Pendulum Period Calculator
Calculate the period of a simple pendulum from its length and local gravity — small-angle and exact large-amplitude period, frequency, angular frequency and swings per minute, for Earth, the Moon, Mars or a custom g.
Input
From the pivot to the centre of the bob.
Maximum swing angle from vertical, in degrees. Adds the exact large-angle period.
Output
| Metric | Value |
|---|---|
| No data yet | |
More ways to use this tool
REST API
curl -X POST https://api.iotools.cloud/v1/tool/pendulum-period-calculator \
-H "Authorization: Bearer YOUR_API_KEY" \
-H "Content-Type: application/json" \
-d '{
"length": "1",
"lengthUnit": "m",
"body": "earth",
"gravity": "",
"amplitude": ""
}'Swap in your own key from your account. The tool's fields are the body — no wrapper.
Ask an AI agent
Use the IOTools `pendulum-period-calculator` tool (Pendulum Period Calculator) on this input:
YOUR_INPUT_HEREPaste this at any agent connected to the IOTools MCP server, then add your input.
Embed widget
<iframe
src="https://iotools.cloud/embed/pendulum-period-calculator/"
width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
title="Pendulum Period Calculator — iotools.cloud"
sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
allow="clipboard-write"
style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>Drop this into your own page — free, no key required, just a link back.
| Cost per API/MCP call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
Also available with
Guides
Find how long one full swing of a simple pendulum takes from just its length and the local gravity. Results update as you type and include frequency, angular frequency and swings per minute.
How to use it
- Enter the length — pivot to the centre of the bob — and pick a unit.
- Choose gravity: Earth, the Moon, Mars, Venus, Jupiter, the Sun, or a custom value in m/s².
- Optionally enter an amplitude in degrees to get the exact period for big swings.
The formula
T = 2π √(L / g)
This small-angle formula is accurate to well under 1% for swings up to about 15°. The period depends on length and gravity only — not on the bob's mass. Quadrupling the length doubles the period.
Large swings
For wider swings the true period is longer. With an amplitude entered, the calculator uses the exact solution via the arithmetic–geometric mean, T = T₀ / AGM(1, cos(θ₀/2)), and reports how far the small-angle estimate is off. At 60° the exact period is about 7% longer.
Seconds pendulum
A pendulum with a 2-second period (1 s per swing) is about 0.994 m long on Earth. The last row of the results gives that length for the gravity you chose.