# Mass-Energy Equivalence Calculator (E = mc²)

Calculate energy from mass or mass from energy using Einstein's E = mc². Shows results in Joules, MeV, and TNT equivalent.

## What this calculates

Einstein's famous equation E = mc² reveals that mass and energy are interchangeable. A small amount of mass contains an enormous amount of energy because the speed of light squared (c² ≈ 9 × 10¹⁶ m²/s²) is such a large number. This calculator converts between mass and energy in both directions, with results in Joules, MeV, and TNT equivalent.

## Inputs

- **Solve For** — options: Energy (from mass), Mass (from energy) — Choose whether to convert mass to energy or energy to mass.
- **Mass** (kg) — min 0 — Mass to convert to energy (used when solving for energy).
- **Energy** (J) — min 0 — Energy to convert to mass (used when solving for mass).

## Outputs

- **Energy** (J) — Energy in Joules
- **Energy** (MeV) — Energy in mega-electronvolts
- **Equivalent Mass** (kg) — Mass equivalent of the energy
- **TNT Equivalent** (tons) — Equivalent energy in tons of TNT

## Details

The mass-energy equivalence E = mc², published by Albert Einstein in 1905 as part of special relativity, shows that mass itself is a form of energy. The speed of light c = 299,792,458 m/s is so large that even tiny amounts of mass correspond to enormous energies.

For example, 1 kilogram of matter fully converted to energy yields about 9 × 10¹⁶ Joules, equivalent to roughly 21.5 megatons of TNT. This is the energy released by a large thermonuclear weapon. In nuclear fission, only about 0.1% of mass is converted; in fusion, about 0.7%. Even these tiny fractions release tremendous energy.

The equation works in reverse too: energy has an equivalent mass. The heat added to a pot of boiling water increases its mass by an immeasurably small amount. At the subatomic scale, the mass of a proton is mostly binding energy of quarks rather than the rest mass of the quarks themselves. E = mc² is not just a theoretical curiosity but the foundation of nuclear power, particle physics, and cosmology.

## Frequently Asked Questions

**Q: What does E = mc² mean?**

A: It means that mass and energy are equivalent and interchangeable. The energy content of an object equals its mass multiplied by the speed of light squared. Even a tiny mass contains enormous energy because c² is about 9 × 10¹⁶ m²/s².

**Q: How much energy is in 1 kg of matter?**

A: One kilogram of matter fully converted to energy yields about 8.99 × 10¹⁶ Joules, or approximately 21.5 megatons of TNT. This is roughly the energy output of 430 Hiroshima-sized atomic bombs.

**Q: Is mass actually destroyed in nuclear reactions?**

A: Yes. In nuclear fission and fusion, a small fraction of mass is converted to energy. In fission (splitting heavy atoms), about 0.1% of mass is converted. In fusion (combining light atoms), about 0.7% is converted. The 'missing' mass appears as kinetic energy of products and radiation.

**Q: What is an electronvolt (eV)?**

A: An electronvolt is the energy gained by an electron moving through a 1-volt potential difference: 1 eV = 1.602 × 10⁻¹⁹ J. Particle physicists commonly use MeV (10⁶ eV) or GeV (10⁹ eV). A proton's rest mass energy is about 938.3 MeV.

**Q: Does E = mc² apply to everyday objects?**

A: Yes, but the effects are unmeasurably small. A hot cup of coffee has slightly more mass than a cold one due to its thermal energy. A compressed spring is slightly heavier than a relaxed one. These mass differences are far too small to detect with any scale.

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Source: https://vastcalc.com/calculators/physics/mass-energy
Category: Physics
Last updated: 2026-04-21