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Physics Tools · Updated October 21, 2026 · Reviewed by FormatFlow Editorial

Simple Harmonic Motion Calculator

You can calculate the period and frequency of an ideal spring or simple pendulum, or solve for the missing mass, spring stiffness, length or gravity, with angular frequency included.

Runs in your browserFree · No sign-up · No watermark
m, k or L, g → TRuns in your browser
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Everything runs locally in this tab. No file is uploaded while the tool loads.

This tool runs in your tab. Nothing is uploaded and no copy is stored.

How files are handled

At a glance

Works with
m, k or L, g → T
Processing
In your browser
Price
Free, no account
Updated
October 21, 2026
All Physics Tools

About Simple Harmonic Motion Calculator

Simple harmonic motion describes any oscillation where the restoring force is proportional to displacement. A mass on an ideal spring and a small-angle pendulum are the two standard examples, and each has a period that depends only on the system's properties, not on the amplitude.

This calculator solves the period, frequency and angular frequency for the spring or pendulum model, and can also work backward to find the missing mass, spring stiffness, pendulum length or local gravity. Every step lists the formula, the substituted values and the assumptions that limit the model.

What this tool does

The details that matter when you use Simple Harmonic Motion Calculator for real work.

  • Spring and pendulum modes

    Switch between T = 2π√(m/k) for a spring and T = 2π√(L/g) for a pendulum.

  • Solve forward or backward

    Find the period and frequency, or solve for mass, stiffness, length or gravity from a known period.

  • Frequency and angular frequency

    f = 1 ÷ T and ω = 2π ÷ T are reported alongside the period in hertz and radians per second.

  • Unit choices

    Mass in kg or g, length in meters or centimeters, stiffness in N/m and gravity in m/s².

  • Formula steps

    The equation and substitutions are printed, so the period can be verified by hand.

  • Assumptions stated

    The ideal-spring and small-angle pendulum limits are stated on the page rather than hidden.

How to use Simple Harmonic Motion Calculator

No account, no installation — the whole job happens in this browser tab.
  1. 01

    Choose the oscillator

    Select Spring for a mass on a spring or Pendulum for a simple pendulum.

  2. 02

    Choose what to calculate

    Find the period and frequency, or solve for the missing mass, stiffness, length or gravity.

  3. 03

    Enter the known properties

    Use the unit selectors for mass, length and the model-specific quantities; values must be positive.

  4. 04

    Read the period and frequency

    The headline gives the solved value, while the summary shows period, frequency and angular frequency.

  5. 05

    Check the formula

    The panel substitutes the properties into the period equation; Reset clears the fields for another case.

How this tool works

Works with
m, k or L, g → T
Processing
Client-side, in your browser. Nothing is uploaded.
Requirements
Chrome, Edge, Firefox or Safari · JavaScript enabled

Limitations worth knowing

  • Assumes an ideal, massless spring obeying Hooke's law with no damping.
  • Uses the small-angle approximation for the pendulum and does not model large-amplitude corrections.
  • Does not include driving forces, damping or nonlinear effects, so real oscillations may differ.

Privacy and file handling

Mass, stiffness, length and gravity values are processed entirely in your browser. Nothing is uploaded, stored or logged.

Read the full privacy policy

Simple Harmonic Motion Calculator FAQ

Short, direct answers to the questions people ask before using this tool.
What is simple harmonic motion?
Simple harmonic motion is oscillation in which the restoring force is directly proportional to displacement and directed back toward equilibrium. A mass on an ideal spring and a small-angle pendulum both follow this pattern, which gives them a well-defined period and frequency.
How do I calculate the period of a mass on a spring?
Use T = 2π√(m ÷ k), with mass in kilograms and spring stiffness in newtons per meter. A larger mass lengthens the period, while a stiffer spring shortens it; the period is independent of the oscillation amplitude in the ideal model.
How do I calculate the period of a pendulum?
Use T = 2π√(L ÷ g), with pendulum length in meters and gravitational acceleration in m/s². The period depends on the length and the local gravity, not on the bob's mass, as long as the small-angle approximation holds.
Does the period of a pendulum depend on its amplitude?
Only weakly, within the small-angle approximation used here. For larger swings the real period is slightly longer than the simple formula predicts, so the small-angle result is an approximation whose error grows with amplitude.
What is angular frequency in simple harmonic motion?
Angular frequency is ω = 2π ÷ T, measured in radians per second. It describes how fast the oscillation phase advances and connects the period to sinusoidal equations of motion, while ordinary frequency f = 1 ÷ T counts cycles per second.
Why does the pendulum period not depend on the mass?
In the small-angle regime the restoring force is proportional to mass times displacement over length, so the mass cancels when acceleration is computed. All masses at the same length and gravity therefore swing with the same period.
Can I use the calculator for a real spring with damping?
No. It models an undamped harmonic oscillator, so real damping, friction and air resistance are not included. A damped oscillator has a slightly different frequency and an amplitude that decays over time, which requires a damped-oscillation model.
Why must mass, stiffness, length and gravity be positive?
These quantities are magnitudes in the model: mass and stiffness cannot be zero or negative, and a pendulum needs a positive length and gravity to oscillate. The calculator reports an error instead of producing a mathematically impossible period.

Background reading

Format guides that explain the trade-offs behind Simple Harmonic Motion Calculator.