Energy increases linearly with mass at constant speed of light (c = 2.9979e+8 m/s). The green dot marks the current calculation.
Calculate the energy contained in a given mass using Einstein's mass-energy equivalence. The speed of light squared is an enormous multiplier, meaning even tiny amounts of mass hold vast energy.
E = m × c²
Find the equivalent mass of a given amount of energy. This rearrangement shows how much mass would need to be converted to produce a specific energy output.
m = E ÷ c²
Derive the speed of light from known energy and mass values. In practice c is a universal constant (299,792,458 m/s), but this form is useful for verification.
c = √(E ÷ m)
Einstein's mass-energy equivalence E = mc² shows that mass and energy are two forms of the same thing. Because the speed of light squared (~9 × 10¹⁶) is enormous, even a tiny amount of mass contains a vast amount of energy. This equation underpins nuclear power, particle physics, and our understanding of stellar processes. The speed of light in a vacuum is exactly 299,792,458 m/s. You can rearrange the equation to solve for mass or the speed of light when the other values are known.
How much energy is contained in 1 kg of matter?
This enormous energy is why nuclear reactions (which convert a fraction of a percent of mass to energy) are millions of times more powerful per kilogram than chemical reactions.
Einstein's E = mc² reveals that mass and energy are interchangeable. The speed of light squared (~9 × 10¹⁶ m²/s²) is an enormous conversion factor, which is why nuclear reactions release millions of times more energy per kilogram than chemical reactions. The equation applies to all energy transformations, but the converted mass is only detectable in nuclear and particle physics processes.
Use the formula E = mc². Multiply the mass (in kilograms) by the speed of light squared (c² ≈ 8.988 × 10¹⁶ m²/s²). The result is the energy in joules. For example, 1 kg of matter contains approximately 9 × 10¹⁶ J of energy. To find mass from energy, rearrange to m = E / c².
E = mc² is Einstein's mass-energy equivalence formula from his 1905 special relativity paper. E is energy in joules, m is mass in kilograms, and c is the speed of light (299,792,458 m/s). It shows that mass and energy are interchangeable — a small amount of mass can be converted into an enormous amount of energy because c² is such a large number.
One kilogram of matter contains approximately 9 × 10¹⁶ joules (90 petajoules) of energy. That is equivalent to about 21.5 megatons of TNT, or roughly 1,500 times the energy of the Hiroshima bomb. However, converting all of a mass to energy requires matter-antimatter annihilation — nuclear fission converts only about 0.1% of the mass.
The c² factor arises naturally from the mathematics of special relativity. It reflects the fundamental relationship between space and time in our universe. Dimensionally, energy (kg·m²/s²) requires mass multiplied by a velocity squared. The speed of light appears because it is the universal speed limit — the maximum rate at which energy and information can propagate.
Yes — E = mc² is the basis of nuclear energy. In fission (splitting heavy atoms like uranium-235), about 0.1% of the mass is converted to energy. In fusion (combining light atoms like hydrogen), about 0.7% converts. The "mass defect" — the difference between reactant and product masses — equals the released energy divided by c².
When a particle meets its antiparticle (e.g., electron and positron), they annihilate completely, converting 100% of their combined mass into energy via E = mc². This produces gamma ray photons. It is the most efficient energy conversion possible and is used in PET (positron emission tomography) medical imaging.
Technically yes — every object has rest energy equal to mc². A 70 kg person contains about 6.3 × 10¹⁸ J of rest energy. However, releasing that energy requires nuclear or subatomic processes. Chemical reactions (burning, batteries) convert negligibly small amounts of mass — roughly one part in a billion — so the mass change is unmeasurable with ordinary scales.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.
Einstein's special theory of relativity defines the relationship between energy, mass, and the speed of light:
Where:
Because c² is approximately 9 × 10¹&sup6;, even a tiny mass corresponds to an enormous amount of energy. This equation is the foundation of nuclear energy, particle physics, and our understanding of how stars produce energy.
Nuclear Physics
In nuclear reactions, a small fraction of mass is converted to energy. Here we calculate the total energy equivalent of 1 gram (0.001 kg) of matter.
This is roughly equivalent to 21.5 kilotons of TNT — comparable to the energy released by the Hiroshima bomb from converting only about 0.7 grams of mass.
Astrophysics
The Sun converts hydrogen to helium via nuclear fusion, losing mass that becomes radiant energy. 4.3 million tonnes = 4.3 × 10&sup9; kg per second.
This is the Sun's luminosity — the total power output radiated in all directions. Earth receives only about one billionth of this energy.
Particle Physics
The electron has a rest mass of approximately 9.109 × 10&supmin;³¹ kg. Its rest energy is a fundamental constant in particle physics.
This 0.511 MeV is the energy released when an electron meets a positron and they annihilate — the basis of PET medical imaging.