A Level Physics Formulae — By Exam Board

Measurements

12 cards · free in the app and shown in full here

Algebra and logarithms

Quadratic formula

Varies by board

AQA: AS and A level · OCR A: AS and A level

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

x = (−b ± √(b² − 4ac))/2a

x: a solution of ax² + bx + c = 0
a, b, c: the coefficients

Gives both solutions of ax² + bx + c = 0. In physics usually only the positive root is a possible time or length.

Laws of logarithms

Varies by board

AQA: AS and A level · OCR A: AS and A level

\log (A B) = \log A + \log B

log(AB) = log A + log B

Quotient: $\log (\frac{A}{B}) = \log A - \log B$
Power: $\log (x^{n}) = n \log x$
Natural log of an exponential: $\ln (e^{k x}) = k x$

A, B: positive quantities
n: a power
k: a constant

The same laws hold for ln. They turn an exponential or power law into a straight-line graph: plot ln y against x, or log y against log x.

Geometry

Arc length

In your booklet

AQA: AS and A level · OCR A: AS and A level

s = r θ

s = rθ

s: arc length (m)
r: radius (m)
θ: angle subtended at the centre (rad)

θ must be in radians.

Circle: circumference and area

In your booklet

AQA: AS and A level · OCR A: AS and A level

circumference = 2 π r

circumference = 2πr

Area: $area = π r^{2}$

r: radius (m)

Curved surface area of a cylinder

In your booklet

AQA: AS and A level · OCR A: AS and A level

curved surface area = 2 π r h

curved surface area = 2πrh

r: radius (m)
h: height (m)

Volume of a cylinder

Varies by board

AQA: AS and A level · OCR A: AS and A level

volume = π r^{2} h

volume = πr²h

r: radius (m)
h: height (or length) (m)

For a wire, A = πr² is the cross-sectional area used in resistivity and Young modulus.

Sphere: surface area and volume

In your booklet

AQA: AS and A level · OCR A: AS and A level

surface area = 4 π r^{2}

surface area = 4πr²

Volume: $volume = \frac{4}{3} π r^{3}$

r: radius (m)

4πr² is also the area an intensity spreads over at distance r from a point source.

Area of a trapezium

Varies by board

AQA: AS and A level · OCR A: AS and A level

area = \frac{1}{2} (a + b) h

area = ½(a + b)h

a, b: lengths of the parallel sides (m)
h: perpendicular distance between them (m)

Useful for the area under a straight-line velocity–time graph.

Trigonometry

Pythagoras' theorem

Varies by board

AQA: AS and A level · OCR A: AS and A level

a^{2} = b^{2} + c^{2}

a² = b² + c²

a: hypotenuse
b, c: the other two sides

Combines two perpendicular vectors into a resultant.

Sine rule

Varies by board

AQA: AS and A level · OCR A: AS and A level

\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

a/(sin A) = b/(sin B) = c/(sin C)

a, b, c: sides of a triangle
A, B, C: the angles opposite them

Cosine rule

Varies by board

AQA: AS and A level · OCR A: AS and A level

a^{2} = b^{2} + c^{2} - 2 b c \cos A

a² = b² + c² − 2bc cos A

a, b, c: sides of a triangle
A: the angle opposite a

Gives the resultant of two vectors that are not perpendicular.

Small-angle approximations

Varies by board

AQA: AS and A level · OCR A: AS and A level

\sin θ \approx \tan θ \approx θ

sin θ ≈ tan θ ≈ θ

Cosine: $\cos θ \approx 1$

θ: a small angle (rad)

θ in radians. Used for the simple pendulum, diffraction angles and parallax.

Mechanics and materials

29 cards · full cards in the app

Vectors and moments

Components of a vector

Varies by board

AQA: AS and A level · OCR A: AS and A level

Moment of a force

In your booklet

AQA: AS and A level · OCR A: AS and A level

Torque of a couple

Varies by board

AQA: AS and A level · OCR A: AS and A level

Motion

Velocity and acceleration

Varies by board

AQA: AS and A level · OCR A: AS and A level

v = u + at

In your booklet

AQA: AS and A level · OCR A: AS and A level

s = ½(u + v)t

In your booklet

AQA: AS and A level · OCR A: AS and A level

s = ut + ½at²

In your booklet

AQA: AS and A level · OCR A: AS and A level

v² = u² + 2as

In your booklet

AQA: AS and A level · OCR A: AS and A level

Forces and momentum

Newton's second law (F = ma)

Varies by board

AQA: AS and A level · OCR A: AS and A level

Weight

Learn this

AQA: AS and A level · OCR A: AS and A level

Force and rate of change of momentum

In your booklet

AQA: AS and A level · OCR A: AS and A level

Momentum

Varies by board

AQA: AS and A level · OCR A: AS and A level

Impulse

Varies by board

AQA: AS and A level · OCR A: AS and A level

Pressure

Varies by board

AQA: A level · OCR A: AS and A level

Pressure in a fluid

In your booklet

OCR A: AS and A level

Work, energy and power

Work done by a force

In your booklet

AQA: AS and A level · OCR A: AS and A level

Kinetic energy

Varies by board

AQA: AS and A level · OCR A: AS and A level

Change in gravitational potential energy

Varies by board

AQA: AS and A level · OCR A: AS and A level

Power

In your booklet

AQA: AS and A level · OCR A: AS and A level

Power, force and velocity

In your booklet

AQA: AS and A level · OCR A: AS and A level

Efficiency

In your booklet

AQA: AS and A level · OCR A: AS and A level

Materials

Density

In your booklet

AQA: AS and A level · OCR A: AS and A level

Hooke's law

In your booklet

AQA: AS and A level · OCR A: AS and A level

Elastic potential energy

In your booklet

AQA: AS and A level · OCR A: AS and A level

Elastic energy from the stiffness

Varies by board

AQA: AS and A level · OCR A: AS and A level

Tensile stress

In your booklet

AQA: AS and A level · OCR A: AS and A level

Tensile strain

In your booklet

AQA: AS and A level · OCR A: AS and A level

Young modulus

In your booklet

AQA: AS and A level · OCR A: AS and A level

Young modulus from measurements

Learn this

AQA: AS and A level · OCR A: AS and A level

The mechanics and materials cards, with explanations and board labels, are in the A Level Physics app.

Electricity

14 cards · full cards in the app

Charge, current and p.d.

Current

In your booklet

AQA: AS and A level · OCR A: AS and A level

Current and drift velocity

In your booklet

OCR A: AS and A level

Potential difference

In your booklet

AQA: AS and A level · OCR A: AS and A level

Energy transferred in a component

Varies by board

AQA: AS and A level · OCR A: AS and A level

Electron accelerated through a p.d.

Varies by board

AQA: AS and A level · OCR A: AS and A level

AS booklet: core information must be learnt.

Resistance

Varies by board

AQA: AS and A level · OCR A: AS and A level

Resistivity

In your booklet

AQA: AS and A level · OCR A: AS and A level

Resistors in series

In your booklet

AQA: AS and A level · OCR A: AS and A level

Resistors in parallel

In your booklet

AQA: AS and A level · OCR A: AS and A level

Electrical power

In your booklet

AQA: AS and A level · OCR A: AS and A level

emf and circuits

emf

In your booklet

AQA: AS and A level · OCR A: AS and A level

emf and internal resistance

In your booklet

AQA: AS and A level · OCR A: AS and A level

Terminal p.d.

Varies by board

AQA: AS and A level · OCR A: AS and A level

Potential divider

Varies by board

AQA: AS and A level · OCR A: AS and A level

The electricity cards, with explanations and board labels, are in the A Level Physics app.

Waves and quantum

19 cards · full cards in the app

Progressive waves

Wave equation

In your booklet

AQA: AS and A level · OCR A: AS and A level

Frequency and period

In your booklet

AQA: AS and A level · OCR A: AS and A level

Intensity

In your booklet

OCR A: AS and A level

Intensity and amplitude

Learn this

OCR A: AS and A level

Superposition and stationary waves

First harmonic of a stretched string

In your booklet

AQA: AS and A level

Spacing of nodes

Learn this

AQA: AS and A level · OCR A: AS and A level

Interference and diffraction

Young's double slit

In your booklet

AQA: AS and A level · OCR A: AS and A level

Diffraction grating

In your booklet

AQA: AS and A level · OCR A: A level

Refraction

Refractive index

In your booklet

AQA: AS and A level · OCR A: AS and A level

Snell's law

In your booklet

AQA: AS and A level · OCR A: AS and A level

n sin θ is constant

Varies by board

AQA: AS and A level · OCR A: AS and A level

Critical angle

In your booklet

AQA: AS and A level · OCR A: AS and A level

Refractive index of air

Learn this

AQA: AS and A level · OCR A: AS and A level

Photons and particles

Photon energy

In your booklet

AQA: AS and A level · OCR A: AS and A level

Photoelectric equation

In your booklet

AQA: AS and A level · OCR A: AS and A level

Stopping potential

Learn this

AQA: AS and A level

Planck constant from LEDs

Learn this

OCR A: AS and A level

Photon emitted between energy levels

In your booklet

AQA: AS and A level · OCR A: A level

de Broglie wavelength

In your booklet

AQA: AS and A level · OCR A: AS and A level

The waves and quantum cards, with explanations and board labels, are in the A Level Physics app.

Particles and nuclear

13 cards · full cards in the app

Particle data

Quark properties

In your booklet

AQA: AS and A level · OCR A: A level

Lepton numbers

In your booklet

AQA: AS and A level

Particle rest energies

In your booklet

AQA: AS and A level

Radiation and decay

Inverse-square law for gamma radiation

In your booklet

AQA: A level

Rate of decay

In your booklet

AQA: A level · OCR A: A level

Number of undecayed nuclei

In your booklet

AQA: A level · OCR A: A level

Activity against time

Varies by board

AQA: A level · OCR A: A level

Activity

In your booklet

AQA: A level · OCR A: A level

Half-life

In your booklet

AQA: A level · OCR A: A level

The nucleus and nuclear energy

Nuclear radius

In your booklet

AQA: A level · OCR A: A level

Distance of closest approach

Learn this

AQA: A level

Mass–energy equivalence

In your booklet

AQA: A level · OCR A: A level

Atomic mass unit as an energy

Varies by board

AQA: A level · OCR A: A level

The particles and nuclear cards, with explanations and board labels, are in the A Level Physics app.

Thermal and oscillations

24 cards · full cards in the app

Thermal physics

Specific heat capacity

In your booklet

AQA: A level · OCR A: A level

Specific latent heat

In your booklet

AQA: A level · OCR A: A level

Celsius to kelvin

Learn this

AQA: A level · OCR A: A level

Ideal gases

Ideal gas equation (moles)

In your booklet

AQA: A level · OCR A: A level

Ideal gas equation (molecules)

In your booklet

AQA: A level · OCR A: A level

Boyle's law

Varies by board

AQA: A level · OCR A: A level

Pressure law and Charles's law

Learn this

AQA: A level · OCR A: A level

Kinetic theory equation

In your booklet

AQA: A level · OCR A: A level

Mean kinetic energy of a molecule

In your booklet

AQA: A level · OCR A: A level

Boltzmann constant from R and NA

Learn this

AQA: A level · OCR A: A level

Work done on or by a gas

In your booklet

AQA: A level

Circular motion

Angular speed

In your booklet

AQA: A level · OCR A: A level

Angular frequency

In your booklet

AQA: A level · OCR A: A level

Angular frequency and period

Varies by board

AQA: A level · OCR A: A level

Centripetal acceleration

In your booklet

AQA: A level · OCR A: A level

Centripetal force

In your booklet

AQA: A level · OCR A: A level

Simple harmonic motion

Defining equation of SHM

In your booklet

AQA: A level · OCR A: A level

SHM displacement (cos)

In your booklet

AQA: A level · OCR A: A level

SHM displacement (sin)

Varies by board

AQA: A level · OCR A: A level

SHM speed at displacement x

In your booklet

AQA: A level · OCR A: A level

Maximum speed in SHM

Varies by board

AQA: A level · OCR A: A level

Maximum acceleration in SHM

Varies by board

AQA: A level · OCR A: A level

Period of a mass on a spring

In your booklet

AQA: A level

Period of a simple pendulum

In your booklet

AQA: A level

The thermal and oscillations cards, with explanations and board labels, are in the A Level Physics app.

Fields

40 cards · full cards in the app

Gravitational fields

Newton's law of gravitation

In your booklet

AQA: A level · OCR A: A level

Gravitational field strength

In your booklet

AQA: A level · OCR A: A level

Field strength near a point mass

In your booklet

AQA: A level · OCR A: A level

Gravitational potential

In your booklet

AQA: A level · OCR A: A level

Work done moving a mass in a field

Varies by board

AQA: A level · OCR A: A level

Field strength as potential gradient

In your booklet

AQA: A level

Gravitational potential energy

Varies by board

AQA: A level · OCR A: A level

Kepler's third law

Varies by board

AQA: A level · OCR A: A level

Escape velocity

Learn this

AQA: A level · OCR A: A level

Orbital speed

Learn this

AQA: A level · OCR A: A level

Electric fields

Coulomb's law

In your booklet

AQA: A level · OCR A: A level

Electric field strength

In your booklet

AQA: A level · OCR A: A level

Uniform electric field

In your booklet

AQA: A level · OCR A: A level

Work done moving a charge

Varies by board

AQA: A level · OCR A: A level

Work done across a uniform field

Learn this

AQA: A level

Field strength near a point charge

In your booklet

AQA: A level · OCR A: A level

Electric potential

In your booklet

AQA: A level · OCR A: A level

Field strength as potential gradient (electric)

In your booklet

AQA: A level

Electric potential energy

In your booklet

OCR A: A level

Capacitors

Capacitance

In your booklet

AQA: A level · OCR A: A level

Parallel-plate capacitor with a dielectric

Varies by board

AQA: A level · OCR A: A level

Parallel-plate capacitor

In your booklet

AQA: A level · OCR A: A level

Capacitance of an isolated sphere

In your booklet

OCR A: A level

Capacitors in series

In your booklet

OCR A: A level

Capacitors in parallel

In your booklet

OCR A: A level

Energy stored by a capacitor

In your booklet

AQA: A level · OCR A: A level

Time constant

In your booklet

AQA: A level · OCR A: A level

Capacitor discharge

In your booklet

AQA: A level · OCR A: A level

Capacitor charging

In your booklet

AQA: A level · OCR A: A level

Time to halve

Learn this

AQA: A level

Magnetic fields and induction

Force on a current-carrying wire

In your booklet

AQA: A level · OCR A: A level

Force on a moving charge

In your booklet

AQA: A level · OCR A: A level

Radius of a charged particle's path

Varies by board

AQA: A level · OCR A: A level

Magnetic flux

In your booklet

AQA: A level · OCR A: A level

Flux linkage

Varies by board

AQA: A level · OCR A: A level

Faraday's law

In your booklet

AQA: A level · OCR A: A level

emf of a rotating coil

In your booklet

AQA: A level

rms current and p.d.

In your booklet

AQA: A level

Transformer equation

In your booklet

AQA: A level · OCR A: A level

Transformer efficiency

In your booklet

AQA: A level

The fields cards, with explanations and board labels, are in the A Level Physics app.

Astrophysics

19 cards · full cards in the app

Telescopes

Angular magnification

In your booklet

AQA: A level

Magnification in normal adjustment

In your booklet

AQA: A level

Rayleigh criterion

In your booklet

AQA: A level

Collecting power

Learn this

AQA: A level

Stars and their radiation

Apparent and absolute magnitude

In your booklet

AQA: A level

Magnitude scale

Learn this

AQA: A level

Wien's displacement law

In your booklet

AQA: A level · OCR A: A level

Stefan's law

In your booklet

AQA: A level · OCR A: A level

Schwarzschild radius

In your booklet

AQA: A level

Cosmology

Doppler shift for light

In your booklet

AQA: A level · OCR A: A level

Redshift

In your booklet

AQA: A level

Hubble's law

In your booklet

AQA: A level · OCR A: A level

Age of the universe

Varies by board

AQA: A level · OCR A: A level

Parallax and distance

Varies by board

AQA: A level · OCR A: A level

Astronomical data (AQA)

Wien constant

In your booklet

AQA: A level

Light year (AQA value)

In your booklet

AQA: A level

Parsec (AQA value)

In your booklet

AQA: A level

Astronomical unit

In your booklet

AQA: A level

Hubble constant

In your booklet

AQA: A level

The astrophysics cards, with explanations and board labels, are in the A Level Physics app.

Medical physics

11 cards · full cards in the app

The eye and the ear

Power of a lens

In your booklet

AQA: A level

Magnification of a lens

In your booklet

AQA: A level

Lens equation

In your booklet

AQA: A level

Intensity level

In your booklet

AQA: A level

X-rays

Attenuation of X-rays

In your booklet

AQA: A level · OCR A: A level

Mass attenuation coefficient

In your booklet

AQA: A level

Half-value thickness

Learn this

AQA: A level

Ultrasound and nuclear medicine

Acoustic impedance

In your booklet

AQA: A level · OCR A: A level

Fraction of ultrasound reflected

In your booklet

AQA: A level · OCR A: A level

Doppler ultrasound

In your booklet

OCR A: A level

Effective half-life

In your booklet

AQA: A level

The medical physics cards, with explanations and board labels, are in the A Level Physics app.

Engineering physics

22 cards · full cards in the app

Rotational dynamics

Moment of inertia

In your booklet

AQA: A level

Rotational kinetic energy

In your booklet

AQA: A level

Angular velocity and acceleration

Learn this

AQA: A level

ω₂ = ω₁ + αt

In your booklet

AQA: A level

ω₂² = ω₁² + 2αθ

In your booklet

AQA: A level

θ = ω₁t + ½αt²

In your booklet

AQA: A level

θ = ½(ω₁ + ω₂)t

In your booklet

AQA: A level

Torque

In your booklet

AQA: A level

Angular momentum

In your booklet

AQA: A level

Work and power in rotation

In your booklet

AQA: A level

Thermodynamics

First law of thermodynamics

In your booklet

AQA: A level

Adiabatic and isothermal changes

In your booklet

AQA: A level

Heat engine efficiency

In your booklet

AQA: A level

Maximum theoretical efficiency

In your booklet

AQA: A level

Work done per cycle

In your booklet

AQA: A level

Input power of an engine

In your booklet

AQA: A level

Indicated power

In your booklet

AQA: A level

Brake power and friction power

In your booklet

AQA: A level

Overall, thermal and mechanical efficiency

Learn this

AQA: A level

Coefficient of performance: refrigerator

In your booklet

AQA: A level

Coefficient of performance: heat pump

In your booklet

AQA: A level

Maximum coefficients of performance

Learn this

AQA: A level

The engineering physics cards, with explanations and board labels, are in the A Level Physics app.

Turning points

10 cards · full cards in the app

Discovery of the electron

Force on an electron between plates

In your booklet

AQA: A level

Electron in a magnetic field

In your booklet

AQA: A level

Millikan's oil drop: stationary drop

In your booklet

AQA: A level

Stokes' law

In your booklet

AQA: A level

Light and matter

Permeability of free space

In your booklet

AQA: A level

Speed of electromagnetic waves

In your booklet

AQA: A level

de Broglie wavelength of an accelerated electron

In your booklet

AQA: A level

Special relativity

Time dilation

In your booklet

AQA: A level

Length contraction

In your booklet

AQA: A level

Relativistic energy

In your booklet

AQA: A level

The turning points cards, with explanations and board labels, are in the A Level Physics app.

Electronics

10 cards · full cards in the app

Analogue signal processing

Resonant frequency of an LC circuit

In your booklet

AQA: A level

Q factor

In your booklet

AQA: A level

Op-amp open-loop output

In your booklet

AQA: A level

Inverting amplifier

In your booklet

AQA: A level

Non-inverting amplifier

In your booklet

AQA: A level

Summing amplifier

In your booklet

AQA: A level

Difference amplifier

In your booklet

AQA: A level

Gain–bandwidth product

Learn this

AQA: A level

Digital electronics and communication

Boolean notation

Learn this

AQA: A level

Bandwidth of AM and FM

In your booklet

AQA: A level

The electronics cards, with explanations and board labels, are in the A Level Physics app.

Constants

23 cards · full cards in the app

Fundamental constants

Speed of light in a vacuum

In your booklet

AQA: AS and A level · OCR A: AS and A level

Elementary charge

In your booklet

AQA: AS and A level · OCR A: AS and A level

Planck constant

In your booklet

AQA: AS and A level · OCR A: AS and A level

Acceleration of free fall

In your booklet

AQA: AS and A level · OCR A: AS and A level

Permittivity of free space

In your booklet

AQA: A level · OCR A: A level

Gravitational constant

In your booklet

AQA: A level · OCR A: A level

Avogadro constant

In your booklet

AQA: A level · OCR A: A level

Molar gas constant

In your booklet

AQA: A level · OCR A: A level

Boltzmann constant

In your booklet

AQA: A level · OCR A: A level

Stefan constant

In your booklet

AQA: A level · OCR A: A level

Particle masses

Electron rest mass

In your booklet

AQA: AS and A level · OCR A: AS and A level

Proton rest mass

In your booklet

AQA: AS and A level · OCR A: AS and A level

Neutron rest mass

In your booklet

AQA: AS and A level · OCR A: AS and A level

Alpha particle rest mass

In your booklet

OCR A: A level

Specific charge of the electron

In your booklet

AQA: AS and A level

Specific charge of the proton

In your booklet

AQA: AS and A level

Units and conversions

Atomic mass unit

In your booklet

AQA: A level · OCR A: A level

Electronvolt

Varies by board

AQA: AS and A level · OCR A: AS and A level

Year and day in seconds

In your booklet

OCR A: AS and A level

Astronomical data

Light year

In your booklet

OCR A: A level

Parsec

In your booklet

OCR A: A level

Sun: mass and radius

In your booklet

AQA: A level

Earth: mass and radius

In your booklet

AQA: A level

The constants cards, with explanations and board labels, are in the A Level Physics app.

Formulae: learn it, or look it up?

Measurements

Algebra and logarithms

Quadratic formula

Laws of logarithms

Geometry

Arc length

Circle: circumference and area

Curved surface area of a cylinder

Volume of a cylinder

Sphere: surface area and volume

Area of a trapezium

Trigonometry

Pythagoras' theorem

Sine rule

Cosine rule

Small-angle approximations

Mechanics and materials

Vectors and moments

Components of a vector

Moment of a force

Torque of a couple

Motion

Velocity and acceleration

v = u + at

s = ½(u + v)t

s = ut + ½at²

v² = u² + 2as

Forces and momentum

Newton's second law (F = ma)

Weight

Force and rate of change of momentum

Momentum

Impulse

Pressure

Pressure in a fluid

Work, energy and power

Work done by a force

Kinetic energy

Change in gravitational potential energy

Power

Power, force and velocity

Efficiency

Materials

Density

Hooke's law

Elastic potential energy

Elastic energy from the stiffness

Tensile stress

Tensile strain

Young modulus

Young modulus from measurements

Electricity

Charge, current and p.d.

Current

Current and drift velocity

Potential difference

Energy transferred in a component

Electron accelerated through a p.d.

Resistance

Resistance

Resistivity

Resistors in series

Resistors in parallel

Electrical power

emf and circuits

emf

emf and internal resistance

Terminal p.d.

Potential divider

Waves and quantum

Progressive waves

Wave equation

Frequency and period

Intensity

Intensity and amplitude

Superposition and stationary waves

First harmonic of a stretched string

Spacing of nodes

Interference and diffraction