E = mc² Calculator

Instructions:
  • Enter the mass in the "Mass" field and select the unit of mass.
  • Click "Calculate" to calculate the energy based on the mass and the speed of light.
  • Choose the desired unit for energy from the dropdown.
  • The calculated energy will be displayed in the "Energy" field.
  • Click "Copy" to copy the result to the clipboard.
m/s
Energy vs. Mass
Calculation and Explanation

Formula: E = mc²

Where:

  • E is the energy in joules (J).
  • m is the mass in kilograms (kg).
  • c is the speed of light in meters per second (m/s), approximately 299,792,458 m/s.

This calculator computes the energy (E) based on the mass (m) entered by the user and the speed of light (c) using the famous equation E=mc².

Calculation History

    Albert Einstein’s famous equation, E=mc², stands as a cornerstone of modern physics. It revolutionized our understanding of the relationship between mass and energy, revealing that these two fundamental concepts are not separate but intimately intertwined. This equation encapsulates the profound realization that mass can be converted into energy, and vice versa, highlighting the profound connection between matter and energy.

    The Genesis of the Equation

    In 1905, while working on his theory of special relativity, Einstein postulated that mass and energy are equivalent and can be converted into one another. This groundbreaking idea challenged the prevailing view that mass and energy were distinct and unchanging entities. Einstein’s theory of special relativity showed that mass is not constant but is relative to an observer’s motion. As an object approaches the speed of light, its mass increases, which is directly proportional to the increase in its energy.

    The Formula and Its Implications

    The equation E=mc² expresses the equivalence of mass and energy. In this equation, E represents energy, m represents mass, and c represents the speed of light in a vacuum. The speed of light, approximately 300,000 kilometers per second, is a fundamental constant of nature. The equation E=mc² implies that a small mass can be converted into tremendous energy. This is because the speed of light squared is an incredibly large number.

    Benefits of Understanding Mass-Energy Equivalence

    Understanding the mass-energy equivalence has had profound implications for various fields, including:

    1. Nuclear Physics: Mass-energy equivalence is fundamental to understanding nuclear reactions, such as fission and fusion. These reactions involve the conversion of mass into energy, which is the power source for nuclear reactors and weapons.
    2. Particle Physics: In particle physics, mass-energy equivalence plays a crucial role in understanding the behavior of elementary particles. The energy of a particle can be converted into mass, and vice versa, leading to the creation and annihilation of particles.
    3. Astrophysics: The mass-energy equivalence is essential for understanding the energy sources of stars, including the Sun. Stars generate energy through nuclear fusion, where hydrogen nuclei combine to form helium nuclei, releasing tremendous energy.
    4. Cosmology: The mass-energy equivalence helps explain the universe’s origin in the Big Bang theory. The immense energy released in the Big Bang is believed to have originated from mass conversion into energy.

    Facts about Mass-Energy Equivalence

    1. The Sun converts about 620 million tons of hydrogen into energy every second. This is the source of the Sun’s immense energy output.
    2. A single gram of matter contains an enormous amount of energy, approximately 21,500 terajoules. This energy is equivalent to the explosive power of about 25 million tons of TNT.
    3. The mass-energy equivalence has had practical applications in various fields, including medicine, where it is used in radiation therapy and nuclear imaging techniques.

    References

    1. The World of Physics by Wolfgang Pauli (1948)
    2. Concepts of Physics by H. C. Verma (2011)
    3. Einstein’s Theory of Relativity: An Introduction by Harry Woolf (1987)

    Conclusion

    The mass-energy equivalence, encapsulated in Einstein’s equation E=mc², is a remarkable testament to the interconnectedness of matter and energy. It has revolutionized our understanding of the universe and has had profound implications for various fields of science and technology. As we continue to explore the mysteries of the universe, the mass-energy equivalence will undoubtedly remain a guiding principle in our quest to unravel the fundamental workings of nature.

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