Physics

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Relativistic Kinetic Energy Calculator.

Calculate K=(γ−1)mc² for a speed below c.

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Set your values

Results update as you type.

Kinetic energy: 5,460,117,501,784,992 J

Kinetic energy

0.000000J
Lorentz factor: 1.060752

Lorentz factor

0.000000

Results update automatically as you type.

Use Cases

Physics homework and exam prep

Students can verify calculations for problems involving particles moving at relativistic speeds, such as electrons in accelerators or cosmic rays.

Example: Calculate the kinetic energy of an electron (9.11e-31 kg) moving at 0.9c.

Engineering and research calculations

Engineers and researchers working with particle accelerators or space travel can quickly estimate energy requirements for objects at high speeds.

Example: Estimate the energy needed to accelerate a 1 kg probe to 0.5c.

Frequently Asked Questions

What is relativistic kinetic energy?
Relativistic kinetic energy is the energy an object has due to its motion, calculated using Einstein's formula K=(γ−1)mc², where γ is the Lorentz factor. It accounts for effects at speeds close to the speed of light, unlike classical kinetic energy (1/2 mv²).
Why can't I enter a speed equal to or greater than the speed of light?
The calculator is designed for speeds below c (299,792,458 m/s). At v=c, the Lorentz factor becomes infinite, and the formula yields infinite energy, which is physically impossible. Speeds above c are not allowed by relativity.
How does this calculator handle low speeds?
For speeds much lower than c, the relativistic kinetic energy approaches the classical value (1/2 mv²). The calculator uses the exact relativistic formula, so it remains accurate at all speeds below c, but you may notice negligible difference at everyday speeds.

Tips & Common Mistakes

Tips

  • Ensure the speed is entered in meters per second (m/s) and is less than 299,792,458 m/s.
  • For very low speeds, the result will be nearly equal to classical kinetic energy; use the calculator to see the difference.
  • Use scientific notation for very small or large masses to avoid errors, e.g., 9.11e-31 for electron mass.
  • Double-check your units: mass must be in kilograms (kg) and speed in meters per second (m/s).

Common Mistakes to Avoid

  • Entering a speed greater than or equal to the speed of light, which is invalid and will not produce a result.
  • Using units other than kg and m/s without converting, leading to incorrect energy values.
  • Confusing relativistic kinetic energy with total energy (E=γmc²) or rest energy (mc²).

Last updated: August 13, 2026