Show WorkingRectangle
Area = length × width
Perimeter is the distance all the way round: add up every side.
Both tiersRevision guideFoundation and Higher
GCSE maths formulas: know them, and know when to use them
For GCSE maths exams in 2026 and 2027 you're given a formulae sheet. That helps, but the sheet won't tell you which formula a question needs, or how to use it. Here are the formulas you'll use most, with what each one is for.
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About the formulae sheet. GCSE maths papers in 2025, 2026 and 2027, including the November resits, come with a formulae sheet, and Foundation and Higher get different sheets. Plans for later years may change. Download your exam board's sheet and get to know it before the exam.
01 / Area and perimeterBoth tiers
Area and perimeter
Triangle
Area = ½ × base × height
The height must be at right angles to the base, not the sloping side.
Both tiersParallelogram
Area = base × height
Again, the perpendicular height, not the slanted edge.
Both tiersTrapezium
Area = ½(a + b)h
a and b are the parallel sides, h is the height between them.
Both tiersCircle
Circumference = πd = 2πr
Area = πr2
Use the radius for area. If you're given the diameter, halve it first.
Both tiersArcs and sectors
Arc length = θ⁄360 × 2πr
Sector area = θ⁄360 × πr2
θ is the angle at the centre. It's just a fraction of the whole circle.
Both tiers02 / Volume and surface areaBoth tiers
Volume and surface area
Prism
Volume = area of cross-section × length
Works for any shape with the same cross-section all the way through, including cuboids.
Both tiersCylinder
Volume = πr2h
Curved surface = 2πrh
It's a prism with a circle for its cross-section.
Both tiersPyramid and cone
Volume = ⅓ × base area × height
Cone: ⅓πr2h
A cone's curved surface is πrl, where l is the slant height.
Both tiersSphere
Volume = 4⁄3πr3
Surface area = 4πr2
Hemisphere? Halve the volume, and remember the flat circle on top for surface area.
Both tiers03 / TrianglesRight-angled and beyond
Pythagoras and trigonometry
Pythagoras' theorem
a2 + b2 = c2
Right-angled triangles only. c is the hypotenuse, the longest side, opposite the right angle.
Both tiersTrigonometry (SOHCAHTOA)
sin x = opp⁄hyp · cos x = adj⁄hyp · tan x = opp⁄adj
Use it when a right-angled triangle question involves an angle.
Both tiersSine rule
a⁄sin A = b⁄sin B = c⁄sin C
For triangles without a right angle, when you know a side and its opposite angle.
Higher onlyCosine rule
a2 = b2 + c2 − 2bc cos A
When you know two sides and the angle between them, or all three sides.
Higher onlyArea of any triangle
Area = ½ab sin C
C is the angle between sides a and b.
Higher only04 / AlgebraGraphs and equations
Algebra and graphs
Straight line
y = mx + c
m is the gradient and c is where the line crosses the y-axis.
Both tiersGradient
Gradient = change in y⁄change in x
Up is positive, down is negative. Read it from two clear points on the line.
Both tiersQuadratic formula
x = (−b ± √(b2 − 4ac)) ÷ 2a
For ax2 + bx + c = 0 when it won't factorise neatly.
Higher onlyCircle on a graph
x2 + y2 = r2
A circle centred at the origin with radius r.
Higher only05 / Money, rates and probabilityBoth tiers
Money, rates and probability
Percentage change
Change ÷ original × 100
Always divide by the original amount, not the new one. Practise it in percentages.
Both tiersSimple and compound interest
Simple: P × r⁄100 × n
Compound: P(1 + r⁄100)n
P is the starting amount, r the rate in %, n the number of years.
Both tiersSpeed, density, pressure
Speed = distance ÷ time
Density = mass ÷ volume
Pressure = force ÷ area
Check the units match before you divide.
Both tiersProbability
P(not A) = 1 − P(A)
Independent: P(A and B) = P(A) × P(B)
All the probabilities of every possible outcome add up to 1.
Both tiers06 / Make them stickNot flashcards alone
How to learn formulas so you can use them
Use them in questions
Reciting a formula isn't the hard part. Choosing it is. Do questions where you have to pick the right one.
Spot the clue words
"Hypotenuse" or a missing side in a right-angled triangle points to Pythagoras. An angle in a right-angled triangle points to trigonometry.
Write them from memory
Once a week, write out every formula you can remember, then check. The gaps tell you what to practise.
07 / QuestionsAll questions
Formulas, answered
Do you get a formula sheet in GCSE maths?
For exams in 2025, 2026 and 2027, yes. GCSE maths papers in those years, including the November resits, come with a formulae sheet, and Foundation and Higher have different sheets. Plans for later years may change, so check with your exam board.
Do I still need to learn the formulas?
It still helps a lot. The sheet gives you the formula, but not which one a question needs or how to use it. Knowing them well also saves time in the exam.
Which GCSE maths formulas are Higher only?
The sine rule, the cosine rule, the area of a triangle using ½ab sin C, the quadratic formula and the equation of a circle are Higher only. The other formulas on our formulas page are on both tiers.
Know it. Use it.
Practise with fresh questions every day.
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