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GCSE Maths Formula Sheet

A complete reference sheet of all GCSE maths formulas, beautifully typeset. Covers algebra, geometry, trigonometry, statistics, and more — bookmark and print for revision.

Formula sheet is shown below as a comprehensive reference.

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Algebra

Quadratic formula

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Difference of two squares

a2−b2=(a+b)(a−b)a^2 - b^2 = (a+b)(a-b)

nth term (linear)

Tn=a+(n−1)dT_n = a + (n-1)d

nth term (quadratic)

Tn=an2+bn+cT_n = an^2 + bn + c

Area

Rectangle

A=lwA = lw

Triangle

A=12bhA = \frac{1}{2}bh

Trapezium

A=12(a+b)hA = \frac{1}{2}(a+b)h

Circle

A=πr2A = \pi r^2

Parallelogram

A=bhA = bh

Sector

A=θ360πr2A = \frac{\theta}{360} \pi r^2

Perimeter & Circumference

Circle circumference

C=2πr=πdC = 2\pi r = \pi d

Arc length

L=θ360×2πrL = \frac{\theta}{360} \times 2\pi r

Volume

Cuboid

V=lwhV = lwh

Prism

V=cross-section area×lV = \text{cross-section area} \times l

Cylinder

V=πr2hV = \pi r^2 h

Cone

V=13πr2hV = \frac{1}{3}\pi r^2 h

Sphere

V=43πr3V = \frac{4}{3}\pi r^3

Pyramid

V=13×base area×hV = \frac{1}{3} \times \text{base area} \times h

Surface Area

Cylinder

SA=2πr(r+h)SA = 2\pi r(r + h)

Sphere

SA=4πr2SA = 4\pi r^2

Cone

SA=πr(r+l)SA = \pi r(r + l)

Trigonometry

Pythagoras' theorem

a2+b2=c2a^2 + b^2 = c^2

SOHCAHTOA

sin⁡θ=OH,cos⁡θ=AH,tan⁡θ=OA\sin\theta = \frac{O}{H},\quad \cos\theta = \frac{A}{H},\quad \tan\theta = \frac{O}{A}

Sine rule

asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}

Cosine rule

a2=b2+c2−2bccos⁡Aa^2 = b^2 + c^2 - 2bc\cos A

Area of triangle (trig)

Area=12absin⁡C\text{Area} = \frac{1}{2}ab\sin C

Statistics

Mean

xˉ=∑xn\bar{x} = \frac{\sum x}{n}

Mean from frequency table

xˉ=∑fx∑f\bar{x} = \frac{\sum fx}{\sum f}

Standard deviation (population)

σ=∑(x−xˉ)2n\sigma = \sqrt{\frac{\sum(x-\bar{x})^2}{n}}

Probability

P(A)=favourabletotalP(A) = \frac{\text{favourable}}{\text{total}}

IQR

IQR=Q3−Q1IQR = Q_3 - Q_1

Angles & Polygons

Interior angle sum of polygon

S=(n−2)×180°S = (n-2) \times 180°

Interior angle of regular polygon

angle=(n−2)×180°n\text{angle} = \frac{(n-2) \times 180°}{n}

Exterior angle of regular polygon

exterior=360°n\text{exterior} = \frac{360°}{n}

Proportion & Ratios

Direct proportion

y=kxy = kx

Inverse proportion

y=kxy = \frac{k}{x}

Percentage change

% change=changeoriginal×100\% \text{ change} = \frac{\text{change}}{\text{original}} \times 100

Frequently asked questions

Which formulas are given in the GCSE maths exam?+

In most GCSE papers, some formulas are provided (like the quadratic formula in some papers), but many are not — you must memorise them.

What are the most important GCSE maths formulas?+

Pythagoras theorem, quadratic formula, area formulas, trigonometric ratios, and the standard form for straight lines are among the most tested.

How do I memorise maths formulas?+

Write them out repeatedly, use flashcards, and apply them in practice questions. Using them in context is the most effective memorisation technique.

Are A-Level formulas different from GCSE?+

Yes — A-Level introduces many additional formulas. A-Level students receive a formula booklet in most exams.

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