What is the formula for a simple pendulum's period?

The period is T = 2π√(L/g), where L is the length in metres and g is the local gravity in m/s². A 1 metre pendulum on Earth (g = 9.81) gives T = 2π√(1/9.81) ≈ 2.006 seconds. The √ means length has a square-law grip on time: to double the period you must make the pendulum four times longer, not twice as long.

Does a heavier bob swing faster or slower?

Neither. The mass of the bob cancels out of the equation of motion, so a brass weight and a cork of the same length swing with the same period. Galileo noticed this in a cathedral around 1602, and it is why a grandfather clock keeps time no matter how heavy its pendulum is. Only the length and gravity move the number.

Why does the amplitude not matter?

It does matter a little, but for small swings the effect is tiny. T = 2π√(L/g) is the small-angle approximation, accurate to better than 0.5 percent while the swing stays under about 15 degrees from vertical. Push a pendulum to 45 degrees and the real period is roughly 4 percent longer, so wide swings drift slow. This calculator assumes the small-angle case.

How long is a pendulum that ticks once per second?

Switch to the period-to-length mode and enter T = 1 second. On Earth you get L = g(T/2π)² ≈ 0.248 metres, about 24.8 cm. A pendulum that completes a full back-and-forth in two seconds (the classic seconds pendulum, one tick each way) is near 0.994 metres, which is why metre-long clock pendulums are so common.

How does the period change on the Moon?

Lower gravity means a longer period. Because T scales as 1/√g, a 1 metre pendulum that takes 2.006 seconds on Earth takes about 4.93 seconds on the Moon (g = 1.62), roughly 2.46 times as long. Pick the Moon preset to see it, or type any g. A clock tuned on Earth would run badly slow on the Moon until its pendulum was shortened.

Is this accurate enough for a real clock or lab report?

For a homework problem, a lab prediction or sizing a metronome it is precise to the millisecond. The limits are physical, not numerical: it ignores air resistance, the mass of the rod, the size of the bob and large-amplitude correction, all of which a real clock maker tunes out empirically. Treat the answer as the ideal small-angle value and measure to confirm.

Check a physics homework answer

A worksheet asks for the period of a 0.5 metre pendulum. Enter 0.5, keep gravity at 9.81, and read T ≈ 1.42 seconds and f ≈ 0.70 Hz. The copy button gives you the formula line and the numbers to paste into your write-up, so you can verify your hand calculation in one step.

Size a pendulum for a target beat

Building a metronome or a kinetic sculpture that should swing once a second? Switch to period-to-length mode, type 1 second, and the tool returns 0.248 metres. Want a slow 3 second swing instead? Type 3 and it gives 2.24 metres, so you cut the rod to length before gluing.

Teach why mass does not matter

Demonstrate Galileo's result in class without a stopwatch. Show that changing the length changes the period while the mass never appears in the formula. Share the URL with a fixed length so every student opens the same setup, then have them predict before you run the real swing.

Compare gravity across worlds

Set a 1 metre pendulum and click through Earth, Moon and Mars. The period stretches from about 2.0 to 4.9 to 3.3 seconds, a concrete way to feel how weak lunar gravity is, far better than a table of numbers.

Pendulum Period Calculator — T = 2π√(L/g)

T = 2π√(L/g) — solve a simple pendulum's period, frequency or length, with Earth, Moon and Mars gravity, browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

What do you know?

Pendulum length L (m)

Gravity g (m/s²)

Gravity preset

Results

Period T2.006 s

Frequency f0.498 Hz

Half-period (one swing)1.003 s

T = 2π·√(L/g) · Valid for swings under about 15°. Period does not depend on the bob mass or the amplitude.

What this tool does

Free simple pendulum period calculator. Enter the length of a pendulum and it returns the period T from the textbook formula T = 2π√(L/g), the frequency f = 1/T in hertz, and the half-period (the time for one swing across). Flip the mode and it works backward: type the period you want, such as the one-second-per-swing beat of a seconds pendulum, and read the length you need to build. Pick Earth (9.81), Moon (1.62) or Mars (3.72) gravity from a preset, or type your own g for a physics lab. The result makes the surprising part of pendulum physics obvious: the period depends only on length and gravity, never on the mass of the bob and never on the amplitude as long as the swing stays under about 15 degrees. One click copies a clean text summary, and the shareable URL reproduces your exact length, period and gravity. Everything runs in your browser, nothing is uploaded.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Student; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Pendulum Period Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Check a physics homework answer
A worksheet asks for the period of a 0.5 metre pendulum. Enter 0.5, keep gravity at 9.81, and read T ≈ 1.42 seconds and f ≈ 0.70 Hz. The copy button gives you the formula line and the numbers to paste into your write-up, so you can verify your hand calculation in one step.
Size a pendulum for a target beat
Building a metronome or a kinetic sculpture that should swing once a second? Switch to period-to-length mode, type 1 second, and the tool returns 0.248 metres. Want a slow 3 second swing instead? Type 3 and it gives 2.24 metres, so you cut the rod to length before gluing.
Teach why mass does not matter
Demonstrate Galileo's result in class without a stopwatch. Show that changing the length changes the period while the mass never appears in the formula. Share the URL with a fixed length so every student opens the same setup, then have them predict before you run the real swing.
Compare gravity across worlds
Set a 1 metre pendulum and click through Earth, Moon and Mars. The period stretches from about 2.0 to 4.9 to 3.3 seconds, a concrete way to feel how weak lunar gravity is, far better than a table of numbers.

Common pitfalls

Entering the length in centimetres instead of metres. The formula expects metres, so a 50 cm pendulum is 0.5, not 50. Typing 50 returns a 14 second period. The field is labelled in metres for this reason.
Confusing the period with one swing. The period T is a full round trip. The time for a single one-way swing is T/2, the half-period. A seconds pendulum ticks every 1 second, so its full period is 2 seconds.
Trusting the result for a wide swing. T = 2π√(L/g) is only the small-angle case. Past about 15 degrees the real period runs measurably longer, so a wide release lags the prediction.

Privacy

Every calculation runs in your browser tab as plain JavaScript. No length, period or result leaves the page and nothing is logged. The shareable URL does encode your inputs in the query string, so a link pasted into chat records those values in the recipient server's access log.

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Pendulum Period Calculator — T = 2π√(L/g)

Results

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Pendulum Period Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Check a physics homework answer

Size a pendulum for a target beat

Teach why mass does not matter

Compare gravity across worlds

Common pitfalls

Privacy

FAQ

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