Physics Formula Sheets

Every essential equation organized by topic. Variable definitions, SI units, and links to full articles included.

⚙️

Mechanics Formulas

Newton's laws, kinematics, energy, momentum, gravity, circular motion

20+ Formulas

🔥

Thermodynamics Formulas

Laws of thermodynamics, ideal gas, heat capacity, entropy, Carnot

15+ Formulas

〰️

Waves & EM Formulas

Wave equations, Doppler, optics, Coulomb, Ohm's law, photons

20+ Formulas

⚙️ Mechanics

Newton's Second Law

F = ma

F=force (N), m=mass (kg), a=acceleration (m/s²)

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Kinematic Eq. 1

v = u + at

v=final velocity, u=initial velocity, a=acceleration, t=time

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Kinematic Eq. 2

s = ut + ½at²

s=displacement (m), u=initial speed (m/s)

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Kinematic Eq. 3

v² = u² + 2as

Eliminates time — use when t is unknown

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Momentum

p = mv

p=momentum (kg·m/s), m=mass, v=velocity (vector)

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Impulse-Momentum

J = FΔt = Δp

J=impulse (N·s), F=average force, Δt=time interval

Kinetic Energy

KE = ½mv²

KE=kinetic energy (J), m=mass (kg), v=speed (m/s)

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Gravitational PE

PE = mgh

g=9.8 m/s², h=height above reference point

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Work

W = Fd·cosθ

W=work (J), F=force (N), d=displacement (m), θ=angle

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Power

P = W/t = Fv

P=power (W=J/s), W=work, t=time, F=force, v=speed

Universal Gravitation

F = Gm₁m₂/r²

G=6.674×10⁻¹¹ N·m²/kg², r=center-to-center distance

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Centripetal Accel.

a_c = v²/r = ω²r

v=speed, r=radius, ω=angular velocity (rad/s)

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Spring Force (Hooke)

F = -kx

k=spring constant (N/m), x=displacement from equilibrium

Elastic PE

PE_spring = ½kx²

k=spring constant, x=compression/extension (m)

Projectile Range

R = v₀²sin(2θ)/g

v₀=launch speed, θ=launch angle, g=9.8 m/s²

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🔥 Thermodynamics

First Law

ΔU = Q - W

ΔU=change in internal energy, Q=heat in, W=work by system

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Ideal Gas Law

PV = nRT

P=pressure (Pa), V=volume (m³), n=moles, R=8.314 J/(mol·K)

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Specific Heat

Q = mcΔT

Q=heat (J), m=mass (kg), c=specific heat (J/kg·K)

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Carnot Efficiency

η = 1 - T_c/T_h

T_c=cold reservoir (K), T_h=hot reservoir (K)

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Entropy Change

ΔS = Q_rev/T

For reversible processes, T in Kelvin

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RMS Speed

v_rms = √(3RT/M)

R=8.314 J/(mol·K), T=temperature (K), M=molar mass (kg/mol)

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Thermal Expansion

ΔL = αL₀ΔT

α=coefficient of linear expansion, L₀=original length

Boltzmann Equation

S = k_B ln(Ω)

k_B=1.381×10⁻²³ J/K, Ω=number of microstates

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〰️ Waves & Optics

Wave Equation

v = fλ

v=wave speed (m/s), f=frequency (Hz), λ=wavelength (m)

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Period

T = 1/f

T=period (s), f=frequency (Hz)

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Snell's Law

n₁sinθ₁ = n₂sinθ₂

n=refractive index, θ=angle from normal

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Doppler Effect

f' = f(v±v_o)/(v∓v_s)

v=wave speed, v_o=observer speed, v_s=source speed

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Sound Level

β = 10 log(I/I₀)

β in dB, I₀=10⁻¹² W/m² (threshold of hearing)

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Critical Angle

sinθ_c = n₂/n₁

For total internal reflection, requires n₁ > n₂

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Mirror/Lens Eq.

1/f = 1/d_o + 1/d_i

f=focal length, d_o=object distance, d_i=image distance

Refractive Index

n = c/v

c=3×10⁸ m/s (speed of light), v=speed in medium

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⚡ Electromagnetism

Coulomb's Law

F = kq₁q₂/r²

k=8.99×10⁹ N·m²/C², q=charges (C), r=distance (m)

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Electric Field

E = F/q = kQ/r²

E in N/C or V/m, Q=source charge (C)

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Ohm's Law

V = IR

V=voltage (V), I=current (A), R=resistance (Ω)

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Electric Power

P = IV = I²R = V²/R

P=power (W), I=current (A), V=voltage (V)

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Resistivity

R = ρL/A

ρ=resistivity (Ω·m), L=length (m), A=cross section (m²)

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Series Resistors

R_T = R₁ + R₂ + ...

Total resistance increases in series

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Parallel Resistors

1/R_T = 1/R₁ + 1/R₂

Total resistance decreases in parallel

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Electric Potential

V = kQ/r

V=electric potential (V=J/C), Q=source charge

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⚛️ Modern Physics

Mass-Energy

E = mc²

c=3×10⁸ m/s, rest energy of matter

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Lorentz Factor

γ = 1/√(1−v²/c²)

γ=1 at rest, approaches ∞ as v→c

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Time Dilation

Δt' = γΔt₀

Δt₀=proper time, moving clocks run slower

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Length Contraction

L = L₀/γ

L₀=proper length, moving objects appear shorter

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Photon Energy

E = hf = hc/λ

h=6.626×10⁻³⁴ J·s (Planck's constant)

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Photoelectric Effect

KE_max = hf − φ

φ=work function (J or eV), f=frequency (Hz)

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de Broglie Wavelength

λ = h/p = h/(mv)

h=Planck's constant, p=momentum (kg·m/s)

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Heisenberg Uncertainty

ΔxΔp ≥ ℏ/2

ℏ=h/2π=1.055×10⁻³⁴ J·s

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📐 Physical Constants

Speed of Light

c = 2.998×10⁸ m/s

Exact by definition in SI; speed of light in vacuum

Planck's Constant

h = 6.626×10⁻³⁴ J·s

Quantum of action; ℏ = h/2π = 1.055×10⁻³⁴ J·s

Gravitational Constant

G = 6.674×10⁻¹¹ N·m²/kg²

Universal gravitational constant

Boltzmann Constant

k_B = 1.381×10⁻²³ J/K

Links temperature to molecular kinetic energy

Elementary Charge

e = 1.602×10⁻¹⁹ C

Charge of a proton (or magnitude of electron charge)

Coulomb's Constant

k = 8.988×10⁹ N·m²/C²

k = 1/(4πε₀), ε₀=8.854×10⁻¹² F/m

Standard Gravity

g = 9.807 m/s²

Standard acceleration of free fall at Earth's surface

Gas Constant

R = 8.314 J/(mol·K)

R = N_A · k_B; N_A=6.022×10²³ mol⁻¹