Skip to content

Essential Physics Equations

Find physics equations, symbols, and SI units.

Classical mechanics

How forces change motion, how energy is transferred, and why momentum is conserved.

Newton’s second law

∑F=ma\textcolor{#e11d48}{\sum} \textcolor{#e11d48}{\mathbf{F}} = \textcolor{#7c3aed}{m}\textcolor{#2563eb}{\mathbf{a}}

Conservation of linear momentum

∑ipi,initial=∑ipi,final\textcolor{#e11d48}{\sum_{\textcolor{#e11d48}{i}}} \textcolor{#0f766e}{\mathbf{p}_{i,\mathrm{initial}}} = \textcolor{#e11d48}{\sum_{\textcolor{#e11d48}{i}}} \textcolor{#0f766e}{\mathbf{p}_{i,\mathrm{final}}}

Kinetic energy

K=12mv2\textcolor{#be185d}{K} = \frac{1}{2}\textcolor{#7c3aed}{m}\textcolor{#0369a1}{v}^2

Work–energy theorem

Wnet=ΔK\textcolor{#c2410c}{W_{\mathrm{net}}} = \Delta \textcolor{#be185d}{K}

Newton’s law of gravitation

F=Gm1m2r2\textcolor{#e11d48}{F} = \textcolor{#a16207}{G}\frac{\textcolor{#7c3aed}{m_1}\textcolor{#7c3aed}{m_2}}{\textcolor{#4d7c0f}{r}^2}

Oscillations, waves, and optics

Repeating motion, the propagation of disturbances, and the bending of light.

Simple harmonic motion

d2xdt2=−ω2x\frac{d^2\textcolor{#0369a1}{x}}{d\textcolor{#2563eb}{t}^2} = -\textcolor{#c2410c}{\omega}^2 \textcolor{#0369a1}{x}

Wave speed, frequency, and wavelength

vphase=fλ\textcolor{#0369a1}{v_{\mathrm{phase}}} = \textcolor{#7c3aed}{f}\textcolor{#4d7c0f}{\lambda}

Snell’s law of refraction

n1sin⁡θ1=n2sin⁡θ2\textcolor{#0f766e}{n_1}\sin\textcolor{#c2410c}{\theta_1} = \textcolor{#0f766e}{n_2}\sin\textcolor{#c2410c}{\theta_2}

Electromagnetism

Charges, currents, and fields. The four Maxwell equations below connect electricity, magnetism, and light.

Coulomb’s law

F=14πε0∣q1q2∣r2\textcolor{#e11d48}{F} = \frac{1}{4\textcolor{#a16207}{\pi}\textcolor{#a16207}{\varepsilon_0}}\frac{|\textcolor{#c2410c}{q_1}\textcolor{#c2410c}{q_2}|}{\textcolor{#4d7c0f}{r}^2}

Lorentz force

F=q(E+v×B)\textcolor{#e11d48}{\mathbf{F}} = \textcolor{#c2410c}{q}\left(\textcolor{#e11d48}{\mathbf{E}} + \textcolor{#0369a1}{\mathbf{v}}\times\textcolor{#0f766e}{\mathbf{B}}\right)

Gauss’s law for electricity

∯SE⋅dA=Qencε0\textcolor{#e11d48}{\oiint_{\textcolor{#4d7c0f}{S}}} \textcolor{#e11d48}{\mathbf{E}}\cdot \textcolor{#0369a1}{d\mathbf{A}} = \frac{\textcolor{#c2410c}{Q_{\mathrm{enc}}}}{\textcolor{#a16207}{\varepsilon_0}}

Gauss’s law for magnetism

∯SB⋅dA=0\textcolor{#e11d48}{\oiint_{\textcolor{#4d7c0f}{S}}} \textcolor{#0f766e}{\mathbf{B}}\cdot \textcolor{#0369a1}{d\mathbf{A}} = 0

Faraday’s law of induction

∮CE⋅dℓ=−dΦBdt\textcolor{#e11d48}{\oint_{\textcolor{#4d7c0f}{C}}} \textcolor{#e11d48}{\mathbf{E}}\cdot \textcolor{#0369a1}{d\boldsymbol{\ell}} = -\frac{d\textcolor{#be185d}{\Phi_B}}{d\textcolor{#2563eb}{t}}

Ampère–Maxwell law

∮CB⋅dℓ=μ0 Ienc+μ0ε0dΦEdt\textcolor{#e11d48}{\oint_{\textcolor{#4d7c0f}{C}}} \textcolor{#0f766e}{\mathbf{B}}\cdot \textcolor{#0369a1}{d\boldsymbol{\ell}} = \textcolor{#7c3aed}{\mu_0}\,\textcolor{#c2410c}{I_{\mathrm{enc}}} + \textcolor{#7c3aed}{\mu_0}\textcolor{#a16207}{\varepsilon_0}\frac{d\textcolor{#be185d}{\Phi_E}}{d\textcolor{#2563eb}{t}}

Ohm’s law

V=IR\textcolor{#7c3aed}{V} = \textcolor{#c2410c}{I}\textcolor{#0f766e}{R}

Thermodynamics and statistical physics

Heat, work, temperature, and the connection between microscopic states and macroscopic behaviour.

Ideal gas law

PV=nRT\textcolor{#be185d}{P}\textcolor{#7c3aed}{V} = \textcolor{#0f766e}{n}\textcolor{#0f766e}{R}\textcolor{#0369a1}{T}

First law of thermodynamics

ΔU=Q−W\Delta \textcolor{#e11d48}{U} = \textcolor{#c2410c}{Q} - \textcolor{#c2410c}{W}

Second law of thermodynamics

ΔSisolated≥0\Delta \textcolor{#4d7c0f}{S_{\mathrm{isolated}}} \geq 0

Boltzmann’s entropy formula

S=kBln⁡Ω\textcolor{#4d7c0f}{S} = \textcolor{#2563eb}{k_{\mathrm{B}}}\ln\textcolor{#be185d}{\Omega}

Relativity and spacetime

The relationship between mass and energy, the dependence of elapsed time on motion, and gravity as spacetime geometry.

Mass–energy equivalence

E0=mc2\textcolor{#e11d48}{E_0} = \textcolor{#7c3aed}{m}\textcolor{#0369a1}{c}^2

Relativistic energy–momentum relation

E2=p2c2+m2c4\textcolor{#e11d48}{E}^2 = \textcolor{#0f766e}{p}^2\textcolor{#0369a1}{c}^2 + \textcolor{#7c3aed}{m}^2\textcolor{#0369a1}{c}^4

Time dilation

Δt=Δτ1−v2/c2\Delta \textcolor{#2563eb}{t} = \frac{\Delta\textcolor{#2563eb}{\tau}}{\sqrt{1-\textcolor{#0369a1}{v}^2/\textcolor{#0369a1}{c}^2}}

Einstein’s field equations

Gμν+Λgμν=8πGc4Tμν\textcolor{#a16207}{G_{\mu\nu}} + \textcolor{#c2410c}{\Lambda} \textcolor{#2563eb}{g_{\mu\nu}} = \frac{8\textcolor{#a16207}{\pi} \textcolor{#a16207}{G}}{\textcolor{#0369a1}{c}^4}\textcolor{#0369a1}{T_{\mu\nu}}

Quantum physics

Energy quanta, matter waves, probability amplitudes, and the limits on jointly sharp measurements.

Photon energy

E=hf\textcolor{#e11d48}{E} = \textcolor{#a16207}{h}\textcolor{#7c3aed}{f}

De Broglie wavelength

λ=hp\textcolor{#4d7c0f}{\lambda} = \frac{\textcolor{#a16207}{h}}{\textcolor{#0f766e}{p}}

Time-dependent Schrödinger equation

iℏ∂ψ∂t=[−ℏ22m∇2+V]ψ\textcolor{#e11d48}{i}\textcolor{#a16207}{\hbar}\frac{\partial\textcolor{#7c3aed}{\psi}}{\partial \textcolor{#2563eb}{t}} = \left[-\frac{\textcolor{#a16207}{\hbar}^2}{2\textcolor{#7c3aed}{m}}\nabla^2 + \textcolor{#7c3aed}{V}\right]\textcolor{#7c3aed}{\psi}

Born rule for position

P(r∈R)=∫R∣ψ(r,t)∣2 d3r\textcolor{#be185d}{P}(\textcolor{#4d7c0f}{\mathbf{r}}\in\textcolor{#4d7c0f}{\mathcal{R}}) = \textcolor{#e11d48}{\int_{\textcolor{#4d7c0f}{\mathcal{R}}}} |\textcolor{#7c3aed}{\psi}(\textcolor{#4d7c0f}{\mathbf{r}},\textcolor{#2563eb}{t})|^2\,d^3\textcolor{#4d7c0f}{r}

Heisenberg uncertainty principle

Δx Δpx≥ℏ2\Delta \textcolor{#0369a1}{x}\,\Delta \textcolor{#0f766e}{p_x} \geq \frac{\textcolor{#a16207}{\hbar}}{2}