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GCSE Maths formulae, given vs memorise.

For 2026 exams you get a formulae sheet inside every paper. Here is exactly what is on it, and the 36 formulae it does not give you that you still have to know by heart.

Given to you in the 2026 exam

These 13 formulae are printed on the sheet inside every paper. Ofqual sets the sheet, so AQA, Edexcel and OCR all use the same one (OCR sometimes prints a formula next to the question instead). Foundation tier gets everything without a Higher tag. Boards release a fresh sheet each year, so revise from the copy your school gives you.

Perimeter, area and volume

arealength

Area of a trapezium

12(a+b)h\tfrac{1}{2}(a + b)h

a and b are the parallel sides, h is the perpendicular distance between them.

Volume of a prism

area of cross-section×length\text{area of cross-section} \times \text{length}

Works for any prism, a cylinder included.

Circumference of a circle

2πr=πd2\pi r = \pi d

Area of a circle

πr2\pi r^{2}

Pythagoras and trigonometry

abcAABCcab

Pythagoras' theorem

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

c is the hypotenuse, the side opposite the right angle.

Trigonometric ratios

sin⁡A=opphypcos⁡A=adjhyptan⁡A=oppadj\sin A = \dfrac{\text{opp}}{\text{hyp}} \qquad \cos A = \dfrac{\text{adj}}{\text{hyp}} \qquad \tan A = \dfrac{\text{opp}}{\text{adj}}

Right-angled triangles only. SOH CAH TOA.

Sine rule

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

Any triangle.

Cosine rule

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

Any triangle.

Area of a triangle

Higher
12 absin⁡C\tfrac{1}{2}\,ab\sin C

When you know two sides and the angle between them.

Quadratic formula

Quadratic formula

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

Solves ax² + bx + c = 0.

Compound interest

Compound interest

total=P(1+r100)n\text{total} = P\left(1 + \dfrac{r}{100}\right)^{n}

P is the starting amount, r the percentage rate per period, n the number of periods.

Probability

Addition rule

P(A or B)=P(A)+P(B)−P(A and B)P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)

Multiplication rule

Higher
P(A and B)=P(A∣B) P(B)P(A \text{ and } B) = P(A \mid B)\,P(B)

Not on the sheet, learn these

The sheet is short on purpose. Everything below still has to come from memory, and these are the ones students most often lose marks for forgetting.

Area and perimeter

Area of a rectangle

length×width\text{length} \times \text{width}

Area of a triangle

12×base×height\tfrac{1}{2} \times \text{base} \times \text{height}

Area of a parallelogram

base×height\text{base} \times \text{height}

Arc length

θ360×πd\dfrac{\theta}{360} \times \pi d

The fraction θ ÷ 360 of the full circumference.

Area of a sector

θ360×πr2\dfrac{\theta}{360} \times \pi r^{2}

The fraction θ ÷ 360 of the full area.

Volume and surface area

Volume of a cuboid

length×width×height\text{length} \times \text{width} \times \text{height}
Lesson

Volume of a cylinder

πr2h\pi r^{2} h
Lesson

Surface area of a cylinder

2πr2+2πrh2\pi r^{2} + 2\pi r h

Two circular ends plus the curved side.

Lesson

Volume of a sphere

Higher
43πr3\tfrac{4}{3}\pi r^{3}
Lesson

Surface area of a sphere

Higher
4πr24\pi r^{2}
Lesson

Volume of a cone

Higher
13πr2h\tfrac{1}{3}\pi r^{2} h
Lesson

Curved surface area of a cone

Higher
πrl\pi r l

l is the slant height, not the vertical height.

Lesson

Volume of a pyramid

Higher
13×base area×height\tfrac{1}{3} \times \text{base area} \times \text{height}
Lesson

Angles

Sum of interior angles of a polygon

(n−2)×180∘(n - 2) \times 180^{\circ}

n is the number of sides.

Lesson

Exterior angle of a regular polygon

360∘n\dfrac{360^{\circ}}{n}

Interior angle and exterior angle add to 180°.

Lesson

Straight-line graphs

Equation of a straight line

y=mx+cy = mx + c

m is the gradient, c is where it crosses the y-axis.

Lesson

Gradient

change in ychange in x\dfrac{\text{change in } y}{\text{change in } x}
Lesson

Midpoint of a line segment

(x1+x22, y1+y22)\left(\dfrac{x_{1} + x_{2}}{2},\ \dfrac{y_{1} + y_{2}}{2}\right)
Lesson

Compound measures

Speed

distancetime\dfrac{\text{distance}}{\text{time}}
Lesson

Density

massvolume\dfrac{\text{mass}}{\text{volume}}
Lesson

Pressure

forcearea\dfrac{\text{force}}{\text{area}}
Lesson

Percentages and growth

Percentage change

changeoriginal amount×100\dfrac{\text{change}}{\text{original amount}} \times 100
Lesson

Depreciation

total=P(1−r100)n\text{total} = P\left(1 - \dfrac{r}{100}\right)^{n}

The compound interest formula with a minus, for something losing value.

Lesson

Algebra (Higher)

Difference of two squares

Higher
a2−b2=(a+b)(a−b)a^{2} - b^{2} = (a + b)(a - b)
Lesson

Equation of a circle centred on the origin

Higher
x2+y2=r2x^{2} + y^{2} = r^{2}

Trigonometry (Higher)

sin 30° = cos 60°

Higher
12\tfrac{1}{2}
Lesson

sin 45° = cos 45°

Higher
12\dfrac{1}{\sqrt{2}}
Lesson

sin 60° = cos 30°

Higher
32\dfrac{\sqrt{3}}{2}
Lesson

tan 30°

Higher
13\dfrac{1}{\sqrt{3}}
Lesson

tan 45°

Higher
11
Lesson

tan 60°

Higher
3\sqrt{3}
Lesson

Probability and statistics

Probability of an outcome

favourable outcomestotal outcomes\dfrac{\text{favourable outcomes}}{\text{total outcomes}}
Lesson

Expected number of occurrences

probability×number of trials\text{probability} \times \text{number of trials}
Lesson

Probability of two independent events

P(A and B)=P(A)×P(B)P(A \text{ and } B) = P(A) \times P(B)
Lesson

Mean

sum of the valueshow many values\dfrac{\text{sum of the values}}{\text{how many values}}
Lesson

Mean from a frequency table

∑fx∑f\dfrac{\sum fx}{\sum f}

Multiply each value by its frequency, add those up, divide by the total frequency.

Lesson

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