E=mc² Calculator

Our free online E=mc² calculator helps you compute mass-energy equivalence using Einstein's famous equation. Convert between mass and energy instantly using the speed of light constant. Perfect for physics students, researchers, and anyone curious about relativity.

What is E=mc²?

E=mc² is Einstein's mass-energy equivalence equation from his special theory of relativity. It states that energy (E) equals mass (m) times the speed of light (c) squared. This equation reveals that mass and energy are two forms of the same thing and can be converted into each other.

\[ E = mc^2 \]

Where:

E = energy (in joules)
m = mass (in kilograms)
c = speed of light in vacuum (≈ 299,792,458 m/s)

How to Use the Calculator

Choose whether you want to calculate energy from mass or mass from energy. Enter the known value and select the appropriate units. The calculator uses the exact speed of light constant and supports multiple mass and energy units including kg, g, lb, oz, J, kJ, MJ, GJ, cal, and kWh.

Examples

Example 1: Energy from 1 kg of Mass

How much energy is contained in 1 kilogram of matter?

\[ E = 1 \times (299,792,458)^2 = 8.9876 \times 10^{16} \text{ joules} \]

This is approximately the energy output of a 21-megaton nuclear bomb.

Example 2: Mass Equivalent of 1 kWh

What is the mass equivalent of 1 kilowatt-hour of energy?

\[ m = \frac{3,600,000}{(299,792,458)^2} = 4.0 \times 10^{-11} \text{ kg} \]

This is about 40 picograms - an incredibly small amount of mass for a substantial amount of energy.

Frequently Asked Questions

What does E=mc² mean in simple terms?

E=mc² means that mass and energy are interchangeable. A small amount of mass can be converted into a huge amount of energy because the speed of light squared (c²) is an enormous number (about 90 quadrillion). This is why nuclear reactions produce such immense energy from tiny amounts of matter.

Can I change the speed of light value?

Yes, the calculator lets you adjust the speed of light value. The default is 299,792,458 m/s (the exact speed of light in vacuum). You can change it for approximation purposes or educational demonstrations.

What units does the calculator support?

The calculator supports multiple mass units (kg, g, mg, lb, oz) and energy units (J, kJ, MJ, GJ, cal, kWh). It automatically converts between units for accurate calculations.

Where is E=mc² used in real life?

E=mc² is fundamental to nuclear power generation, nuclear weapons, particle physics, and understanding stellar processes like fusion in stars. It also explains why the sun produces so much energy and is used in medical PET scans.

What is the difference between calculating E from m and m from E?

The calculator supports both directions. Given mass, it computes the equivalent energy (E = mc²). Given energy, it computes the equivalent mass (m = E/c²). Both use the same fundamental relationship between mass and energy.

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