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Pendulum Kinetic Energy Calculator — result sheet
Estimate height drop, ideal speed, potential-energy loss, and kinetic-energy gain for a pendulum released from rest at one angle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Height above the lowest point = L(1 − cos θ); height drop = L(cos θcurrent − cos θrelease); potential-energy loss = mgΔh; speed from rest = √(2gΔh); kinetic energy = ½mv².
This page follows mechanical-energy conservation for an ideal pendulum. It compares the release and current angles, calculates the vertical drop, and reports the ideal speed and kinetic energy gained when the bob starts from rest and non-conservative losses are neglected.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Pendulum bob mass — kg; minimum 1.0E-6; maximum 1000000
- Pendulum length — m; minimum 1.0E-6; maximum 1000000
- Release angle from downward vertical — degrees; minimum 0; maximum 179.999
- Current angle from downward vertical — degrees; minimum 0; maximum 179.999
- Gravitational acceleration — m/s²; minimum 1.0E-6; maximum 100
Worked example
| Input | Value |
|---|---|
| Pendulum bob mass | 1 |
| Pendulum length | 1 |
| Release angle from downward vertical | 30 |
| Current angle from downward vertical | 0 |
| Gravitational acceleration | 9.80665 |
The bob drops 0.133975 m, loses about 1.314 J of potential energy, and reaches about 1.620 m/s at the lowest point in the ideal model.
Assumptions and limits
- The bob is modeled as a point mass at the end of a rigid massless length.
- The bob starts from rest at the release angle.
- Current angle is at or below the release angle on the same side of the swing.
- Air resistance, pivot friction, string flex, and impacts are ignored.
- Angles are measured from the downward vertical in degrees.
- The result is an ideal mechanics estimate, not a measured speed or safety assessment.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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