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Physics

Pendulum Period

T = 2π√(L/g). Free online Pendulum Period. Calculate pendulum period online — fast, accurate, mobile-friendly, no signup needed.

Period T = 2π√(L/g) for small angles.
Period (s)
2.006067

Derivation

  1. ├── 01GivenL = 1
  2. ├── 02Formula2 × π × √(t / 9.81)
  3. └── 03Compute Period (s)2.006067
Did you know?

Galileo noticed a swinging chandelier in Pisa Cathedral (1583) and realised a pendulum’s period depends only on its length — the foundation of the first accurate clocks.

§01What is

Understanding the Pendulum Period

The Pendulum Period computes Period (s) from 1 input: length (m). T = 2π√(L/g).

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Pendulum Period sits in that toolkit — it T = 2π√(L/g). Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

2 × π × √(t / 9.81)

Where

L
Length (m)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Length (m) = 1.

  1. 01Start by noting the input — Length (m): 1.
  2. 02Substitute these values into the formula: 2 × π × √(t / 9.81)
  3. 03Compute Period (s): the calculator returns 2.00607.
  4. 04Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Pendulum Period Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Length (m) halved

L = 0.5 (from 1)

Keep every other input at its default and halve the length (m). See how period (s) responds.

  1. 01New Length (m): 0.5
  2. 02Baseline Period (s): 2.00607
  3. 03New Period (s): 1.4185
  4. 04Period (s) decreases by 29.3% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Length (m) doubled

L = 2 (from 1)

Keep every other input at its default and double the length (m). See how period (s) responds.

  1. 01New Length (m): 2
  2. 02Baseline Period (s): 2.00607
  3. 03New Period (s): 2.83701
  4. 04Period (s) increases by 41.4% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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