Einstein's E = mc² shows that mass at rest stores energy.
About this calculator
Einstein's E = mc² shows that mass at rest stores energy. Enter mass in kilograms; the calculator multiplies by c² where c = 299,792,458 m/s.
Example: 0.001 kg (1 gram) has rest energy about 9 × 10¹³ J — roughly the yield of a large conventional bomb if fully converted. In practice only nuclear reactions convert a small fraction of mass to energy.
Compare everyday energy scales with the [[kinetic-energy]] calculator (½mv²) — at ordinary speeds KE is far less than mc². The [[gravitational-potential-energy]] calculator covers mgh on Earth. Nuclear binding problems often follow this with the [[ideal-gas-law]] or [[wavelength]] calculators in different chapters. For force and acceleration at non-relativistic speeds, use the [[force]] calculator.
Common uses
- Modern physics and relativity homework
- Orders-of-magnitude exercises on nuclear energy
- Comparing rest energy to kinetic energy at everyday speeds
- Understanding why small mass defects release large energy in fission
- Exam prep for CBSE Class 12 dual nature and atoms units
Frequently asked questions
What is the rest energy of 0.001 kg (1 gram)?
E = mc² = 0.001 × (2.998 × 10⁸)² ≈ 9 × 10¹³ J. Enter mass 0.001. The result is shown in scientific notation because the number is huge.
Why is c squared in E = mc²?
Dimensional analysis requires energy (joules) from mass (kg). Multiplying by (m/s)² gives kg·m²/s² = J. c links spacetime in relativity.
Is kinetic energy the same as mc²?
No. mc² is total rest energy. Kinetic energy ½mv² adds for motion and is negligible compared to mc² until speeds approach c.
What mass has rest energy of about 1 joule?
m = E/c² ≈ 1 / (9 × 10¹⁶) ≈ 1.1 × 10⁻¹⁷ kg — about 10 picograms. Enter tiny masses to explore the scale.