E=mc² 计算器 - 质能等价计算器 | 免费在线物理工具

What is E=mc²?

Einstein's Revolutionary Formula
The Meaning of Each Component
Historical Significance

E=mc² is Albert Einstein's most famous equation, published in 1905 as part of his Special Theory of Relativity. This deceptively simple formula reveals a profound truth about the universe: mass and energy are fundamentally the same thing, just in different forms.

Breaking Down the Formula

In E=mc²: E represents energy, m represents mass, and c represents the speed of light in a vacuum (approximately 299,792,458 meters per second). The equation shows that even a small amount of mass contains an enormous amount of energy.

The speed of light squared (c²) is such a large number that it means even tiny amounts of mass can release tremendous amounts of energy. This is why nuclear reactions can produce such powerful explosions from relatively small amounts of fuel.

Mind-Boggling Energy Examples

1 kg of mass contains 9 × 10¹⁶ joules of energy
A paperclip (1 gram) contains enough energy to power a city for hours
The energy in a single atom is enough to power a light bulb for years

Step-by-Step Guide to Using the E=mc² Calculator

Choosing Your Calculation Type
Entering Values and Units
Interpreting Results

Our E=mc² calculator makes it easy to explore the relationship between mass and energy. You can calculate energy from mass, mass from energy, or explore different unit conversions.

Mass to Energy Conversion

To calculate energy from mass: Enter the mass value, select the appropriate unit (kg, g, lb, or atomic mass units), choose 'Mass to Energy' calculation type, and click Calculate. The result will show the equivalent energy in your chosen units.

Energy to Mass Conversion

To calculate mass from energy: Enter the energy value, select the appropriate unit (J, eV, MeV, GeV), choose 'Energy to Mass' calculation type, and click Calculate. The result will show the equivalent mass.

Common Conversion Examples

Convert 1 kg to energy: 9 × 10¹⁶ J
Convert 1 MeV to mass: 1.78 × 10⁻³⁰ kg
Convert 1 atomic mass unit to energy: 931.5 MeV

Real-World Applications of E=mc²

Nuclear Power Generation
Medical Applications
Astrophysical Phenomena

E=mc² has countless applications in modern technology and science, from nuclear power plants to medical imaging devices.

Nuclear Power and Weapons

Nuclear fission and fusion reactions convert small amounts of mass into enormous amounts of energy. In nuclear power plants, uranium atoms split apart, converting about 0.1% of their mass into energy. This is why nuclear fuel is so energy-dense compared to chemical fuels.

Medical Applications

Positron Emission Tomography (PET) scans use the mass-energy equivalence principle. When a positron meets an electron, both particles annihilate, converting their mass entirely into energy in the form of gamma rays.

Astrophysics and Cosmology

Stars like our Sun convert hydrogen into helium through nuclear fusion, releasing energy according to E=mc². This process powers stars for billions of years and creates the elements that make up our world.

Real-World Energy Conversions

Nuclear power plants convert 0.1% of fuel mass to energy
PET scans use electron-positron annihilation
The Sun converts 4 million tons of mass to energy every second

Common Misconceptions and Correct Methods

Mass vs. Weight Confusion
Energy Conservation Misunderstandings
Relativistic Effects

Many people misunderstand E=mc² and its implications. Let's clarify some common misconceptions.

Mass vs. Weight

Mass and weight are different concepts. Mass is the amount of matter in an object, while weight is the force of gravity acting on that mass. E=mc² deals with mass, not weight. An object has the same mass whether it's on Earth, the Moon, or in space.

Energy Conservation

E=mc² doesn't violate energy conservation. When mass is converted to energy (or vice versa), the total amount of mass-energy remains constant. The equation shows that mass and energy are interchangeable forms of the same fundamental quantity.

Everyday Applications

While E=mc² applies to all matter, the energy release is only noticeable in nuclear reactions. Chemical reactions involve only the rearrangement of electrons and release much less energy, typically less than one part in a billion of the mass-energy.

Energy Release Comparisons

Chemical reactions release ~10⁻⁹ of mass-energy
Nuclear reactions release ~10⁻³ of mass-energy
Antimatter annihilation releases 100% of mass-energy

Mathematical Derivation and Examples

Theoretical Foundation
Unit Conversions
Advanced Applications

E=mc² emerges from Einstein's Special Theory of Relativity, which shows that energy and momentum are conserved in all reference frames.

Mathematical Derivation

The equation comes from the relativistic energy-momentum relation: E² = (mc²)² + (pc)², where p is momentum. For objects at rest (p=0), this simplifies to E=mc². This shows that even stationary objects have energy due to their mass.

Unit Conversions

Common units for mass-energy calculations include: 1 atomic mass unit (u) = 931.5 MeV, 1 eV = 1.602 × 10⁻¹⁹ J, and 1 kg = 8.988 × 10¹⁶ J. These conversions make it easier to work with different scales, from atomic to macroscopic.

Relativistic Effects

At speeds approaching the speed of light, relativistic effects become important. The total energy of a moving object is E = γmc², where γ is the Lorentz factor. This shows that kinetic energy also contributes to the object's effective mass.

Key Conversion Factors

1 u = 931.5 MeV = 1.492 × 10⁻¹⁰ J
1 kg = 8.988 × 10¹⁶ J = 5.61 × 10²⁶ eV
Rest energy of electron: 511 keV

1 千克转能量

1 MeV 转质量

核聚变示例

原子质量单位