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#1 Mass-Energy Equivalence Calculator 2025

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E=mc² Calculator (Mass-Energy Equivalence)

How to Use the E=mc² Calculator:

This calculator determines the energy equivalent of a given mass based on Albert Einstein's famous equation, E=mc².

  • Mass (m): Enter the amount of mass for which you want to calculate the energy.
  • Mass Unit: Select the unit of the mass you entered from the dropdown menu. The available units include kilograms (kg), grams (g), milligrams (mg), micrograms (µg), atomic mass units (amu), pounds (lb), and ounces (oz).

After entering the mass and selecting its unit, click the "Calculate Energy" button. The equivalent energy will be displayed in various units (Joules, electronvolts, kWh, etc.), along with a step-by-step breakdown of the calculation.

Interpreting the Results:

The equation E=mc² reveals that a small amount of mass can be converted into a tremendous amount of energy. This is because the mass (m) is multiplied by the square of the speed of light (c²), which is a very large number.

  • Joules (J): The standard SI unit of energy.
  • Electronvolts (eV, keV, MeV, GeV): Units commonly used in particle physics.
  • Kilowatt-hours (kWh): A unit often used for electrical energy consumption.
  • Kilocalories (kcal): A unit often associated with food energy.

This calculation demonstrates the potential energy locked within mass, which is the principle behind nuclear power and nuclear weapons.

Theory: Mass-Energy Equivalence

Albert Einstein's theory of special relativity, published in 1905, introduced the concept of mass-energy equivalence. This principle is encapsulated in the iconic equation:

E = mc²

Where:

  • E represents Energy.
  • m represents Mass.
  • c represents the speed of light in a vacuum.

Explanation:

The equation states that energy (E) and mass (m) are interchangeable; they are different forms of the same thing. Mass can be thought of as concentrated energy. If mass is converted into energy, the amount of energy produced is equal to the mass multiplied by the square of the speed of light.

The speed of light (c) is a fundamental physical constant, approximately 299,792,458 meters per second (m/s). Because c² is an extraordinarily large number (approximately 9 x 10¹⁶ m²/s²), even a tiny amount of mass can be converted into a vast quantity of energy.

Formulas Used in this Calculator:

1. Speed of Light (c):

c = 299,792,458 m/s

2. Mass Conversion to Kilograms (mkg):

The input mass is first converted to kilograms (kg), the SI base unit for mass.

If input is grams (g): m_kg = m_input / 1000 If input is milligrams (mg): m_kg = m_input / 1,000,000 If input is micrograms (µg): m_kg = m_input / 1,000,000,000 If input is atomic mass units (amu): m_kg = m_input * 1.66053906660 × 10⁻²⁷ kg/amu If input is pounds (lb): m_kg = m_input * 0.45359237 kg/lb If input is ounces (oz): m_kg = m_input * 0.0283495231 kg/oz

3. Energy Calculation (E):

E_Joules = m_kg * c²

4. Energy Unit Conversions:

The calculated energy in Joules is then converted to other common units:

Electronvolts (eV): E_eV = E_Joules / (1.602176634 × 10⁻¹⁹ J/eV) Kilowatt-hours (kWh): E_kWh = E_Joules / (3.6 × 10⁶ J/kWh) Kilocalories (kcal): E_kcal = E_Joules / (4184 J/kcal)

(And multiples like kJ, MJ, GJ, keV, MeV, GeV)

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