Understanding $E = mc^2$

Einstein’s mass-energy equivalence, encapsulated in the famous equation $E=mc^2$, is one of the most profound concepts in modern physics. Proposed by Albert Einstein in his 1905 paper, it established that mass ($m$) and energy ($E$) are fundamentally interchangeable; they are two forms of the same thing.

The equation states that the energy contained within a mass is equal to that mass multiplied by the speed of light ($c$) squared. Because the speed of light is an extremely large number ($c \approx 2.998 \times 10^8 \text{ m/s}$), and it is squared, even a tiny amount of mass is equivalent to an enormous amount of energy.

This principle is the theoretical basis for nuclear reactions, such as nuclear fission (used in power plants and atomic bombs) and nuclear fusion (which powers the sun). In these reactions, a small amount of mass is converted directly into a massive release of energy, demonstrating the equation’s immense practical importance. The mass deficit—the tiny difference in mass between the reactants and the products—is what is converted into the kinetic energy of the resulting particles.

Conversion to Electron Volts (eV): While Joules ($J$) are the standard SI unit for energy, electron volts (eV) are commonly used in particle physics and chemistry. One electron volt is defined as the kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. The conversion is: $1 \text{ eV} \approx 1.602 \times 10^{-19} \text{ J}$. This unit allows physicists to work with more manageable numbers when dealing with subatomic particles.

How to Use the Calculator

1. Enter Mass ($m$): Input the mass of the object or substance you are converting into energy. This value must be in kilograms (kg). You can enter values in standard or scientific notation (e.g., $0.001$ or $1 \text{e-3}$).
2. Click Calculate: Press the “Calculate Energy” button.
3. Review Output: The calculator will dynamically display the results, including the formula substitution steps and the final energy values in two units:
   • Energy in Joules ($E$): The standard SI unit.
   • Energy in electron volts ($E$ in eV): The standard unit for particle physics.
4. Formula Rendering: All equations, symbols, and results are displayed using $\LaTeX$ for professional academic presentation, ensured by MathJax.