Maths Formulas for Class 10 — Complete Chapter-Wise List
All Maths formulas for Class 10 CBSE and ICSE — chapter-wise covering Real Numbers, Trigonometry, Geometry, Mensuration, and Statistics.
Class 10 Maths has approximately 80–100 key formulas across 15 chapters. This complete chapter-wise list covers every formula you need for CBSE and ICSE board exams 2026. Bookmark this page and revise daily during your preparation.
Chapter 1: Real Numbers
| Formula | Description |
|---|---|
| HCF × LCM = Product of two numbers | For any two positive integers a and b |
| HCF(a,b) = a × b ÷ LCM(a,b) | To find HCF when LCM is known |
| Euclid's Division Lemma: a = bq + r | Where 0 ≤ r < b |
Chapter 2: Polynomials
| Formula | For Polynomial ax² + bx + c |
|---|---|
| Sum of zeroes (α + β) | = −b/a |
| Product of zeroes (αβ) | = c/a |
| Polynomial from zeroes | x² − (α + β)x + αβ |
Chapter 3: Pair of Linear Equations
| Condition | Formula (for a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0) |
|---|---|
| Unique solution (intersecting) | a₁/a₂ ≠ b₁/b₂ |
| No solution (parallel) | a₁/a₂ = b₁/b₂ ≠ c₁/c₂ |
| Infinite solutions (coincident) | a₁/a₂ = b₁/b₂ = c₁/c₂ |
Chapter 4: Quadratic Equations
| Formula | Description |
|---|---|
| Quadratic formula: x = (−b ± √(b²−4ac)) / 2a | Roots of ax² + bx + c = 0 |
| Discriminant: D = b² − 4ac | Determines nature of roots |
| D > 0: Two distinct real roots | Roots are real and different |
| D = 0: Two equal real roots | Both roots are −b/2a |
| D < 0: No real roots | Roots are imaginary |
| Sum of roots = −b/a | Same as polynomial relationship |
| Product of roots = c/a | Same as polynomial relationship |
Chapter 5: Arithmetic Progressions (AP)
| Formula | Description |
|---|---|
| nth term: aₙ = a + (n−1)d | a = first term, d = common difference |
| Sum of n terms: Sₙ = n/2 [2a + (n−1)d] | When first term and d are known |
| Sum of n terms: Sₙ = n/2 [a + l] | When first term (a) and last term (l) are known |
| Common difference: d = aₙ − aₙ₋₁ | Difference between consecutive terms |
| Number of terms: n = (l − a)/d + 1 | When first, last term and d are known |
Practise with these formulas
Super Tutor has chapter-wise practice problems for Class 10 Maths — apply every formula with instant feedback and step-by-step solutions.
Practise Maths — FreeChapter 6: Triangles (Similarity)
| Formula / Theorem | Description |
|---|---|
| BPT (Basic Proportionality): DE ∥ BC → AD/DB = AE/EC | Thales theorem for parallel line in triangle |
| AAA / AA similarity | If angles are equal, triangles are similar |
| SSS similarity: sides in proportion | All sides in same ratio → similar triangles |
| SAS similarity | One angle equal + adjacent sides proportional |
| Area ratio = (side ratio)² | For similar triangles |
| Pythagoras: a² + b² = c² | For right-angled triangle (c = hypotenuse) |
Chapter 7: Coordinate Geometry
| Formula | Expression |
|---|---|
| Distance formula | d = √[(x₂−x₁)² + (y₂−y₁)²] |
| Section formula (internal) | P = ((m₁x₂ + m₂x₁)/(m₁+m₂), (m₁y₂ + m₂y₁)/(m₁+m₂)) |
| Midpoint formula | M = ((x₁+x₂)/2, (y₁+y₂)/2) |
| Area of triangle | = ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| |
| Collinearity condition | Area of triangle = 0 |
Chapter 8: Introduction to Trigonometry
| Ratio | Formula |
|---|---|
| sin θ | = Opposite / Hypotenuse |
| cos θ | = Adjacent / Hypotenuse |
| tan θ | = Opposite / Adjacent = sin θ / cos θ |
| cosec θ | = 1 / sin θ |
| sec θ | = 1 / cos θ |
| cot θ | = 1 / tan θ = cos θ / sin θ |
Standard Angle Values
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | undefined |
Trigonometric Identities
| Identity |
|---|
| sin²θ + cos²θ = 1 |
| 1 + tan²θ = sec²θ |
| 1 + cot²θ = cosec²θ |
| sin(90° − θ) = cos θ |
| cos(90° − θ) = sin θ |
| tan(90° − θ) = cot θ |
Chapter 10: Circles
| Formula / Property | Description |
|---|---|
| Tangent ⊥ Radius | Tangent at any point is perpendicular to radius |
| Tangent lengths from external point are equal | PA = PB (tangents from P) |
| Length of tangent = √(d² − r²) | d = distance from centre to external point, r = radius |
Chapters 12–13: Surface Area & Volume
| Shape | Surface Area | Volume |
|---|---|---|
| Cube (side a) | 6a² | a³ |
| Cuboid (l × b × h) | 2(lb + bh + hl) | lbh |
| Cylinder (r, h) | CSA: 2πrh, TSA: 2πr(r+h) | πr²h |
| Cone (r, h, l) | CSA: πrl, TSA: πr(r+l) | ⅓πr²h |
| Sphere (r) | 4πr² | ⁴⁄₃πr³ |
| Hemisphere (r) | CSA: 2πr², TSA: 3πr² | ⅔πr³ |
| Frustum (r₁, r₂, h, l) | CSA: π(r₁+r₂)l, TSA: π(r₁+r₂)l + πr₁² + πr₂² | ⅓πh(r₁² + r₂² + r₁r₂) |
Slant height of cone: l = √(r² + h²). Slant height of frustum: l = √(h² + (r₁ − r₂)²)
Chapter 14: Statistics
| Measure | Formula (Grouped Data) |
|---|---|
| Mean (Direct) | x̄ = Σfᵢxᵢ / Σfᵢ |
| Mean (Assumed Mean) | x̄ = a + Σfᵢdᵢ / Σfᵢ (where dᵢ = xᵢ − a) |
| Mean (Step Deviation) | x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h (where uᵢ = dᵢ/h) |
| Median | l + [(n/2 − cf) / f] × h |
| Mode | l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h |
| Empirical relationship | 3 Median = Mode + 2 Mean |
Chapter 15: Probability
| Formula | Description |
|---|---|
| P(E) = Favourable outcomes / Total outcomes | Basic probability formula |
| P(E) + P(not E) = 1 | Complementary events |
| 0 ≤ P(E) ≤ 1 | Probability range |
| P(certain event) = 1 | Event that always happens |
| P(impossible event) = 0 | Event that never happens |
Formulas listed are based on the CBSE Class 10 syllabus 2025–2026. ICSE students should note that some additional formulas may be required (e.g., section formula for external division). Verify with your specific board syllabus. Last updated: February 2026.
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Try Super Tutor — It's FreeFrequently Asked Questions
How many formulas are there in Class 10 Maths?
There are approximately 80–100 key formulas across all chapters in Class 10 Maths. The most formula-heavy chapters are Trigonometry (~25 formulas), Mensuration (~20 formulas), and Coordinate Geometry (~10 formulas). You do not need to memorise all of them — understanding the derivation helps you recall them during exams.
Which chapter has the most formulas in Class 10 Maths?
Trigonometry has the most formulas — trigonometric ratios, identities, complementary angle relations, and values of standard angles. Mensuration (Surface Area and Volume) is a close second with formulas for every shape. These two chapters combined carry 25–30 marks in the board exam.
How to memorise Maths formulas for board exams?
Best techniques: (1) Write each formula 5 times daily for a week, (2) Create a formula sheet and revise it every morning, (3) Solve 5 problems per formula — application helps retention better than rote learning, (4) Use mnemonics for trigonometric values (e.g., 'Some People Have Curly Brown Hair Through Proper Brushing' for sin/cos/tan ratios), (5) Practise deriving formulas — if you understand the derivation, you can reconstruct forgotten formulas during the exam.
Are formulas given in the CBSE board exam?
No, CBSE does not provide a formula sheet during the board exam. You must memorise all required formulas. However, some formulas are given as part of the question (e.g., 'using the quadratic formula, solve...'). For mensuration, formulas for uncommon shapes may be provided in the question. But standard formulas for area, volume, trigonometry, and coordinate geometry must be memorised.
Which formulas are most important for scoring in Class 10 Maths?
Top 10 most-tested formulas: (1) Quadratic formula, (2) Distance formula, (3) Section formula, (4) Trigonometric identities (sin²θ + cos²θ = 1), (5) Area of triangle using coordinates, (6) Surface area and volume of cylinder/cone/sphere, (7) AP formulas (nth term and sum), (8) HCF × LCM = Product of numbers, (9) Mean/Median/Mode formulas for grouped data, (10) Probability = favourable/total outcomes.