Every GCSE Physics equation on one sheet

Ek = ½ m v²

kinetic energy = 0.5 × mass × speed²

• Ek kinetic energy: joules, J
• m mass: kilograms, kg
• v speed: metres per second, m/s

Spec ref 8463 4.1.1.2

Ee = ½ k e²

elastic potential energy = 0.5 × spring constant × extension²

• Ee elastic potential energy: joules, J
• k spring constant: newtons per metre, N/m
• e extension: metres, m

Assumes the limit of proportionality has not been exceeded.

Spec ref 8463 4.1.1.2

Ep = m g h

gravitational potential energy = mass × gravitational field strength × height

• Ep gravitational potential energy: joules, J
• m mass: kilograms, kg
• g gravitational field strength (always given): newtons per kilogram, N/kg
• h height: metres, m

Spec ref 8463 4.1.1.2

ΔE = m c Δθ

change in thermal energy = mass × specific heat capacity × temperature change

• ΔE change in thermal energy: joules, J
• m mass: kilograms, kg
• c specific heat capacity: joules per kilogram per degree Celsius, J/kg °C
• Δθ temperature change: degrees Celsius, °C

Spec ref 8463 4.1.1.3

P = E / t

power = energy transferred ÷ time

• P power: watts, W
• E energy transferred: joules, J
• t time: seconds, s

Spec ref 8463 4.1.1.4

P = W / t

power = work done ÷ time

• P power: watts, W
• W work done: joules, J
• t time: seconds, s

Spec ref 8463 4.1.1.4

efficiency = useful output energy transfer / total input energy transfer

efficiency = useful output energy transfer ÷ total input energy transfer

• efficiency: no unit (ratio)

Efficiency may be given as a decimal or a percentage.

Spec ref 8463 4.1.2.2

efficiency = useful power output / total power input

efficiency = useful power output ÷ total power input

• efficiency: no unit (ratio)

Spec ref 8463 4.1.2.2

Q = I t

charge flow = current × time

• Q charge flow: coulombs, C
• I current: amperes, A
• t time: seconds, s

Spec ref 8463 4.2.1.2

V = I R

potential difference = current × resistance

• V potential difference: volts, V
• I current: amperes, A
• R resistance: ohms, Ω

Spec ref 8463 4.2.1.3

P = V I

power = potential difference × current

• P power: watts, W
• V potential difference: volts, V
• I current: amperes, A

Spec ref 8463 4.2.4.1

P = I² R

power = current² × resistance

• P power: watts, W
• I current: amperes, A
• R resistance: ohms, Ω

Spec ref 8463 4.2.4.1

E = P t

energy transferred = power × time

• E energy transferred: joules, J
• P power: watts, W
• t time: seconds, s

Spec ref 8463 4.2.4.2

E = Q V

energy transferred = charge flow × potential difference

• E energy transferred: joules, J
• Q charge flow: coulombs, C
• V potential difference: volts, V

Spec ref 8463 4.2.4.2

Vp × Ip = Vs × Is

pd across primary × current in primary = pd across secondary × current in secondary

• Vp potential difference across primary coil: volts, V
• Ip current in primary coil: amperes, A
• Vs potential difference across secondary coil: volts, V
• Is current in secondary coil: amperes, A

Separate Physics meets this in the magnetism topic; Combined Science in the national grid.

Spec ref 8463 4.7.3.4

ρ = m / V

density = mass ÷ volume

• ρ density: kilograms per metre cubed, kg/m³
• m mass: kilograms, kg
• V volume: metres cubed, m³

Spec ref 8463 4.3.1.1

E = m L

energy for a change of state = mass × specific latent heat

• E energy for a change of state: joules, J
• m mass: kilograms, kg
• L specific latent heat: joules per kilogram, J/kg

Spec ref 8463 4.3.2.3

p V = constant

pressure × volume = constant

• p pressure: pascals, Pa
• V volume: metres cubed, m³

For a fixed mass of gas at constant temperature.

Spec ref 8463 4.3.3.2

W = m g

weight = mass × gravitational field strength

• W weight: newtons, N
• m mass: kilograms, kg
• g gravitational field strength (always given): newtons per kilogram, N/kg

Spec ref 8463 4.5.1.3

W = F s

work done = force × distance

• W work done: joules, J
• F force: newtons, N
• s distance: metres, m

Distance is measured along the line of action of the force.

Spec ref 8463 4.5.2

F = k e

force = spring constant × extension

• F force: newtons, N
• k spring constant: newtons per metre, N/m
• e extension: metres, m

Applies up to the limit of proportionality; e can be a compression.

Spec ref 8463 4.5.3

M = F d

moment of a force = force × distance

• M moment of a force: newton-metres, Nm
• F force: newtons, N
• d distance: metres, m

d is the perpendicular distance between the pivot and the force's line of action.

Spec ref 8463 4.5.4

p = F / A

pressure = force normal to a surface ÷ area of that surface

• p pressure: pascals, Pa
• F force normal to a surface: newtons, N
• A area of that surface: metres squared, m²

Spec ref 8463 4.5.5.1.1

p = h ρ g

pressure due to a column of liquid = height of column × density of the liquid × gravitational field strength

• p pressure: pascals, Pa
• h height of the column: metres, m
• ρ density of the liquid: kilograms per metre cubed, kg/m³
• g gravitational field strength (always given): newtons per kilogram, N/kg

Spec ref 8463 4.5.5.1.2

s = v t

distance travelled = speed × time

• s distance travelled: metres, m
• v speed: metres per second, m/s
• t time: seconds, s

For constant speed; use average speed for non-uniform motion.

Spec ref 8463 4.5.6.1.2

a = Δv / t

acceleration = change in velocity ÷ time taken

• a acceleration: metres per second squared, m/s²
• Δv change in velocity: metres per second, m/s
• t time: seconds, s

Spec ref 8463 4.5.6.1.5

v² − u² = 2 a s

(final velocity)² − (initial velocity)² = 2 × acceleration × distance

• v final velocity: metres per second, m/s
• u initial velocity: metres per second, m/s
• a acceleration: metres per second squared, m/s²
• s distance: metres, m

For uniform acceleration.

Spec ref 8463 4.5.6.1.5

F = m a

resultant force = mass × acceleration

• F resultant force: newtons, N
• m mass: kilograms, kg
• a acceleration: metres per second squared, m/s²

Spec ref 8463 4.5.6.2.2

p = m v

momentum = mass × velocity

• p momentum: kilogram metres per second, kg m/s
• m mass: kilograms, kg
• v velocity: metres per second, m/s

Spec ref 8463 4.5.7.1

F = m Δv / Δt

force = change in momentum ÷ time taken

• F force: newtons, N
• m mass: kilograms, kg
• Δv change in velocity: metres per second, m/s
• Δt time taken: seconds, s

Force equals the rate of change of momentum.

Spec ref 8463 4.5.7.3

T = 1 / f

period = 1 ÷ frequency

• T period: seconds, s
• f frequency: hertz, Hz

Spec ref 8463 4.6.1.2

v = f λ

wave speed = frequency × wavelength

• v wave speed: metres per second, m/s
• f frequency: hertz, Hz
• λ wavelength: metres, m

Spec ref 8463 4.6.1.2

magnification = image height / object height

magnification = image height ÷ object height

• magnification: no unit (ratio)

A ratio with no units; measure both heights in the same unit (mm or cm).

Spec ref 8463 4.6.2.5

F = B I l

force = magnetic flux density × current × length

• F force: newtons, N
• B magnetic flux density: tesla, T
• I current: amperes, A
• l length: metres, m

Only when the conductor is at right angles to the magnetic field.

Spec ref 8463 4.7.2.2

Vp / Vs = np / ns

pd across primary ÷ pd across secondary = turns on primary ÷ turns on secondary

• Vp potential difference across primary coil: volts, V
• Vs potential difference across secondary coil: volts, V
• np number of turns on primary coil: no unit
• ns number of turns on secondary coil: no unit

Spec ref 8463 4.7.3.4