Pendulum Calculator
Calculate simple pendulum period and frequency from length and gravity.
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Formula result
Check before you use it
What the numbers show
The answer estimates how long one oscillation takes and how often the pendulum repeats under the ideal small-angle model.
Use pendulum calculator for oscillation timing checks, gravity comparisons, and introductory simple-harmonic-motion work.
For a simple pendulum, mass does not change the period.
Copy-ready formula handoff
Use this after solving the live calculator result, then paste the answer into a lab note, homework check, or engineering review.
T = 2*pi*sqrt(L / g), f = 1 / T
- Period: Time for one full oscillation.
- Pendulum length: Length from pivot to the pendulum bob center.
- Gravity: Local gravitational acceleration.
- Frequency: Oscillation count per second.
- The formula assumes small-angle oscillation.
- The pendulum is treated as simple and ideal.
- Using string length only to the bottom of the bob instead of pivot-to-center length.
- Applying the small-angle period formula to large swing angles without expecting a longer real period.
Pendulum Calculator result: [paste the solved value from the calculator above]. Formula used: T = 2*pi*sqrt(L / g), f = 1 / T Inputs checked: Period, Pendulum length, Gravity, Frequency. Assumptions: The formula assumes small-angle oscillation. The pendulum is treated as simple and ideal. Worked example: Pendulum length is 1.2 m on Earth. Enter L = 1.2 m and Earth gravity. Apply T = 2*pi*sqrt(L/g). Invert the period to get frequency. Next check: Using string length only to the bottom of the bob instead of pivot-to-center length.
Equation context
Built for oscillation timing checks, gravity comparisons, and introductory simple-harmonic-motion work. This page pairs the live calculator with the governing formula, variable glossary, and a worked example so the result is easier to trust and reuse.
Quick entry points
Use the calculator to verify arithmetic after you set up the formula yourself.
Change one input at a time to see which variable is driving the result.
Review the formula notes before using the answer in a lab or design check.
Variables to track
Time for one full oscillation. Unit: s.
Length from pivot to the pendulum bob center. Unit: m.
Local gravitational acceleration. Unit: m/s^2.
Oscillation count per second. Unit: Hz.
Formula method and unit assumptions
Formula and example
Worked example
Pendulum length is 1.2 m on Earth
- 1Enter L = 1.2 m and Earth gravity.
- 2Apply T = 2*pi*sqrt(L/g).
- 3Invert the period to get frequency.
Pendulums make the relationship between gravity and timing very intuitive because the formula is compact and physically interpretable.
Assumptions
Common mistakes
Related formula checks
Equation context and next checks
Formula and variable setup for Pendulum Calculator
Calculate simple pendulum period and frequency from length and gravity. The page is designed to help you move from the known values to the correct formula without rebuilding the derivation every time.
For pendulum calculator, the safest workflow is to confirm the unit system first, then map each symbol to the physical quantity in your problem statement before solving.
- T: Period (s) - Time for one full oscillation.
- L: Pendulum length (m) - Length from pivot to the pendulum bob center.
- g: Gravity (m/s^2) - Local gravitational acceleration.
- f: Frequency (Hz) - Oscillation count per second.
How to read the result
The answer estimates how long one oscillation takes and how often the pendulum repeats under the ideal small-angle model.
This tool is especially useful for oscillation timing checks, gravity comparisons, and introductory simple-harmonic-motion work. The output becomes more trustworthy when you compare nearby cases instead of relying on one single run.
- Period and frequency
- Custom gravity support
- Simple harmonic reference
Assumptions and limits
The calculator applies the standard textbook relation for this topic, which makes it a strong first-pass answer but not always a full real-world model.
Before you use the result in a lab, design review, or report, check whether the simplified assumptions still match the physical system you care about.
- The formula assumes small-angle oscillation.
- The pendulum is treated as simple and ideal.
- Air resistance and pivot friction are ignored.
Quick glossary
Time for one full oscillation.
Length from pivot to the pendulum bob center.
Local gravitational acceleration.
A simplified physics model that omits secondary effects so the first-order relationship is easier to inspect.
Formula checks before using the result
Formula questions
Checks before using the result
When should I use the pendulum calculator?
Use pendulum calculator for oscillation timing checks, gravity comparisons, and introductory simple-harmonic-motion work, especially when the governing formula is already known and the main need is a fast, transparent calculation.
What is the main thing the pendulum calculator tells me?
The answer estimates how long one oscillation takes and how often the pendulum repeats under the ideal small-angle model.
What can make the pendulum calculator answer inaccurate?
The answer is exact for the formula and assumptions on the page, but it can drift when the real system violates those assumptions. Common limits include The formula assumes small-angle oscillation. The pendulum is treated as simple and ideal. Air resistance and pivot friction are ignored.
Formula references and related examples
Formula Basis