E = mc² Calculator
Calculate the equivalence between mass and energy using Einstein's famous equation
Enter the mass in kilograms
How to Use This Calculator
Select Calculation Mode
Choose whether you want to calculate energy from mass or mass from energy.
Enter Your Value
Input the mass in kilograms or energy in Joules depending on your selected mode.
Calculate
Click "Calculate" to get the equivalent energy or mass using E = mc².
Interpret Results
Review the calculated energy (also shown in TNT equivalents for perspective) or mass. The results demonstrate the enormous amount of energy contained in matter.
Formula
E = mc²
where E is energy, m is mass, and c is the speed of light (299,792,458 m/s)
Example 1: Energy from Mass
Given: Mass = 1 kg
E = 1 × (299,792,458)²
E = 1 × 8.987551787 × 10¹⁶
E = 8.988 × 10¹⁶ J
This is equivalent to approximately 21.48 megatons of TNT!
Example 2: Mass from Energy
Given: Energy = 1 × 10¹⁵ J
m = E / c²
m = 1 × 10¹⁵ / (299,792,458)²
m = 1 × 10¹⁵ / 8.987551787 × 10¹⁶
m = 0.0111 kg (about 11.1 grams)
Example 3: Nuclear Energy
Given: Mass defect = 0.001 kg (1 gram) in nuclear reaction
E = 0.001 × (299,792,458)²
E = 8.988 × 10¹³ J
This is equivalent to approximately 21.48 kilotons of TNT
About E = mc²
E = mc² is perhaps the most famous equation in physics, discovered by Albert Einstein as part of his theory of special relativity. It states that mass and energy are equivalent and can be converted into each other. The equation shows that even a small amount of mass contains an enormous amount of energy.
The Meaning of E = mc²
This equation means that mass is a form of energy. When mass is converted to energy (as in nuclear reactions), or when energy is converted to mass (as in particle creation), the relationship is governed by this simple but profound equation. The factor c² (speed of light squared) is a huge number, which is why even tiny amounts of mass can release enormous amounts of energy.
When to Use This Calculator
- Physics Education: Teaching students about mass-energy equivalence
- Nuclear Physics: Calculating energy released in nuclear reactions
- Particle Physics: Understanding particle creation and annihilation
- Astrophysics: Calculating energy from stellar processes
- Engineering: Understanding nuclear power and weapons
Why Use Our Calculator?
- ✅ Instant Results: Calculate mass-energy equivalence immediately
- ✅ Bidirectional: Calculate either energy from mass or mass from energy
- ✅ Educational: Clear explanations and examples
- ✅ 100% Free: No registration or payment required
- ✅ Accurate: Uses precise values for the speed of light
- ✅ Practical: Shows TNT equivalents for energy perspective
Applications of E = mc²
Nuclear Power: Nuclear reactors convert a tiny fraction of mass into energy. For example, in a nuclear fission reaction, about 0.1% of the mass is converted to energy, which is still enormous.
Nuclear Weapons: Atomic bombs convert a small amount of mass (typically less than 1 gram) into explosive energy equivalent to thousands of tons of TNT.
Particle Physics: In particle accelerators, high-energy collisions can convert energy into mass, creating new particles. This is how the Higgs boson and other particles are discovered.
Stellar Processes: In stars, nuclear fusion converts mass into energy. The Sun converts about 4 million tons of mass into energy every second, powering the star.
Interesting Facts
- 1 gram of mass is equivalent to about 21.5 kilotons of TNT
- The energy in 1 kg of mass could power a 100-watt light bulb for about 285 million years
- In nuclear fusion, only about 0.7% of mass is converted to energy
- In nuclear fission, about 0.1% of mass is converted to energy
- The Sun loses about 4 million tons of mass per second due to E = mc²
Frequently Asked Questions
What does E = mc² mean?
E = mc² means that energy (E) and mass (m) are equivalent and can be converted into each other. The c² factor (speed of light squared) is a conversion factor showing how much energy is contained in a given amount of mass.
Why is c² so large?
The speed of light (c) is about 299,792,458 m/s, so c² is approximately 9 × 10¹⁶ m²/s². This huge number means that even a tiny amount of mass contains an enormous amount of energy. This is why nuclear reactions can release so much energy from so little mass.
Can we convert mass to energy?
Yes! This happens in nuclear reactions. In nuclear fission and fusion, a small amount of mass is converted to energy. This is how nuclear power plants and nuclear weapons work. However, converting all mass to energy is not practical with current technology.
Can we convert energy to mass?
Yes! This happens in particle accelerators. When high-energy particles collide, their kinetic energy can be converted into mass, creating new particles. This is how physicists discover new particles like the Higgs boson.
Why don't we see mass-energy conversion in everyday life?
In chemical reactions, the mass-energy conversion is so tiny it's undetectable. For example, burning coal converts only about one part in a billion of mass to energy. Nuclear reactions are different because they involve the strong nuclear force, which allows for much larger mass-energy conversions.
How much energy is in 1 kg of mass?
According to E = mc², 1 kg of mass is equivalent to approximately 8.99 × 10¹⁶ Joules, which is about 21.48 megatons of TNT. This is equivalent to the energy released by a very large nuclear weapon.