Why is the period independent of amplitude?
For small angles, the restoring force is approximately linear in displacement, making the oscillation isochronous. This breaks down for large amplitudes.
Pendulum Period Calculator
T = 2π √(L/g)
Calculate the period of a simple pendulum from its length. T = 2π√(L/g) — valid for small angles.
Calculate
Enter values above to calculate
How it calculates
1
Ensure L is in metres and g in m/s²
2
Compute: T = 2π × √(L/g)
3
Result in seconds
Formula
T = 2π √(L/g)
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| T | Period | s |
| L | Pendulum length | m |
| g | Gravitational acceleration | m/s² |
| f | Frequency = 1/T | Hz |
→ Simple Harmonic Motion article
How to Use This Calculator
This pendulum period calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula T = 2π √(L/g) is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
Find the period of a 1.0 m pendulum on Earth (g = 9.81 m/s²).
Step 1: T = 2π √(L/g)
Step 2: T = 2π √(1.0/9.81)
Step 3: T = 2π × 0.3193
Answer: T ≈ 2.007 s (the "seconds pendulum")
Common Mistakes
- The formula assumes small angles (< ~15°). Larger angles give longer periods
- Period is independent of mass — a heavier bob has the same period
- On the Moon (g = 1.62 m/s²), the period is √(9.81/1.62) ≈ 2.46× longer
Related
Frequently Asked Questions
How does period depend on length?
T ∝ √L. Quadrupling length doubles the period.