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IB Physics Formula Booklet.

Every equation from the IB DP Physics (2025) data booklet — searchable, filterable by theme, and rendered exactly as you'll see them in the exam.

144 formulas

A.1Kinematics

Space, time & motion

Final velocity

v = u + at

Displacement

s = ut + \tfrac{1}{2}at^{2}

Velocity–displacement

v^{2} = u^{2} + 2as

Displacement (average velocity)

s = \frac{(u + v)}{2}\,t

A.2Forces & momentum

Space, time & motion

Newton's second law

F = ma = \frac{\Delta p}{\Delta t}

Static friction

F_{f} \le \mu_{s} F_{N}

Dynamic friction

F_{f} = \mu_{d} F_{N}

Hooke's law

F_{H} = -kx

Linear momentum

p = mv

Impulse

J = F\Delta t = \Delta p

Angular velocity

\omega = \frac{2\pi}{T} = 2\pi f

Linear speed (circular)

v = \omega r

Centripetal acceleration

a = \frac{v^{2}}{r} = \omega^{2} r = \frac{4\pi^{2}r}{T^{2}}

Centripetal force

F = \frac{mv^{2}}{r} = m\omega^{2} r

A.3Work, energy & power

Space, time & motion

Work done

W = Fs\cos\theta

Kinetic energy

E_{k} = \tfrac{1}{2}mv^{2} = \frac{p^{2}}{2m}

Gravitational PE (near surface)

\Delta E_{p} = mg\Delta h

Elastic potential energy

E_{H} = \tfrac{1}{2}k(\Delta x)^{2}

Power

P = \frac{\Delta W}{\Delta t} = Fv

Efficiency

\eta = \frac{E_{\text{output}}}{E_{\text{input}}} = \frac{P_{\text{output}}}{P_{\text{input}}}

A.4Rigid body mechanics

Space, time & motion

TorqueHL

\tau = Fr\sin\theta

Rotational kinematicsHL

\omega_{f} = \omega_{i} + \alpha t

Angular displacementHL

\Delta\theta = \omega_{i}t + \tfrac{1}{2}\alpha t^{2}

Angular velocity–displacementHL

\omega_{f}^{2} = \omega_{i}^{2} + 2\alpha\Delta\theta

Newton's second law (rotation)HL

\tau = I\alpha

Moment of inertiaHL

I = \Sigma mr^{2}

Angular momentumHL

L = I\omega

Angular impulseHL

\Delta L = \tau\Delta t

Rotational kinetic energyHL

E_{k} = \tfrac{1}{2}I\omega^{2}

A.5Galilean & special relativity

Space, time & motion

Galilean transformationHL

x' = x - vt

Galilean velocity additionHL

u' = u - v

Lorentz factorHL

\gamma = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}

Lorentz transformation (position)HL

x' = \gamma(x - vt)

Lorentz transformation (time)HL

t' = \gamma\left(t - \frac{vx}{c^{2}}\right)

Relativistic velocity additionHL

u' = \frac{u - v}{1 - \frac{uv}{c^{2}}}

Time dilationHL

\Delta t = \gamma\Delta t_{0}

Length contractionHL

L = \frac{L_{0}}{\gamma}

Spacetime intervalHL

(\Delta s)^{2} = (c\Delta t)^{2} - (\Delta x)^{2}

B.1Thermal energy transfers

The particulate nature of matter

Specific heat capacity

Q = mc\Delta T

Latent heat

Q = mL

Thermal conduction

\frac{\Delta Q}{\Delta t} = kA\frac{\Delta T}{\Delta x}

Stefan–Boltzmann law

P = e\sigma A T^{4}

Wien's displacement law

\lambda_{\text{max}} T = 2.9 \times 10^{-3}\ \text{m K}

Apparent brightness

b = \frac{L}{4\pi d^{2}}

B.2Greenhouse effect

The particulate nature of matter

Intensity

I = \frac{P}{A}

Albedo

\alpha = \frac{\text{total scattered power}}{\text{total incident power}}

B.3Gas laws

The particulate nature of matter

Pressure

P = \frac{F}{A}

Amount of substance

n = \frac{N}{N_{A}}

Ideal gas law

PV = nRT = Nk_{B}T

Combined gas law

\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}

Average translational KE

\bar{E}_{k} = \tfrac{3}{2}k_{B}T

Internal energy (ideal monatomic gas)

U = \tfrac{3}{2}nRT = \tfrac{3}{2}Nk_{B}T

Pressure (kinetic theory)

P = \tfrac{1}{3}\rho v^{2}

B.4Thermodynamics

The particulate nature of matter

First law of thermodynamicsHL

Q = \Delta U + W

Work done by a gasHL

W = P\Delta V

Change in internal energyHL

\Delta U = \tfrac{3}{2}nR\Delta T

Entropy changeHL

\Delta S = \frac{\Delta Q}{T}

Entropy (statistical)HL

S = k_{B}\ln\Omega

Adiabatic process (monatomic)HL

PV^{\frac{5}{3}} = \text{constant}

Carnot efficiencyHL

\eta_{\text{max}} = 1 - \frac{T_{c}}{T_{h}}

B.5Current & circuits

The particulate nature of matter

Electric current

I = \frac{\Delta q}{\Delta t}

Potential difference

V = \frac{W}{q}

Ohm's law / resistance

R = \frac{V}{I}

Resistivity

\rho = \frac{RA}{L}

Electrical power

P = VI = I^{2}R = \frac{V^{2}}{R}

Resistors in series

R_{s} = R_{1} + R_{2} + \ldots

Resistors in parallel

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \ldots

EMF and internal resistance

\varepsilon = I(R + r)

C.1Simple harmonic motion

Wave behaviour

Period and frequency

T = \frac{1}{f} = \frac{2\pi}{\omega}

Defining equation of SHM

a = -\omega^{2}x

Mass–spring period

T = 2\pi\sqrt{\frac{m}{k}}

Simple pendulum period

T = 2\pi\sqrt{\frac{l}{g}}

Displacement in SHMHL

x = x_{0}\sin(\omega t + \phi)

Velocity in SHMHL

v = \omega x_{0}\cos(\omega t + \phi)

Velocity–displacement in SHMHL

v = \pm\,\omega\sqrt{x_{0}^{2} - x^{2}}

Total energy in SHMHL

E_{T} = \tfrac{1}{2}m\omega^{2}x_{0}^{2}

Potential energy in SHMHL

E_{p} = \tfrac{1}{2}m\omega^{2}x^{2}

C.2Wave model

Wave behaviour

Wave speed

v = f\lambda = \frac{\lambda}{T}

C.3Wave phenomena

Wave behaviour

Double-slit fringe spacing

s = \frac{\lambda D}{d}

Snell's law

\frac{n_{1}}{n_{2}} = \frac{\sin\theta_{2}}{\sin\theta_{1}} = \frac{v_{2}}{v_{1}}

Refractive index

n = \frac{c}{v}

Critical angle

\sin\theta_{c} = \frac{n_{2}}{n_{1}}

Single-slit diffraction (first minimum)HL

\theta = \frac{\lambda}{b}

Diffraction grating maximaHL

n\lambda = d\sin\theta

Constructive interference

\text{path difference} = n\lambda

Destructive interference

\text{path difference} = \left(n + \tfrac{1}{2}\right)\lambda

C.4Standing waves & resonance

Wave behaviour

Harmonics (string / open-open pipe)

f_{n} = \frac{nv}{2L}

Harmonics (closed-open pipe)

f_{n} = \frac{nv}{4L},\quad n = 1, 3, 5, \ldots

C.5Doppler effect

Wave behaviour

Doppler shift (light, v ≪ c)

\frac{\Delta f}{f} = \frac{\Delta\lambda}{\lambda} \approx \frac{v}{c}

Moving sourceHL

f' = f\left(\frac{v}{v \pm u_{s}}\right)

Moving observerHL

f' = f\left(\frac{v \pm u_{o}}{v}\right)

D.1Gravitational fields

Fields

Newton's law of gravitation

F = G\frac{m_{1}m_{2}}{r^{2}}

Gravitational field strength

g = \frac{F}{m} = G\frac{M}{r^{2}}

Orbital speed

v_{\text{orbital}} = \sqrt{\frac{GM}{r}}

Gravitational potential energyHL

E_{p} = -G\frac{m_{1}m_{2}}{r}

Gravitational potentialHL

V_{g} = -\frac{GM}{r}

Field strength from potentialHL

g = -\frac{\Delta V_{g}}{\Delta r}

Escape speedHL

v_{\text{esc}} = \sqrt{\frac{2GM}{r}}

D.2Electric & magnetic fields

Fields

Coulomb's law

F = k\frac{q_{1}q_{2}}{r^{2}}

Coulomb constant

k = \frac{1}{4\pi\varepsilon_{0}}

Electric field strength

E = \frac{F}{q}

Field of a point charge

E = k\frac{Q}{r^{2}}

Uniform field (parallel plates)

E = \frac{V}{d}

Electric potentialHL

V_{e} = k\frac{Q}{r}

Electric potential energyHL

E_{p} = k\frac{q_{1}q_{2}}{r}

Work and potential difference

W = q\Delta V_{e}

D.3Motion in electromagnetic fields

Fields

Force on a moving charge

F = qvB\sin\theta

Force on a current-carrying wire

F = BIL\sin\theta

Radius of circular motion in a field

r = \frac{mv}{qB}

Force per length between parallel wires

\frac{F}{L} = \frac{\mu_{0}I_{1}I_{2}}{2\pi r}

D.4Electromagnetic induction

Fields

Magnetic fluxHL

\Phi = BA\cos\theta

Faraday's lawHL

\varepsilon = -N\frac{\Delta\Phi}{\Delta t}

EMF of a moving conductorHL

\varepsilon = BvL

E.1Structure of the atom

Nuclear & quantum physics

Photon energy

E = hf = \frac{hc}{\lambda}

Hydrogen energy levels

E_{n} = -\frac{13.6}{n^{2}}\ \text{eV}

Quantised angular momentum (Bohr)HL

mvr = \frac{nh}{2\pi}

Nuclear radiusHL

R = R_{0}A^{\frac{1}{3}}

E.2Quantum physics

Nuclear & quantum physics

Photoelectric equationHL

E_{\text{max}} = hf - \Phi

de Broglie wavelengthHL

\lambda = \frac{h}{p} = \frac{h}{mv}

Compton scatteringHL

\lambda' - \lambda = \frac{h}{m_{e}c}(1 - \cos\theta)

E.3Radioactive decay

Nuclear & quantum physics

Decay lawHL

N = N_{0}e^{-\lambda t}

ActivityHL

A = \lambda N = A_{0}e^{-\lambda t}

Half-life and decay constantHL

T_{\frac{1}{2}} = \frac{\ln 2}{\lambda}

E.4Fission

Nuclear & quantum physics

Mass–energy equivalence

E = mc^{2}

E.5Fusion & stars

Nuclear & quantum physics

Stellar luminosity

L = \sigma A T^{4} = 4\pi R^{2}\sigma T^{4}

Apparent brightness

b = \frac{L}{4\pi d^{2}}

Wien's law (stellar temperature)

\lambda_{\text{max}} = \frac{2.9 \times 10^{-3}}{T}\ \text{m}

Physical constants

Acceleration of free fall (Earth)

g = 9.81\ \text{m s}^{-2}

Gravitational constant

G = 6.67 \times 10^{-11}\ \text{N m}^{2}\,\text{kg}^{-2}

Speed of light in vacuum

c = 3.00 \times 10^{8}\ \text{m s}^{-1}

Planck's constant

h = 6.63 \times 10^{-34}\ \text{J s}

Elementary charge

e = 1.60 \times 10^{-19}\ \text{C}

Electron rest mass

m_{e} = 9.110 \times 10^{-31}\ \text{kg}

Proton rest mass

m_{p} = 1.673 \times 10^{-27}\ \text{kg}

Neutron rest mass

m_{n} = 1.675 \times 10^{-27}\ \text{kg}

Unified atomic mass unit

u = 1.661 \times 10^{-27}\ \text{kg} = 931.5\ \text{MeV}\,c^{-2}

Boltzmann constant

k_{B} = 1.38 \times 10^{-23}\ \text{J K}^{-1}

Gas constant

R = 8.31\ \text{J K}^{-1}\,\text{mol}^{-1}

Avogadro's constant

N_{A} = 6.02 \times 10^{23}\ \text{mol}^{-1}

Stefan–Boltzmann constant

\sigma = 5.67 \times 10^{-8}\ \text{W m}^{-2}\,\text{K}^{-4}

Coulomb constant

k = 8.99 \times 10^{9}\ \text{N m}^{2}\,\text{C}^{-2}

Permittivity of free space

\varepsilon_{0} = 8.85 \times 10^{-12}\ \text{C}^{2}\,\text{N}^{-1}\,\text{m}^{-2}

Permeability of free space

\mu_{0} = 4\pi \times 10^{-7}\ \text{T m A}^{-1}

Electronvolt

1\ \text{eV} = 1.60 \times 10^{-19}\ \text{J}

How to use the IB Physics data booklet effectively

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IB Physics Formula Booklet.

A.1Kinematics

A.2Forces & momentum

A.3Work, energy & power

A.4Rigid body mechanics

A.5Galilean & special relativity

B.1Thermal energy transfers

B.2Greenhouse effect

B.3Gas laws

B.4Thermodynamics

B.5Current & circuits

C.1Simple harmonic motion

C.2Wave model

C.3Wave phenomena

C.4Standing waves & resonance

C.5Doppler effect

D.1Gravitational fields

D.2Electric & magnetic fields

D.3Motion in electromagnetic fields

D.4Electromagnetic induction

E.1Structure of the atom

E.2Quantum physics

E.3Radioactive decay

E.4Fission

E.5Fusion & stars

Physical constants

How to use the IB Physics data booklet effectively

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