GCSE & A-Level Formula Sheets
Every equation and formula you need for your Maths and Science exams — listed by subject and topic. Download official formula sheets from AQA, Edexcel, OCR and WJEC, and learn exactly what you need to memorise versus what's provided on the day.
GCSE Maths Formula Sheet
The formulas below are split into two groups: those given on the exam paper and those you must memorise. All exam boards (AQA, Edexcel, OCR) provide a formula sheet for Higher tier papers.
Provided on the Formula Sheet
Area & Volume
- Area of trapezium = 1⁄2(a + b)h
- Volume of prism = area of cross-section × length
- Volume of cone = 1⁄3πr²h
- Surface area of sphere = 4πr²
- Volume of sphere = 4⁄3πr³
Algebra & Trigonometry
- Quadratic formula: x = (-b ± √(b² - 4ac)) / 2a
- Cosine rule: a² = b² + c² - 2bc cos(A)
- Sine rule: a/sin(A) = b/sin(B) = c/sin(C)
- Area of triangle = 1⁄2ab sin(C)
- Compound interest: Total = P × (1 + r/100)n
Must Memorise (NOT on the Sheet)
Basic Shapes
- Area of rectangle = length × width
- Area of triangle = 1⁄2 × base × height
- Area of circle = πr²
- Circumference = 2πr (or πd)
- Area of parallelogram = base × height
Key Relationships
- Pythagoras: a² + b² = c²
- Speed = distance / time
- Density = mass / volume
- Pressure = force / area
- Percentage change = (change / original) × 100
Probability & Stats
- Probability = favourable outcomes / total outcomes
- Mean = sum of values / number of values
- P(A or B) = P(A) + P(B) - P(A and B)
- P(not A) = 1 - P(A)
GCSE Physics Equation Sheet
All GCSE Physics equations provided in the exam, organised by topic. These cover AQA, Edexcel and OCR — the specific layout varies by board, but the core equations are the same.
Forces & Motion
- Weight: W = mg
- Work done: W = Fd
- Force: F = ma
- Momentum: p = mv
- Moment: M = Fd
- Pressure: p = F/A
- Pressure in fluid: p = hρg
- Spring constant: F = ke
Energy
- Kinetic energy: KE = 1⁄2mv²
- GPE: GPE = mgh
- Elastic PE: EPE = 1⁄2ke²
- Specific heat: E = mcΔθ
- Specific latent heat: E = mL
- Efficiency = useful output / total input
- Power: P = E/t
Electricity
- Charge: Q = It
- Voltage: V = IR
- Power: P = IV
- Power: P = I²R
- Energy transferred: E = QV
- Energy: E = Pt
Waves
- Wave speed: v = fλ
- Period: T = 1/f
- Magnification = image height / object height
Magnetism & EM
- Force on conductor: F = BIl
- Transformer: Vp/Vs = Np/Ns
- Power: VpIp = VsIs
Atomic & Nuclear
- Energy of photon: E = hf
- Half-life: the time for half the radioactive nuclei to decay
GCSE Chemistry Formula Sheet
GCSE Chemistry has fewer "formula sheet" equations than Physics, but the calculations you need are still essential. Most exam boards provide a periodic table and some key relationships.
Quantitative Chemistry
- Relative formula mass (Mr) = sum of relative atomic masses
- Moles: n = mass / Mr
- Moles (solutions): n = concentration × volume
- Concentration = moles / volume (in dm³)
- Concentration (g/dm³) = mass / volume
Yields & Economy
- Percentage yield = (actual yield / theoretical yield) × 100
- Atom economy = (Mr of desired product / Mr of all products) × 100
- Percentage by mass = (Ar × number of atoms / Mr) × 100
- Molar volume (at RTP) = 24 dm³/mol
- Volume of gas = moles × 24 (at RTP)
A-Level Maths Formula Booklet
A comprehensive formula booklet is provided for all A-Level Maths exams. Below are the most important formulas you'll use, split by Pure Maths, Mechanics and Statistics.
Pure — Algebra & Series
- Binomial expansion: (a + b)n
- Laws of logarithms: log(ab) = log a + log b
- Arithmetic series: Sn = n⁄2(2a + (n-1)d)
- Geometric series: Sn = a(1 - rn) / (1 - r)
- Sum to infinity: S∞ = a / (1 - r), |r| < 1
Pure — Calculus
- Differentiation: d/dx(xn) = nxn-1
- Chain rule: dy/dx = dy/du × du/dx
- Product rule: d/dx(uv) = u(dv/dx) + v(du/dx)
- Quotient rule: d/dx(u/v) = (v(du/dx) - u(dv/dx)) / v²
- Integration: ∫xndx = xn+1/(n+1) + c
Pure — Trigonometry
- sin²θ + cos²θ = 1
- tanθ = sinθ / cosθ
- Double angle: sin(2A) = 2sinAcosA
- Double angle: cos(2A) = cos²A - sin²A
- Small angle: sinθ ≈ θ, cosθ ≈ 1 - θ²/2
Mechanics (SUVAT)
- v = u + at
- s = ut + 1⁄2at²
- v² = u² + 2as
- s = 1⁄2(u + v)t
- Where: s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time
Statistics
- Mean of X: μ = ΣxP(X = x)
- Variance: Var(X) = E(X²) - [E(X)]²
- Binomial: P(X = r) = nCr pr(1-p)n-r
- Normal: X ~ N(μ, σ²)
Vectors & Coordinate Geometry
- Midpoint: ((x1+x2)/2, (y1+y2)/2)
- Distance: d = √((x2-x1)² + (y2-y1)²)
- Equation of circle: (x-a)² + (y-b)² = r²
A-Level Physics Equations Sheet
The A-Level Physics data sheet is more comprehensive than GCSE. Below are the key equations organised by topic, covering all major exam boards. The actual booklet also includes physical constants and data tables.
Mechanics
- SUVAT: v = u + at, s = ut + 1⁄2at²
- Newton's 2nd: F = ma
- Impulse: FΔt = Δp
- Work done: W = Fs cosθ
- KE = 1⁄2mv²
- Power: P = Fv
- Moment: τ = Fd
Materials & Waves
- Young's modulus: E = stress / strain
- Stress: σ = F/A
- Strain: ε = ΔL/L
- Wave speed: v = fλ
- Diffraction grating: d sinθ = nλ
- Refractive index: n = c/v = sinθ1/sinθ2
Electricity
- Ohm's law: V = IR
- Resistivity: R = ρL/A
- Power: P = IV = I²R = V²/R
- EMF: ε = I(R + r)
- Energy: E = VIt
- Charge: Q = It
Fields
- Gravitational field: g = F/m = GM/r²
- Gravitational PE: Ep = -GMm/r
- Electric field: E = F/Q = V/d
- Coulomb's law: F = kQ1Q2/r²
- Capacitance: C = Q/V
- Capacitor energy: E = 1⁄2CV²
Quantum & Nuclear
- Photon energy: E = hf = hc/λ
- de Broglie: λ = h/mv
- Einstein's: E = mc²
- Radioactive decay: N = N0e-λt
- Half-life: t½ = ln2 / λ
- Activity: A = λN
Thermal & Gases
- Ideal gas: pV = nRT
- Ideal gas: pV = NkT
- KE of molecule: 1⁄2m<c²> = 3⁄2kT
- Specific heat: E = mcΔθ
- Specific latent heat: E = mL
Key Physical Constants (provided in data booklet)
A-Level Chemistry Data Booklet
The A-Level Chemistry data booklet provides physical constants, key formulae, standard electrode potentials, and spectroscopy data. Below are the essential calculation formulas.
Thermodynamics
- Enthalpy change: ΔH = mcΔT
- Hess's Law: ΔHrxn = ΣΔHf(products) - ΣΔHf(reactants)
- Bond enthalpy: ΔH = Σ(bonds broken) - Σ(bonds formed)
- Gibbs free energy: ΔG = ΔH - TΔS
- Feasibility: reaction spontaneous when ΔG < 0
Kinetics & Equilibria
- Rate = k[A]m[B]n
- Arrhenius equation: k = Ae-Ea/RT
- Kc = [products]coefficients / [reactants]coefficients
- Kp = partial pressures of products / reactants
- pH = -log10[H+]
- Kw = [H+][OH-] = 1.0 × 10-14 mol²dm-6
Electrochemistry & Moles
- Ecell = Ecathode - Eanode
- Faraday: Q = nF (F = 96,485 C/mol)
- Moles: n = mass / Mr
- Ideal gas: pV = nRT
- Concentration = n / V (mol/dm³)
A-Level Further Maths Formula Booklet
The Further Maths formula booklet extends the standard A-Level Maths booklet with additional content for complex numbers, matrices, differential equations, hyperbolic functions, advanced mechanics, and decision maths. It is provided in all Further Maths exams.
Read full guide →How to Use Formula Sheets Effectively
Know what IS and ISN'T on the sheet
The biggest mistake students make is assuming everything is on the formula sheet. Basic formulas like speed = distance/time, density = mass/volume, and simple area calculations are usually NOT provided. Download the official formula sheet from your exam board early in your revision and highlight what you need to memorise separately.
Practice navigating the sheet under timed conditions
During the exam, time pressure is real. You need to be able to find the formula you need quickly — within 5-10 seconds. Practice doing past papers with the formula sheet beside you. Note which formulas you look up most often and where they are on the sheet. Consider lightly annotating the sheet during revision (but remember you can't bring your annotated version into the exam).
Memorise derived relationships anyway
Even if a formula is on the sheet, knowing it by heart saves precious time. For example, while V=IR is provided in Physics, you should automatically know that R=V/I and I=V/R without having to look it up or rearrange. The same applies to Maths — know your trigonometric identities, not just where to find them.
Use the sheet to check, not to learn from scratch
The formula sheet is a safety net, not a teaching tool. If you're seeing a formula for the first time in the exam, you won't know when to apply it or how to use it correctly. Learn every formula during revision, understand what each variable represents, and practice applying it in different contexts. Then use the sheet in the exam as a quick reference to confirm you've remembered correctly.
Understand the conditions and limitations
Many formulas only apply in specific situations. For example, SUVAT equations in Physics only work for constant acceleration. The binomial expansion formula in Maths has conditions on the value of n. The formula sheet doesn't tell you these conditions — that's knowledge you need to bring to the exam. Make sure you know not just the formula, but when and how to use it.
Official Exam Board Websites
Download links above go directly to official PDFs. For other subjects or WJEC, visit the exam board websites below.
Frequently Asked Questions
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