E = mc²: 1 kg at rest contains ~9.0×10¹⁶ J ≈ 21.5 megatons TNT
One kilogram of matter, if fully converted to energy via E=mc², yields approximately 9.0×10¹⁶ joules — equivalent to 21.5 megatons of TNT, or about 1,400 Hiroshima bombs. In practice, nuclear fission converts only ~0.1% of mass to energy, and fusion about 0.7%. Complete conversion occurs only in matter-antimatter annihilation.
E = mc²
Einstein's mass-energy equivalence, E = mc², is the most famous equation in physics. Published in a short 1905 paper titled 'Does the Inertia of a Body Depend Upon Its Energy Content?', it reveals that mass is a form of energy. Every kilogram of matter contains c² ≈ 9×10¹⁶ joules of intrinsic energy — enough to power a city for years.
Relativistic Energy
The full relativistic energy of a moving object is E = γmc², where γ is the Lorentz factor. This can be decomposed as rest energy (mc²) plus kinetic energy ((γ−1)mc²). At low speeds, the kinetic term reduces to the classical ½mv². But as v → c, γ → ∞ and the energy required to accelerate further grows without bound — this is why no massive object can reach the speed of light.
The Energy-Momentum Relation
More fundamental than E = mc² is the energy-momentum relation: E² = (pc)² + (mc²)². For a particle at rest (p = 0), this gives E = mc². For a photon (m = 0), it gives E = pc. This equation unifies the physics of massive and massless particles and is the workhorse of particle physics calculations.
Real-World Implications
Nuclear fission (as in uranium reactors) converts about 0.1% of mass to energy. Nuclear fusion (as in the Sun and hydrogen bombs) converts about 0.7%. Matter-antimatter annihilation achieves 100% conversion. The simulator lets you explore these scales — from subatomic particles to everyday objects — and compare their energy content against familiar references like TNT, nuclear weapons, and stellar output.
FAQ
What does E=mc² mean?
E=mc² states that mass and energy are equivalent and interconvertible. A mass m at rest contains an intrinsic energy E₀ = mc², where c is the speed of light (≈3×10⁸ m/s). Because c² is enormous (~9×10¹⁶ m²/s²), even tiny masses correspond to vast energies. This equation, derived by Einstein in 1905, is arguably the most famous equation in physics.
What is relativistic kinetic energy?
In special relativity, kinetic energy is K = (γ−1)mc², where γ is the Lorentz factor. At low speeds this reduces to the familiar ½mv², but at relativistic speeds the kinetic energy grows without bound as v→c. At v = 0.866c (γ=2), the kinetic energy equals the rest energy. At higher speeds, kinetic energy dominates.
How much energy is in 1 gram of matter?
One gram (10⁻³ kg) contains E = 10⁻³ × (3×10⁸)² = 9×10¹³ joules, equivalent to about 21.5 kilotons of TNT — roughly the yield of the Hiroshima bomb. This illustrates why nuclear weapons, which convert only a tiny fraction of mass to energy, are so destructive.
What is the energy-momentum relation?
The full relativistic energy-momentum relation is E² = (pc)² + (mc²)², where p is relativistic momentum. For massless particles (photons), this gives E = pc. For particles at rest (p=0), it gives E = mc². This relation is fundamental to particle physics and is used daily at particle accelerators like the LHC.