Modern Physics formula sheet

41 rows · 5 sections · PhysRef · sample of the first 6 rows

Modern Physics formula sheet. Every modern physics equation in PhysRef on one sheet — 41 formulas across 5 topics, each with its equation set in real maths, a symbol key and the SI unit of every symbol.
Quantity	Equation	Symbols	SI units
Special Relativity
Lorentz Factor	$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$	\gamma = lorentz factor · v = relative velocity · c = speed of light	\gamma: dimensionless · v: m/s · c: m/s
Time Dilation	$\Delta t = \gamma \Delta t_0 = \frac{\Delta t_0}{\sqrt{1 - \frac{v^2}{c^2}}}$	\Delta t = dilated time (observed) · \Delta t_0 = proper time · \gamma = lorentz factor · v = relative velocity · c = speed of light	\Delta t: s · \Delta t_0: s · \gamma: dimensionless · v: m/s · c: m/s
Length Contraction	$L = \frac{L_0}{\gamma} = L_0\sqrt{1 - \frac{v^2}{c^2}}$	L = contracted length · L_0 = proper length · \gamma = lorentz factor · v = relative velocity · c = speed of light	L: m · L_0: m · \gamma: dimensionless · v: m/s · c: m/s
Relativistic Momentum	$p = \gamma mv = \frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}}$	p = relativistic momentum · \gamma = lorentz factor · m = rest mass · v = velocity	p: kg·m/s · \gamma: dimensionless · m: kg · v: m/s
Mass-Energy Equivalence	$E = mc^2$	E = rest energy · m = rest mass · c = speed of light	E: J · m: kg · c: m/s
Relativistic Total Energy	$E = \gamma mc^2 = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}}$	E = total energy · \gamma = lorentz factor · m = rest mass · c = speed of light	E: J · \gamma: dimensionless · m: kg · c: m/s

Built from the 41 modern physics entries in the PhysRef reference, grouped by the topics that category page uses. Every equation here is free to read on its own page at /formulas.

Every row on this sheet is also free on its own page — browse the Modern Physics formulas. Premium pays for the sheet, not the physics.