E = mc² Calculator
Convert mass to energy using Einstein’s theory of relativity with high-precision results.
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Calculation Steps
Albert Einstein’s most famous equation, E = mc^2, changed our fundamental understanding of the universe. It revealed that mass and energy are not two separate things, but rather two forms of the same phenomenon. This calculator allows you to explore that relationship by converting between mass, energy, and the speed of light.
The Breakdown of the Formula
E (Energy): The total kinetic energy contained within a body, measured in Joules (J).
m (Mass): The “rest mass” of an object, typically measured in Kilograms (kg).
c (Speed of Light): A physical constant representing the speed of light in a vacuum, approximately 299,792,458 meters per second.
In the equation, the speed of light is squared (c^2). Because the speed of light is such a massive number, even a tiny amount of mass can be converted into a staggering amount of energy.
Mathematical Variations
Depending on which value you are looking for, the formula can be rearranged:
- To find Energy:
E = m × c² - To find Mass:
m = E / c² - To find the Speed of Light:
c = √(E / m)
Why is this Equation Significant?
Before 1905, scientists believed mass and energy were governed by separate laws of conservation. Einstein proved that mass can be “extinguished” to create energy, a principle that explains:
- Stellar Nucleosynthesis: How the Sun produces energy by fusing hydrogen atoms into helium, losing a small amount of mass in the process.
- Nuclear Power: The immense energy released during nuclear fission (splitting atoms) or fusion.
- Radioactive Decay: Why certain elements lose weight as they emit radiation over time.
Examples of Mass-Energy Conversion
To put the power of E = mc^2 into perspective, consider these scenarios:
| Initial Mass | Resulting Energy (approx.) | Comparison |
| 1 Gram | 90 Terajoules | Enough to power 2,500 average homes for a year. |
| 1 Kilogram | 90 Petajoules | Roughly the energy of a 21-megaton blast. |
| 1 Paperclip | 25 Million kWh | The energy required to drive an electric car around the Earth 3,000 times. |
How to Use This Calculator
- Select your Target: Choose whether you want to solve for Energy, Mass, or Speed.
- Input Values: Enter your known data. Our tool supports multiple units, from atomic mass units (u) for subatomic physics to solar masses for galactic calculations.
- Adjust Precision: Use the precision dropdown to see results in scientific notation or standard decimals, ensuring your significant figures meet your academic or professional requirements.
FAQs
Q1. Does an object get heavier when it moves?
A: In modern physics, we distinguish between “rest mass” and “relativistic mass.” While an object’s rest mass remains constant, the total energy (and thus its resistance to acceleration) increases as it approaches the speed of light. This calculator specifically uses rest mass.
Q2. Why is the speed of light squared?
A: The “squared” aspect comes from the kinetic energy relationship. In classical physics, kinetic energy is expressed as 1/2mv². Einstein found that for a body at rest, the internal energy is proportional to the square of the universal speed limit, c.
Q3. Can we turn energy back into mass?
A: Yes. While we often see mass turning into energy (like in a battery or a star), the reverse is also possible. In high-energy particle accelerators, photons (light energy) can collide to create matter particles, such as electrons and positrons.
Sources: Calculator Soup, Omni Calculator, Hexa Calculator, 1728 Software Systems, E=mc² Explained, Symbolab, CalcTool, vCalc, Mera Calculator.
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