GCSE Physics equations: all 37, by topic

Every equation you need, grouped by topic, with what each symbol means and its units. 27 of these you have to memorise for AQA — the rest are printed on the equation sheet in the exam. 10 are Higher tier only.

Memorise means the equation is not given to you in that board’s exam — you have to recall it. Given means it appears on the equation sheet. Boards differ, so check your own.

Energy

Ek = ½ × m × v²Memorise (AQA)

Ek: kinetic energy (J)
m: mass (kg)
v: speed (m/s)

Rearranged: v = √(2Ek / m) · m = 2Ek / v²

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: given

Ep = m × g × hMemorise (AQA)

Ep: gravitational potential energy (J)
m: mass (kg)
g: gravitational field strength (N/kg)
h: height (vertical) (m)

Rearranged: h = Ep / (m × g) · m = Ep / (g × h)

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

Ep = ½ × k × e²Higher onlyGiven (AQA)

Ep: elastic potential energy (J)
k: spring constant (N/m)
e: extension (m)

Rearranged: e = √(2Ep / k) · k = 2Ep / e²

AQA: given · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

W = F × sMemorise (AQA)

W: work done (J)
F: force applied (N)
s: distance moved in direction of force (m)

Rearranged: F = W / s · s = W / F

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

P = E / tMemorise (AQA)

P: power (W)
E: energy transferred (J)
t: time taken (s)

Rearranged: E = P × t · t = E / P

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

efficiency = useful energy output / total energy inputMemorise (AQA)

efficiency: efficiency ((dimensionless, 0-1 or × 100 for %))

Rearranged: efficiency = useful power output / total power input

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

Electricity

E (kWh) = P (kW) × t (hours)Memorise (AQA)

E: energy transferred (for billing) (kWh)
P: power rating of appliance (kW)
t: time appliance is on (hours)

Rearranged: cost = E (kWh) × unit cost

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

Q = I × tMemorise (AQA)

Q: charge (C)
I: current (A)
t: time (s)

Rearranged: I = Q / t · t = Q / I

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

V = I × RMemorise (AQA)

V: potential difference (V)
I: current (A)
R: resistance (Ω)

Rearranged: I = V / R · R = V / I

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

P = V × IMemorise (AQA)

P: electrical power (W)
V: potential difference (V)
I: current (A)

Rearranged: V = P / I · I = P / V

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

P = I² × RMemorise (AQA)

P: electrical power (W)
I: current (A)
R: resistance (Ω)

Rearranged: I = √(P / R) · R = P / I²

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

E = Q × VMemorise (AQA)

E: energy transferred (J)
Q: charge (C)
V: potential difference (V)

Rearranged: Q = E / V · V = E / Q

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

Particle model of matter

ρ = m / VMemorise (AQA)

ρ: density (kg/m³)
m: mass (kg)
V: volume (m³)

Rearranged: m = ρ × V · V = m / ρ

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: given

ΔE = m × c × ΔθMemorise (AQA)

ΔE: change in thermal energy (J)
m: mass (kg)
c: specific heat capacity (J/kg°C)
Δθ: temperature change (°C)

Rearranged: c = ΔE / (m × Δθ) · m = ΔE / (c × Δθ) · Δθ = ΔE / (m × c)

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: given

E = m × LGiven (AQA)

E: energy for change of state (J)
m: mass (kg)
L: specific latent heat (J/kg)

Rearranged: m = E / L · L = E / m

AQA: given · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

p × V = constant (at constant T, fixed mass)Higher onlyGiven (AQA)

p: pressure (Pa)
V: volume (m³)

Rearranged: p₁ × V₁ = p₂ × V₂

AQA: given · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

Atomic structure and radioactivity

N = N₀ × (½)ⁿGiven (AQA)

N: number of undecayed nuclei remaining (or activity, or count rate) after n half-lives (dimensionless count (or Bq, or counts/s))
N₀: initial number of undecayed nuclei (or initial activity, or initial count rate) (dimensionless count (or Bq, or counts/s))
n: number of half-lives elapsed (dimensionless)

Rearranged: N / N₀ = (½)ⁿ · n = log(N / N₀) / log(½)

AQA: given · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

A = ΔN / ΔtGiven (AQA)

A: activity (number of decays per second) (Bq (becquerel = decay/s))
ΔN: number of nuclei that have decayed (dimensionless count)
Δt: time interval (s)

Rearranged: ΔN = A × Δt · Δt = ΔN / A

AQA: given · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

Forces

Ep = ½ × k × e²Higher onlyGiven (AQA)

Ep: elastic potential energy (J)
k: spring constant (N/m)
e: extension (m)

Rearranged: e = √(2Ep / k) · k = 2Ep / e²

AQA: given · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

W = F × sMemorise (AQA)

W: work done (J)
F: force applied (N)
s: distance moved in direction of force (m)

Rearranged: F = W / s · s = W / F

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

W = m × gMemorise (AQA)

W: weight (N)
m: mass (kg)
g: gravitational field strength (N/kg)

Rearranged: m = W / g · g = W / m

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

M = F × dMemorise (AQA)

M: moment of force (N·m)
F: force (N)
d: perpendicular distance from pivot to line of action of force (m)

Rearranged: F = M / d · d = M / F

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

p = F / AMemorise (AQA)

p: pressure (Pa)
F: force (N)
A: contact area (m²)

Rearranged: F = p × A · A = F / p

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

p = h × ρ × gHigher onlyGiven (AQA)

p: pressure due to fluid column (Pa)
h: depth of fluid (m)
ρ: density of fluid (kg/m³)
g: gravitational field strength (N/kg)

Rearranged: h = p / (ρ × g) · ρ = p / (h × g)

AQA: given · Edexcel: memorise · OCR A: given · OCR B: given · Eduqas: given

F = k × eMemorise (AQA)

F: force (load on spring) (N)
k: spring constant (N/m)
e: extension (m)

Rearranged: k = F / e · e = F / k

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

Motion

Ek = ½ × m × v²Memorise (AQA)

Ek: kinetic energy (J)
m: mass (kg)
v: speed (m/s)

Rearranged: v = √(2Ek / m) · m = 2Ek / v²

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: given

s = v × tMemorise (AQA)

s: distance travelled (m)
v: speed (constant or average) (m/s)
t: time (s)

Rearranged: v = s / t · t = s / v

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

v = u + a × tMemorise (AQA)

v: final velocity (m/s)
u: initial velocity (m/s)
a: acceleration (uniform) (m/s²)
t: time (s)

Rearranged: a = (v − u) / t · t = (v − u) / a · u = v − a × t

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

v² − u² = 2 × a × sHigher onlyGiven (AQA)

v: final velocity (m/s)
u: initial velocity (m/s)
a: acceleration (uniform) (m/s²)
s: displacement (m)

Rearranged: v = √(u² + 2as) · u = √(v² − 2as) · a = (v² − u²) / (2s) · s = (v² − u²) / (2a)

AQA: given · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

s = ½ × (u + v) × tGiven (AQA)

s: displacement (m)
u: initial velocity (m/s)
v: final velocity (m/s)
t: time (s)

Rearranged: t = 2s / (u + v) · (u + v) = 2s / t

AQA: given · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

F = m × aMemorise (AQA)

F: resultant force (N)
m: mass (kg)
a: acceleration (m/s²)

Rearranged: a = F / m · m = F / a

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

p = m × vHigher onlyMemorise (AQA)

p: momentum (kg·m/s)
m: mass (kg)
v: velocity (m/s)

Rearranged: v = p / m · m = p / v

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

F = Δp / Δt = m × (v − u) / tHigher onlyGiven (AQA)

F: resultant force (N)
Δp: change in momentum (kg·m/s)
Δt: time for the change (s)
m: mass (constant) (kg)
v: final velocity (m/s)
u: initial velocity (m/s)
t: duration (s)

Rearranged: Δp = F × Δt · Δt = Δp / F · F = m × a (equivalent form when mass is constant)

AQA: given · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

Waves

v = f × λMemorise (AQA)

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

Rearranged: f = v / λ · λ = v / f

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

T = 1 / fMemorise (AQA)

T: period (s)
f: frequency (Hz)

Rearranged: f = 1 / T

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

n = sin i / sin rHigher onlyGiven (AQA)

n: refractive index of medium (relative to vacuum/air) (no unit (dimensionless))
i: angle of incidence (measured from normal) (°)
r: angle of refraction (measured from normal) (°)

Rearranged: sin i = n × sin r · sin r = sin i / n

Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

m = image height / object heightMemorise (AQA)

m: magnification (linear) (no unit (dimensionless))
image height: height of image formed by lens (m (or cm/mm consistently))
object height: height of object placed in front of lens (m (or cm/mm consistently))

Rearranged: image height = m × object height · object height = image height / m

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

Magnetism and electromagnetism

F = B × I × LHigher onlyMemorise (AQA)

F: force on conductor (N)
B: magnetic flux density (T)
I: current (A)
L: length of conductor in the field (m)

Rearranged: B = F / (I × L) · I = F / (B × L) · L = F / (B × I)

AQA: memorise · Edexcel: memorise · OCR A: memorise · OCR B: memorise · Eduqas: memorise

Vp / Vs = Np / NsHigher onlyMemorise (AQA)

Vp: primary voltage (input) (V)
Vs: secondary voltage (output) (V)
Np: number of turns on primary coil (no unit)
Ns: number of turns on secondary coil (no unit)

Rearranged: Vs = Vp × (Ns / Np) · Np = Ns × (Vp / Vs) · Ns = Np × (Vs / Vp)

AQA: memorise · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

Ip × Vp = Is × VsHigher onlyMemorise (AQA)

Ip: current in primary coil (A)
Vp: voltage across primary coil (V)
Is: current in secondary coil (A)
Vs: voltage across secondary coil (V)

Rearranged: Is = (Ip × Vp) / Vs · Ip = (Is × Vs) / Vp · Vs = (Ip × Vp) / Is

AQA: memorise · Edexcel: given · OCR A: given · OCR B: given · Eduqas: given

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