Modern Physics & Relativity Formulas
A complete list of modern physics & relativity formulas, covering mass-energy equivalence, special relativity, photons, the photoelectric effect, and quantum relations.
14 formulas. Use the interactive searcher to solve for any variable and convert units.
Open the interactive searcher →Mass–energy
E = m·c²
E energyJm masskgc speed of lightm/s
Photon energy
E = h·f
E energyJh Planck constantJ·sf frequencyHz
de Broglie wavelength
λ = h / p
λ wavelengthmh Planck constantJ·sp momentumkg·m/s
Photoelectric effect
E = h·f − φ
E kinetic energyJh Planck constantJ·sf frequencyHzφ work functionJ
Relativistic momentum
p = γ·m·v
p momentumkg·m/sγ Lorentz factorm masskgv velocitym/s
Lorentz factor
γ = 1 / √(1 − v²/c²)
γ Lorentz factorv velocitym/sc speed of lightm/s
Time dilation
Δt = γ·Δt₀
Δt dilated timesγ Lorentz factorΔt₀ proper times
Length contraction
L = L₀ / γ
L contracted lengthmL₀ proper lengthmγ Lorentz factor
Relativistic energy
E = γ·m·c²
E total energyJγ Lorentz factorm masskgc speed of lightm/s
Energy–momentum relation
E² = (p·c)² + (m·c²)²
E energyJp momentumkg·m/sc speed of lightm/sm masskg
Heisenberg uncertainty
Δx·Δp ≥ ħ / 2
Δx position uncertaintymΔp momentum uncertaintykg·m/sħ reduced Planck constantJ·s
Bohr radius / energy
E_n = −13.6 eV / n²
E_n energy leveleVn quantum number
Rydberg formula
1/λ = R·(1/n₁² − 1/n₂²)
λ wavelengthmR Rydberg constant1/mn₁ quantum numbern₂ quantum number
Compton wavelength shift
Δλ = (h/m_e·c)·(1 − cosθ)
Δλ wavelength shiftmh Planck constantJ·sm_e electron masskgc speed of lightm/sθ scattering anglerad