Mass Energy Calculator
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What is Mass-Energy Equivalence?
Mass-energy equivalence is one of the most famous concepts in physics, expressed by Einstein's equation E = mc². This fundamental principle states that mass and energy are interchangeable - a small amount of mass can be converted into an enormous amount of energy.
The equation shows that energy (E) equals mass (m) multiplied by the speed of light (c) squared. Since the speed of light is approximately 299,792,458 meters per second, even tiny amounts of mass correspond to tremendous amounts of energy.
This calculator performs precise conversions between mass and energy using Einstein's formula, supporting various units for both mass (kg, g, atomic mass units) and energy (Joules, electron volts, calories, etc.). It's essential for understanding nuclear reactions, particle physics, and stellar processes.
How It Works
Choose Type
Mass to Energy or Energy to Mass
Enter Value
Input mass or energy with units
Apply E=mc²
Calculate using Einstein's formula
Get Results
View conversions in multiple units
Einstein's Mass-Energy Equivalence:
Formula: E = mc² (Energy = Mass × Speed of Light²)
Reverse: m = E/c² (Mass = Energy / Speed of Light²)
Speed of Light: c = 299,792,458 m/s (exact value)
Key Insight: A tiny amount of mass converts to enormous energy due to c²
Applications: Nuclear reactions, particle physics, stellar fusion, atomic energy
Common Examples
1 Gram of Matter
Proton Rest Mass
Electron Rest Mass
Calculation Reference Table
| Mass | Energy (Joules) | Energy (eV) | Equivalent | Real-World Context |
|---|---|---|---|---|
| 1 kg | 9.0 × 10¹⁶ J | 5.6 × 10³⁵ eV | 25 billion kWh | Power entire city for months |
| 1 g | 9.0 × 10¹³ J | 5.6 × 10³² eV | 25 million kWh | Hiroshima bomb energy |
| 1 u (atomic) | 1.49 × 10⁻¹⁰ J | 931.5 MeV | Atomic mass unit | Nuclear binding energy |
| Proton mass | 1.50 × 10⁻¹⁰ J | 938.3 MeV | Proton rest energy | Particle accelerators |
| Electron mass | 8.19 × 10⁻¹⁴ J | 0.511 MeV | Electron rest energy | Pair production threshold |
| 1 mg | 9.0 × 10¹⁰ J | 5.6 × 10²⁹ eV | 25,000 kWh | Small nuclear reaction |
Frequently Asked Questions
What does E=mc² actually mean?
E=mc² means that energy (E) and mass (m) are interchangeable. A small amount of mass can be converted into an enormous amount of energy because it's multiplied by c² (the speed of light squared), which is approximately 9 × 10¹⁶ m²/s². This explains why nuclear reactions release so much energy from tiny amounts of matter.
How accurate is this calculator?
This calculator uses the exact value of the speed of light (299,792,458 m/s) as defined by international standards. All unit conversions are based on precise scientific constants, including the atomic mass unit (1.66053906660 × 10⁻²⁷ kg) and electron volt (1.602176634 × 10⁻¹⁹ J). Results are accurate to the precision of your input values.
When is mass-energy conversion actually observed?
Mass-energy conversion occurs in nuclear reactions (fission and fusion), radioactive decay, particle-antiparticle annihilation, and stellar processes. In chemical reactions, the mass change is too small to measure directly, but in nuclear processes, measurable amounts of mass are converted to energy, powering stars and nuclear reactors.
Why is the speed of light squared in the equation?
The c² factor comes from the relationship between energy and momentum in special relativity. It represents the conversion factor between mass and energy units. Since c is very large (about 300 million m/s), c² is enormous (about 9 × 10¹⁶ m²/s²), which is why small masses correspond to huge energies.
What are the practical applications of E=mc²?
E=mc² is fundamental to nuclear power generation, medical imaging (PET scans), carbon dating, particle accelerators, nuclear weapons, stellar astrophysics, and understanding how the sun produces energy. It also explains why elements heavier than iron can only be formed in supernovae, where extreme energies are available.
Can matter be completely converted to energy?
Complete mass-to-energy conversion occurs only in matter-antimatter annihilation, where 100% of the mass becomes energy (usually gamma rays). In nuclear fission, only about 0.1% of mass is converted to energy, while in fusion, about 0.7% is converted. Chemical reactions convert less than 0.000001% of mass to energy.
What units should I use for calculations?
For atomic and nuclear physics, use atomic mass units (u) for mass and electron volts (eV, MeV, GeV) for energy. For macroscopic calculations, use kilograms for mass and joules for energy. The calculator automatically handles conversions between all supported units, so you can input values in whatever units are most convenient.
How does this relate to nuclear binding energy?
Nuclear binding energy is the energy required to separate a nucleus into individual protons and neutrons. It equals the mass difference between the separated nucleons and the intact nucleus, multiplied by c². This "mass defect" explains why atomic masses are slightly less than the sum of their constituent particles.
Is E=mc² the complete equation?
E=mc² is the rest mass energy equation for objects at rest. The complete relativistic energy equation is E² = (mc²)² + (pc)², where p is momentum. For objects at rest (p=0), this reduces to E=mc². For massless particles like photons, m=0, so E=pc. This calculator focuses on rest mass energy conversions.