Why can an object not reach the speed of light?

As velocity increases toward c, the Lorentz factor γ grows without bound, so the energy required to accelerate the object increases without limit. An infinite amount of energy would be needed to reach exactly c, which is physically impossible for any massive object.

What is the Lorentz factor γ?

γ = 1/√(1−v²/c²). At low speeds γ ≈ 1, so relativistic effects are negligible. At 87% of c, γ ≈ 2; at 99% of c, γ ≈ 7.09; at 99.9% of c, γ ≈ 22.4.

What is rest energy (mc²)?

Rest energy is the energy equivalent of an object's mass at rest, given by Einstein's famous equation E = mc². For a 1 kg mass, rest energy equals about 89.9 petajoules (8.99×10¹⁶ J).

How does relativistic KE differ from classical KE?

Classical KE = ½mv² is accurate only when v ≪ c. Relativistic KE = (γ−1)mc² reduces to ½mv² at low speeds but grows much faster at high speeds. At 10% of c the difference is less than 1%; at 90% of c it is over 100%.

What is an electron-volt (eV)?

1 eV = 1.602176634×10⁻¹⁹ joules. Particle physicists prefer eV because the energies of subatomic particles are extremely small in joules. High-energy physics uses MeV (10⁶ eV), GeV (10⁹ eV), and TeV (10¹² eV).

What value of c does this calculator use?

The exact defined value: c = 299,792,458 m/s (metres per second), as set by the 2019 SI redefinition.

Relativistic Kinetic Energy Calculator

Enter rest mass and velocity (m/s or % of c) to compute the Lorentz factor, relativistic kinetic energy in joules and electron-volts, and classical KE for comparison.

Inputs

Rest Mass (m)

Velocity (v)

c = 299,792,458 m/s

Quick examples

Results

Enter values above and click Calculate to see results.

Lorentz Factor Reference

v/c (%)	γ	Correction vs. classical
10%	1.005	+0.76%
50%	1.155	+23.8%
87%	2.000	+172%
99%	7.089	+1,142%
99.9%	22.37	+4,182%
99.99%	70.71	+13,845%

Correction = (KE_relativistic − KE_classical) / KE_classical × 100%

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Summary

At speeds approaching the speed of light, classical kinetic energy (½mv²) underestimates the true energy of a moving object. Special relativity accounts for this with KE = (γ−1)mc², where γ = 1/√(1−v²/c²) is the Lorentz factor. This calculator takes rest mass and velocity as inputs and returns every intermediate quantity: γ, rest energy mc², total energy γmc², relativistic KE in both joules and electron-volts, and the classical approximation so you can see how large the relativistic correction is.

How it works

Enter the rest mass of the object in kilograms.
Enter the velocity either in metres per second (m/s) or as a percentage of the speed of light (% c).
The calculator computes the Lorentz factor γ = 1/√(1−v²/c²).
Rest energy mc², total energy γmc², and relativistic kinetic energy (γ−1)mc² are displayed in joules and electron-volts.
Classical kinetic energy ½mv² appears alongside so you can compare the two.
An error is shown if the entered velocity equals or exceeds c (299,792,458 m/s), since that is physically impossible for a massive object.

Use cases

Physics students checking special-relativity homework involving particle energetics.
Particle physicists converting beam kinetic energy between joules and electron-volts.
Aerospace researchers estimating energy budgets for hypothetical near-lightspeed vehicles.
Teachers demonstrating where classical mechanics breaks down relative to relativistic mechanics.
Science communicators illustrating how much energy would be needed to accelerate a 1 kg mass to 99% of c.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu