E=mc2 Calculator

| Added in Physics

Understanding E=mc²

Einstein's famous equation, E=mc², revolutionized physics by showing that mass and energy are fundamentally the same thing in different forms. The equation tells us that energy (E) equals mass (m) times the speed of light (c) squared.

The Formula

[\text{Energy (E)} = \text{mass (m)} \times c^2]

Where c = 299,792,458 m/s (the speed of light in a vacuum)

Example Calculation

Let's calculate the energy equivalent of a 2 kg object:

Step-by-Step Calculation:

  1. First, measure the mass: Mass = 2 kg
  2. Next, use the speed of light squared:
    (299,792,458 m/s)² = 8.98755179 × 10¹⁶ (m²/s²)
  3. Finally, multiply them together:
    Energy = 2 kg × 8.98755179 × 10¹⁶ m²/s²

This results in: Energy = 1.79751036 × 10¹⁷ Joules (J)

So, that 2 kg object contains approximately 1.79751036 × 10¹⁷ Joules of energy!

Putting This in Perspective

To understand how much energy this is:

  • 1.8 × 10¹⁷ Joules is roughly equivalent to the energy released by 43 megatons of TNT
  • This is more than twice the energy of the largest nuclear weapon ever tested
  • It could power an average U.S. household for over 4 million years

This demonstrates why nuclear reactions, which convert just a tiny fraction of mass to energy, can be so powerful.

Frequently Asked Questions

E=mc² is Albert Einstein's famous equation from his theory of special relativity. It shows that energy (E) and mass (m) are interchangeable, related by the speed of light squared (c²). This equation demonstrates that a small amount of mass contains an enormous amount of energy.

The energy is calculated by multiplying the mass (in kilograms) by the speed of light squared (299,792,458 m/s)². The result is expressed in Joules (J), the standard unit of energy in physics.

The speed of light (c) is approximately 299,792,458 meters per second. When squared, this becomes about 8.98755179 × 10¹⁶ m²/s². This enormous number explains why even tiny amounts of mass represent huge amounts of energy.

E=mc² explains the energy released in nuclear reactions, both in nuclear power plants and atomic weapons. It also describes how stars produce energy through fusion, and is fundamental to understanding particle physics and cosmology.

In practice, complete conversion of mass to energy is extremely difficult. Nuclear reactions only convert a small fraction of mass to energy. However, matter-antimatter annihilation can achieve nearly complete conversion, which is why antimatter is so energetic.