Simple Pendulum Period Calculator

About the Simple Pendulum Period Calculator

The Simple Pendulum Period Calculator computes the period (\( T \)) of a simple pendulum using its length (\( L \)) and acceleration due to gravity (\( g \)). The formula is:

• Period: \( T = 2\pi \sqrt{\frac{L}{g}} \)

This tool is ideal for physics students, educators, and engineers studying oscillatory motion.

• Features:
  • Calculates the period based on pendulum length and gravity.
  • Supports unit conversions: length (m, cm).
  • Offers gravity presets: Earth (9.81 m/s²), Moon (1.625 m/s²), Mars (3.71 m/s²), or Custom.
  • Validates inputs: positive length and gravity.
  • Keypad includes digits, decimal point, pi (π), and standard gravity (g).
  • Clear and backspace functionality, with a "Copy" button for results.
• Practical Applications: Useful in physics education, laboratory experiments, and designing pendulum-based devices (e.g., clocks).
• How to Use:
  • Enter the pendulum length (e.g., 1 m) and select the unit (m or cm).
  • Select a gravity preset (e.g., Earth) or enter a custom gravity value (e.g., 9.81).
  • Use the keypad to insert digits, decimal point, pi (π), or standard gravity (g).
  • Click "Calculate" to compute the period and view steps, then use "Copy" to copy the result.
  • Use "Clear" to reset, or "⌫" to delete the last character.
  • Share or embed the calculator using the action buttons.
• Helpful Tips:
  • Ensure length and gravity are positive.
  • Use Earth’s gravity (9.81 m/s²) for standard conditions, or select presets for other celestial bodies.
  • Results are in seconds (ms if period is small, e.g., < 0.1 s).
  • Assumes small-angle oscillations and no air resistance; for real-world scenarios, results are approximate.
  • The length is measured from the pivot to the center of mass of the pendulum bob.
• Examples:
  • Example 1: Pendulum on Earth:
    • Input: Length = 1 m, Gravity = 9.81 m/s² (Earth)
    • Steps:
      • Period: \( T = 2\pi \sqrt{\frac{1}{9.81}} \approx 2 \cdot 3.14159 \cdot \sqrt{0.101936} \approx 2.006 \, \text{s} \)
    • Result: Period ≈ 2.01 s
  • Example 2: Short Pendulum on Moon:
    • Input: Length = 50 cm (0.5 m), Gravity = 1.625 m/s² (Moon)
    • Steps:
      • Convert: 50 cm = 0.5 m
      • Period: \( T = 2\pi \sqrt{\frac{0.5}{1.625}} \approx 2 \cdot 3.14159 \cdot \sqrt{0.307692} \approx 3.484 \, \text{s} \)
    • Result: Period ≈ 3.48 s
  • Example 3: Tiny Pendulum on Mars:
    • Input: Length = 10 cm (0.1 m), Gravity = 3.71 m/s² (Mars)
    • Steps:
      • Convert: 10 cm = 0.1 m
      • Period: \( T = 2\pi \sqrt{\frac{0.1}{3.71}} \approx 2 \cdot 3.14159 \cdot \sqrt{0.026954} \approx 1.031 \, \text{s} \)
    • Result: Period ≈ 1.03 s

Calculate the period of a simple pendulum with detailed steps using this Simple Pendulum Period Calculator. Share or embed it on your site!