Mass-Energy Calculator - Einstein's E=mc²

This revolutionary physics calculator demonstrates Einstein's most famous equation: E=mc². This equation reveals the profound relationship between mass and energy, showing that mass can be converted into energy and vice versa.

Einstein's Mass-Energy Equivalence

The fundamental equation of mass-energy equivalence is:

E = mc²

Where:

• E: Energy (in joules)
• m: Mass (in kilograms)
• c: Speed of light (299,792,458 m/s)

Relativistic Energy

For objects moving at relativistic speeds, the total energy becomes:

E = γmc²

Where γ (gamma) is the Lorentz factor: γ = 1/√(1 - v²/c²)

Energy Components

• Rest Energy (E₀): Energy equivalent of mass at rest (E₀ = mc²)
• Kinetic Energy (K): Energy due to motion (K = (γ-1)mc²)
• Total Energy (E): Sum of rest and kinetic energy (E = γmc²)

Key Concepts

• Mass-Energy Equivalence: Mass and energy are interchangeable
• Rest Energy: The energy contained in mass even when stationary
• Relativistic Mass: Mass appears to increase with velocity
• Nuclear Binding Energy: Energy released in nuclear reactions

Real-World Applications

• Nuclear Power: Mass is converted to energy in nuclear reactions
• Nuclear Weapons: Small amounts of mass release enormous energy
• Particle Accelerators: Particles gain relativistic energy
• Antimatter Annihilation: Complete conversion of mass to energy
• Solar Fusion: Hydrogen nuclei fuse, releasing binding energy

Fascinating Examples

• 1 kg of Mass: Contains enough energy to power a city for days
• Nuclear Fusion: 0.7% of hydrogen mass converts to energy in the Sun
• Antimatter: Complete annihilation releases 100% of mass as energy
• Chemical Reactions: Only tiny fractions of mass convert to energy
• Nuclear Fission: About 0.1% of uranium mass converts to energy

Energy Units

• Joule (J): SI unit of energy
• Electron Volt (eV): Energy gained by electron in 1V potential
• Mega Electron Volt (MeV): 1 million electron volts
• Giga Electron Volt (GeV): 1 billion electron volts

Interesting Facts

• 1 kg of mass contains about 90 petajoules of energy
• This is equivalent to the energy released by 21 megatons of TNT
• The Sun converts about 4 million tons of mass to energy every second
• Nuclear power plants convert only about 0.1% of fuel mass to energy
• Chemical reactions convert only about 0.0000001% of mass to energy

Historical Significance

Einstein's E=mc² revolutionized our understanding of the universe by showing that:

• Mass and energy are fundamentally the same thing
• Enormous amounts of energy are locked in ordinary matter
• The speed of light is the ultimate speed limit
• Space and time are interconnected (spacetime)