Simple Pendulum Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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Problems involving simple pendulum can look simple until units, signs, or hidden assumptions start changing the answer. For simple pendulum, rotational and oscillatory quantities are tightly linked, but radians, revolutions, frequency, period, and linear speed are not interchangeable. This calculator keeps one defined relationship at the center of the result.

What this calculator does

The Simple Pendulum Calculator turns the physical quantities shown on the form into a focused pendulum period. It is designed for quick scenario checks while keeping the inputs and units visible, so you can change one quantity and immediately see how the modeled result responds.

How to use it

Start with the fields that drive the current calculation: Pendulum length, Gravity. Enter values in the units shown beside each field; the page converts supported units before applying the formula. Keep signs and angles consistent with the labels, then read the headline result together with any supporting metrics rather than copying the number without its unit.

How the calculation works

For the current result, the page uses the small-angle pendulum period T = 2π√(L/g) and f = 1/T. The visible amplitude does not alter the headline period in this current path, so the result is the small-angle approximation.

Example

Using the default example on the page (Pendulum length = 1 m; Gravity = 9.80665 m/s²), the calculator returns pendulum period of 2.006409 s. Change one input at a time and compare the direction of the change with the formula above; that is a quick way to catch a wrong unit, sign, or selected method before you rely on the number.

How to interpret the result

On the Simple Pendulum Calculator, the pendulum period should be read in the rotational or oscillatory unit shown—radians, rad/s, hertz, seconds, or energy as appropriate. Check whether the page is reporting a linear quantity or an angular one; converting between them generally requires a radius or a 2π factor.

Limitations and notes

The current headline uses the small-angle formula and does not apply the visible amplitude to correct the period. For large swing angles, damping, flexible strings, distributed mass, and changing gravity, a more complete pendulum model is needed.