The GCSE Maths Formula Sheet Guide

Yes, if you sit your exams in England. The Department for Education confirmed formulae sheets for GCSE Maths exams in 2025, 2026 and 2027. In May 2026 Ofqual confirmed that they will continue from 2028 "for the lifetime of the current qualifications, including any resit opportunities".

Each board prints its own sheet, but the content is the same: at each tier, AQA, Edexcel, OCR and Eduqas give you exactly the same formulae. Only the wording and the layout differ.

• AQA: a Formulae Sheet insert with every paper.
• Pearson Edexcel: an Exam Aid with every paper.
• OCR: a Formulae Sheet insert for each tier.
• Eduqas: an Additional Formulae sheet, printed inside the question paper from summer 2026, plus Eduqas's own formula list on page 2 of every paper.

In Wales, WJEC works differently. Formula lists are printed in some papers, and what they contain depends on the unit and tier. The WJEC section below explains it.

Every GCSE formula falls into one of four groups, and the group can change with your tier.

• On the sheet: printed on the formula sheet you get with every paper.
• Given in the question: not on the sheet, but printed inside any question that needs it.
• Memorise: tested at your tier, and nobody gives it to you.
• Not on spec: not tested at your tier, so there is nothing to learn.

The last two are not the same thing. A formula your paper will never ask about is not one to memorise, and time spent learning it is time taken from something that will be tested.

Eduqas prints the cone and sphere formulae in its own formula list on page 2 of every paper rather than inside questions. The rows marked 'Depends on board' are explained under Formulae Given Inside the Question.

The Foundation sheet has eight entries. The Higher sheet has the same eight plus five more. The wording below follows AQA's sheet; the other boards say the same thing in slightly different words.

Foundation and Higher

1. Area of a trapezium: $\frac{1}{2}(a + b)h$, where $a$ and $b$ are the parallel sides and $h$ is the perpendicular distance between them.
2. Volume of a prism: area of cross-section $\times$ length.
3. Circumference of a circle: $2\pi r = \pi d$.
4. Area of a circle: $\pi r^2$.
5. Pythagoras' theorem: $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.
6. Trigonometric ratios: $\sin A = \frac{a}{c}$, $\cos A = \frac{b}{c}$, $\tan A = \frac{a}{b}$, in a right-angled triangle with hypotenuse $c$, side $a$ opposite angle $A$ and side $b$ next to it.
7. Compound interest: total accrued $= P\left(1 + \frac{r}{100}\right)^n$, where $P$ is the principal amount, $r$ is the interest rate over a given period and $n$ is the number of times the interest is compounded.
8. Probability: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$.

Higher only

9. Quadratic formula: the solutions of $ax^2 + bx + c = 0$, where $a \neq 0$, are $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
10. Sine rule: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$.
11. Cosine rule: $a^2 = b^2 + c^2 - 2bc\cos A$.
12. Area of a triangle: $\frac{1}{2}ab\sin C$.
13. Conditional probability: $P(A \text{ and } B) = P(A \text{ given } B)P(B)$.

Some formulae are not on the sheet but are printed inside any question that needs them. This is where the boards differ.

• Pyramid: Edexcel has given it in relevant questions since its January 2025 notice, and OCR gives it too. AQA and Eduqas have not said they will, so learn it. Eduqas's summer 2026 examiners' report noted candidates "who could not remember the formula for the volume of a pyramid".
• Kinematics: Pearson says knowledge of the suvat formulae "is not part of our specification", so Edexcel questions will not require them.
• Pressure: OCR says it will give the formula, but its November 2024 Foundation Paper 1 asked for a pressure without printing it. Edexcel and Eduqas have printed it in recent questions without promising to. Learn it whatever your board.

Every England board tests these at both Foundation and Higher, and none of them is on the sheet or given in the question. This is where most formula marks are lost.

Area and perimeter

1. Area of a rectangle: length $\times$ width.
2. Area of a parallelogram: base $\times$ perpendicular height.
3. Area of a triangle: $\frac{1}{2} \times$ base $\times$ perpendicular height.
4. Arc length: $\frac{\theta}{360} \times 2\pi r$.
5. Area of a sector: $\frac{\theta}{360} \times \pi r^2$.

Volume and surface area

6. Volume of a cuboid: length $\times$ width $\times$ height.
7. Surface area of a cuboid: $2(lw + lh + wh)$.
8. Volume of a cylinder: $\pi r^2 h$.
9. Curved surface area of a cylinder: $2\pi rh$.
10. Total surface area of a cylinder: $2\pi r^2 + 2\pi rh$.

Algebra

11. Difference of two squares: $a^2 - b^2 = (a + b)(a - b)$.
12. nth term of a linear sequence: $dn + (a - d)$, where $a$ is the first term and $d$ is the common difference.
13. Direct proportion: $y = kx$.
14. Inverse proportion: $y = \frac{k}{x}$.

Foundation students need to understand and use $y = kx$ and $y = \frac{k}{x}$. Finding $k$ and writing the equation yourself is Higher.

Coordinate geometry

15. Gradient: $m = \frac{y_2 - y_1}{x_2 - x_1}$.
16. Equation of a straight line: $y = mx + c$, where $m$ is the gradient and $c$ is the $y$-intercept.
17. Midpoint: $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.
18. Distance between two points: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

Number and finance

19. Percentage change: $\frac{\text{new} - \text{original}}{\text{original}} \times 100$.
20. One quantity as a percentage of another: $\frac{A}{B} \times 100$.
21. Reverse percentage: original amount $= \frac{\text{new amount}}{\text{multiplier}}$; after a 15% increase, divide by $1.15$.
22. Simple interest: $I = \frac{P \times r \times n}{100}$, for $r$% a year over $n$ years.
23. Depreciation: $P\left(1 - \frac{r}{100}\right)^n$.

Statistics

24. Mean: $\frac{\text{sum of the values}}{\text{number of values}}$.
25. Mean from a frequency table: $\frac{\sum fx}{\sum f}$.
26. Estimated mean from grouped data: $\frac{\sum (f \times \text{midpoint})}{\sum f}$.
27. Median: the $\frac{n + 1}{2}$th value when the data are in order.
28. Range: largest value $-$ smallest value.
29. Pie chart angle: $\frac{\text{frequency}}{\text{total frequency}} \times 360^\circ$.

Probability

30. Probability of an event: $\frac{\text{number of favourable outcomes}}{\text{total number of equally likely outcomes}}$.
31. Relative frequency: $\frac{\text{number of times the outcome happens}}{\text{total number of trials}}$.
32. Expected frequency: $P(A) \times$ number of trials.
33. Probability of an event not happening: $P(\text{not } A) = 1 - P(A)$.
34. Mutually exclusive events: $P(A \text{ or } B) = P(A) + P(B)$.
35. Independent events: $P(A \text{ and } B) = P(A) \times P(B)$.

Compound measures

36. Speed: $\frac{\text{distance}}{\text{time}}$.
37. Density: $\frac{\text{mass}}{\text{volume}}$.
38. Rate of pay: $\frac{\text{pay}}{\text{hours worked}}$.
39. Unit price: $\frac{\text{total cost}}{\text{number of units}}$.

Exact trigonometric values

Every England board expects these at both tiers, so learn them for the non-calculator paper.

Foundation papers do not test these. If you sit Higher, learn them as well.

1. Area of a segment: area of the sector $-$ area of the triangle, $\frac{\theta}{360}\pi r^2 - \frac{1}{2}r^2\sin\theta$.
2. Similar shapes: if lengths are multiplied by $k$, areas are multiplied by $k^2$ and volumes by $k^3$.
3. Completing the square: $x^2 + bx + c = \left(x + \frac{b}{2}\right)^2 - \left(\frac{b}{2}\right)^2 + c$.
4. nth term of a quadratic sequence: $an^2 + bn + c$, where $a$ is half the second difference.
5. Perpendicular lines: $m_1 \times m_2 = -1$.
6. Equation of a circle with centre at the origin: $x^2 + y^2 = r^2$.
7. Interquartile range: upper quartile $-$ lower quartile.
8. Frequency density: $\frac{\text{frequency}}{\text{class width}}$.
9. Product rule for counting: if one choice can be made in $m$ ways and a second in $n$ ways, together they can be made in $m \times n$ ways.

AQA (8300)

AQA gives you a Formulae Sheet insert with every paper; the current sheets are marked "For exams in 2027 only". AQA's specification says the cone, sphere and kinematics formulae "will be given in the exam in the relevant question". AQA has not said it will give the volume of a pyramid or the pressure formula, so learn both.

Pearson Edexcel (1MA1)

Edexcel calls its sheet an Exam Aid, and a copy comes with every paper. The cone and sphere formulae are given in questions, and since January 2025 so is the volume of a pyramid. Pearson says the suvat formulae are not part of its specification. Pearson's newest Exam Aid is for the 2026 exams; its content has not changed since 2024.

OCR (J560)

OCR gives you a Formulae Sheet insert for your tier; the current sheets are for June and November 2027. OCR says the formulae for cones, spheres, pyramids, pressure and kinematics will be given inside the questions that need them.

Eduqas (C300)

Eduqas's Additional Formulae sheet holds the same formulae as the other England boards. From summer 2026 it is printed inside the question paper rather than handed out separately. Every Eduqas paper also has its own formula list on page 2, with the cone, sphere and kinematics formulae. The volume of a pyramid is not on either, so learn it.

The England formula sheet does not apply in Wales. WJEC prints a formula list inside some papers instead, and what it holds depends on your unit and tier.

GCSE Mathematics and Numeracy (Double Award), first awarded November 2026

• Unit 1 (calculator, financial mathematics): the Foundation list gives the area of a trapezium and the volume of an object with a uniform cross-section. The Higher list adds the volume and surface area of a sphere, the volume and curved surface area of a cone, and the Annual Equivalent Rate, $\text{AER} = \left(1 + \frac{i}{n}\right)^n - 1$.
• Unit 2 (non-calculator): no formula list.
• Unit 3 (calculator): the Foundation list gives the trapezium and the uniform cross-section. The Higher list adds the sphere and cone formulae, the sine rule, the cosine rule, $\frac{1}{2}ab\sin C$ and the quadratic formula.

That means Welsh students must memorise several formulae that students in England find on their sheet: the circumference and area of a circle (Units 1 and 3), Pythagoras' theorem (Unit 3), the trigonometric ratios (Unit 3, Higher) and compound interest (Unit 1).

Legacy GCSE Mathematics and Mathematics–Numeracy (resits until June 2027)

Every paper prints a formula list. Foundation gives the area of a trapezium. Intermediate adds the volume of a prism. Higher gives eleven formulae, including the sphere and cone formulae, the sine and cosine rules, the quadratic formula and the Annual Equivalent Rate.

1. Revise with your sheet, not without it. Do past papers with your board's sheet beside you, so you know where each formula sits before the exam.
2. Spend your memory on what is not on it. The Memorise list above is where formula marks are lost, not the sheet.
3. Match the letters before you substitute. The sheet labels its triangles $a$, $b$, $c$ and $A$, $B$, $C$. Label your triangle the same way first.
4. Use a formula when a question gives you one. A formula printed inside a question is there because the question needs it.

• I know which tier I am sitting and which sheet I will get.
• I can write every formula on the Memorise list from memory.
• I can turn the compound interest formula into the depreciation formula.
• I can rebuild the volume of a cylinder from the prism formula.
• I know the exact values of sin and cos for $0^\circ$, $30^\circ$, $45^\circ$, $60^\circ$ and $90^\circ$, and of tan for $0^\circ$, $30^\circ$, $45^\circ$ and $60^\circ$.
• Higher only: I can write the nine Higher-only formulae from memory.
• I have done at least one full paper with my board's formula sheet beside me.

“

The formula sheet gives you the formulae. It does not tell you when to use them, and it does not give you the ones that cost the most marks.

Sir Faraz Hassan

• Ofqual: decisions on GCSE maths, physics and combined science assessment in 2025, 2026 and 2027
• Ofqual: decisions on formulae sheets from 2028 (May 2026)
• AQA: Formulae Sheet, Foundation, 2027
• AQA: Formulae Sheet, Higher, 2027
• Pearson: Foundation tier Exam Aid, 2026
• Pearson: Higher tier Exam Aid, 2026
• Pearson: Notice "Important information on the provision of formulae in GCSE Mathematics"
• OCR: Foundation Tier Formulae Sheet, 2027
• OCR: Higher Tier Formulae Sheet, 2027
• OCR: "Formulae sheet top tips", GCSE (9-1) Mathematics
• Eduqas: Additional Formulae, Foundation Tier
• Eduqas: Additional Formulae, Higher Tier
• WJEC: GCSE Mathematics and Numeracy (Double Award) 3320, Specification