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Relativistic Mass Calculator

Work out relativistic mass instantly with clear inputs, formula shown and shareable results.

About Relativistic Mass Calculator

Relativistic mass is gamma times rest mass, so a 1 kg object at 0.9c has an inertia of 2.294 kg. The extra inertia is really the kinetic energy: (gamma - 1)m0c^2, here 1.16e17 J. Modern practice keeps mass invariant and puts gamma in the energy and momentum instead, but the effect on accelerating the object is the same.

Formulas

Relativistic mass

m = gamma m0

Kinetic energy

KE = (gamma - 1) m0 c^2

Worked example

With the default values below, Relativistic Mass Calculator returns Relativistic Mass of 2.2942. Change any input above and every figure here is recalculated in your browser.

Inputs used

Rest massminimum 0 kg
1 kg
Speed as a fraction of light speedaccepts 0–1
0.9

Results

Relativistic Mass
2.2942 kg
Lorentz Factor
2.2942
Kinetic Energy
1.1631 × 10¹⁷ J
Rest Energy
8.9876 × 10¹⁶ J

Step by step

  1. 1Values used
  2. 2Relativistic mass
  3. 3Kinetic energy
  4. 4Relativistic Mass= 2.2942 kg
  5. 5Lorentz Factor= 2.2942
  6. 6Kinetic Energy= 116,313,000,000,000,000.0000 J
  7. 7Rest Energy= 89,875,500,000,000,000.0000 J

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why do physicists avoid the term relativistic mass?

Because it invites confusion - it is direction-dependent for forces and adds nothing that energy and momentum do not already describe.

Why can nothing reach light speed?

Because gamma diverges as v approaches c, so the energy needed grows without limit. Reaching c would take infinite energy.

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