period of a simple pendulum formula page. More oscillations equations: Time period of a mass on a spring, Maximum speed in simple harmonic motion, Maximum acceleration in simple harmonic motion. See the full list on the a-level physics equation calculator page.