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Class 10 Maths Formulas: Chapter-Wise List (2026-27)

This is a one-page list of class 10 maths formulas for the 2026-27 syllabus, chapter by chapter. Read it after you have studied a chapter, not instead of studying it: a formula you do not understand is easy to misuse. Each chapter is explained in full in our Mathematics Class 10 guide.

Class 10 maths formulas by chapter

1. Real Numbers

  • Euclid’s division lemma: a = bq + r, where 0 ≤ r < b
  • For two positive integers: HCF × LCM = product of the two numbers
  • √p is irrational for every prime p

2. Polynomials

  • Quadratic ax² + bx + c: sum of zeros = −b/a
  • Product of zeros = c/a
  • A quadratic with zeros α and β: x² − (α + β)x + αβ

3. Pair of Linear Equations in Two Variables

  • a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
  • Unique solution: a1/a2 ≠ b1/b2
  • Infinitely many solutions: a1/a2 = b1/b2 = c1/c2
  • No solution: a1/a2 = b1/b2 ≠ c1/c2

4. Quadratic Equations

  • ax² + bx + c = 0, a ≠ 0
  • x = [−b ± √(b² − 4ac)] / 2a
  • Discriminant D = b² − 4ac
  • D > 0: two distinct real roots; D = 0: two equal real roots; D < 0: no real roots

5. Arithmetic Progressions

  • nth term: an = a + (n − 1)d
  • Sum of n terms: Sn = (n/2)[2a + (n − 1)d]
  • Sum using the last term: Sn = (n/2)(a + l)
  • an = Sn − Sn−1

6. Triangles

  • Basic proportionality theorem: if DE ∥ BC in triangle ABC, then AD/DB = AE/EC
  • Similar triangles: corresponding sides are in the same ratio
  • Ratio of areas of similar triangles = (ratio of corresponding sides)²
  • Pythagoras: (hypotenuse)² = (base)² + (perpendicular)²

7. Coordinate Geometry

  • Distance between (x1, y1) and (x2, y2) = √[(x2 − x1)² + (y2 − y1)²]
  • Distance of (x, y) from the origin = √(x² + y²)
  • Section formula (internal, ratio m : n): [(mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)]
  • Mid-point: [(x1 + x2)/2, (y1 + y2)/2]

8. Introduction to Trigonometry

  • sin θ = perpendicular/hypotenuse; cos θ = base/hypotenuse; tan θ = perpendicular/base
  • cosec θ = 1/sin θ; sec θ = 1/cos θ; cot θ = 1/tan θ
  • tan θ = sin θ/cos θ
  • sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ
  • sin(90° − θ) = cos θ; cos(90° − θ) = sin θ; tan(90° − θ) = cot θ

8. Standard angle values

  • sin: 0, 1/2, 1/√2, √3/2, 1 at 0°, 30°, 45°, 60°, 90°
  • cos: 1, √3/2, 1/√2, 1/2, 0 at the same angles
  • tan: 0, 1/√3, 1, √3, not defined at the same angles

9. Some Applications of Trigonometry

  • tan θ = height / horizontal distance
  • Angle of elevation = angle of depression (alternate angles) for the same line of sight
  • Draw a clear figure and mark the right angle before choosing a ratio

10. Circles

  • The tangent at any point of a circle is perpendicular to the radius through the point of contact
  • The lengths of the two tangents drawn from an external point to a circle are equal

11. Areas Related to Circles

  • Circumference = 2πr; area = πr²
  • Length of an arc = (θ/360) × 2πr
  • Area of a sector = (θ/360) × πr²
  • Area of a segment = area of sector − area of triangle

12. Surface Areas and Volumes

  • Cuboid: volume = l × b × h; total surface area = 2(lb + bh + hl)
  • Cube: volume = a³; total surface area = 6a²
  • Cylinder: volume = πr²h; curved surface area = 2πrh; total surface area = 2πr(r + h)
  • Cone: slant height l = √(r² + h²); volume = (1/3)πr²h; curved surface area = πrl; total surface area = πr(r + l)
  • Sphere: surface area = 4πr²; volume = (4/3)πr³
  • Hemisphere: curved surface area = 2πr²; total surface area = 3πr²; volume = (2/3)πr³

13. Statistics

  • Mean (direct): x = Σfixi / Σfi
  • Assumed mean: x = a + Σfidi / Σfi
  • Step deviation: x = a + h × Σfiui / Σfi
  • Mode = l + [(f1 − f0) / (2f1 − f0 − f2)] × h
  • Median = l + [(n/2 − cf) / f] × h
  • Empirical relation: 3 median = mode + 2 mean

14. Probability

  • P(E) = number of favourable outcomes / total number of outcomes
  • 0 ≤ P(E) ≤ 1; P(E) + P(not E) = 1
  • The sum of the probabilities of all elementary events of an experiment is 1

The rationalised syllabus does not include the area of a triangle in coordinate geometry or the frustum of a cone, so they are not listed. Always check the current syllabus on the CBSE Class 10 syllabus page.

Print this as a class 10 formula sheet and keep it above your desk. Use it with your class 10 maths revision notes in the last weeks, and mark the class 10 maths important formulas you keep forgetting.