Class 10 Maths Formulas: Complete Chapter-Wise List
Every Class 10 Maths formula by NCERT chapter: real numbers, algebra, coordinate geometry, trigonometry, circles, mensuration, statistics and probability.
This is every formula in the 14 chapters of the NCERT Class 10 Maths textbook, which CBSE and many state boards follow. Rows marked “not in CBSE 2026-27” are topics CBSE no longer assesses; your state board may still include them. Bookmark this page and revise it daily.
ICSE students: the ICSE syllabus is different and includes topics such as GST, banking, shares and dividends, matrices and the equation of a line, which are not on this sheet. See our ICSE Class 10 Maths important questions instead.
Chapter 1: Real Numbers
Formula / Result
Description
HCF(a, b) × LCM(a, b) = a × b
For any two positive integers a and b
Fundamental Theorem of Arithmetic
Every composite number is a product of primes in exactly one way (apart from order)
√2, √3, √5 are irrational
Proofs by contradiction are in the syllabus
Euclid's division lemma: a = bq + r, 0 ≤ r < b
Not in CBSE 2026-27
Chapter 2: Polynomials
Formula
For the polynomial ax² + bx + c
Sum of zeroes (α + β)
= −b/a
Product of zeroes (αβ)
= c/a
Polynomial from its zeroes
k[x² − (α + β)x + αβ]
Chapter 3: Pair of Linear Equations in Two Variables
Condition
For a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0
Unique solution (intersecting lines)
a₁/a₂ ≠ b₁/b₂
No solution (parallel lines)
a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Infinitely many solutions (coincident lines)
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 (a ≠ 0)
Discriminant: D = b² − 4ac
Decides the nature of the roots
D > 0
Two distinct real roots
D = 0
Two equal real roots, each −b/2a
D < 0
No real roots
Chapter 5: Arithmetic Progressions
Formula
Description
nth term: aₙ = a + (n−1)d
a = first term, d = common difference
Sₙ = n/2 [2a + (n−1)d]
Sum of the first n terms
Sₙ = n/2 (a + l)
When the last term l is known
d = aₙ − aₙ₋₁
Difference between consecutive terms
aₙ = Sₙ − Sₙ₋₁
nth term from the sums
Practise with these formulas
Super Tutor has chapter-wise Class 10 Maths practice quizzes, so you apply every formula with instant feedback.
Basic Proportionality Theorem: DE ∥ BC ⇒ AD/DB = AE/EC
CBSE asks you to prove this one
Converse of BPT
If AD/DB = AE/EC, then DE ∥ BC (statement only)
AAA (AA) similarity
Corresponding angles equal ⇒ triangles similar
SSS similarity
All three pairs of sides in the same ratio ⇒ similar
SAS similarity
One angle equal and the sides including it proportional ⇒ similar
Ratio of areas = (ratio of sides)²
For similar triangles. Not in CBSE 2026-27
Pythagoras: a² + b² = c²
c = hypotenuse. The proof is no longer in the CBSE Class 10 syllabus, but you use the result throughout
Chapter 7: Coordinate Geometry
Formula
Expression
Distance formula
d = √[(x₂−x₁)² + (y₂−y₁)²]
Section formula (internal, ratio m₁ : m₂)
P = ((m₁x₂ + m₂x₁)/(m₁+m₂), (m₁y₂ + m₂y₁)/(m₁+m₂))
Midpoint formula
M = ((x₁+x₂)/2, (y₁+y₂)/2)
Area of a triangle
½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|; area 0 means the points are collinear. Not in CBSE 2026-27
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
not defined
Trigonometric Identities
Identity
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ (0° ≤ θ < 90°)
1 + cot²θ = cosec²θ (0° < θ ≤ 90°)
Chapter 9: Some Applications of Trigonometry
Heights and distances use the same ratios: in the right triangle formed by the object, its shadow or the ground and your line of sight, tan θ = height / horizontal distance. CBSE limits these problems to angles of 30°, 45° and 60° and to no more than two right triangles.
Chapter 10: Circles
Result
Description
Tangent ⊥ radius
The tangent at any point is perpendicular to the radius through the point of contact (proof in syllabus)
Tangents from an external point are equal
PA = PB for tangents from P (proof in syllabus)
Length of tangent = √(d² − r²)
d = distance from the centre to the external point, r = radius
Chapter 11: Areas Related to Circles
Quantity
Formula (radius r, central angle θ in degrees)
Circumference
2πr
Area of circle
πr²
Length of arc
(θ/360) × 2πr
Area of sector
(θ/360) × πr², or ½ × arc length × r
Area of segment
Area of sector − area of the triangle formed by the two radii (CBSE uses θ = 60°, 90° or 120°)
Chapter 12: Surface Areas and Volumes
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, slant height 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). Not in CBSE 2026-27
Slant height of a cone: l = √(r² + h²). For combined solids, add only the surfaces that are exposed, but add the volumes of all the parts.
Chapter 13: Statistics
Measure
Formula (grouped data)
Mean (direct method)
x̄ = Σfᵢxᵢ / Σfᵢ
Mean (assumed mean method)
x̄ = a + Σfᵢdᵢ / Σfᵢ, where dᵢ = xᵢ − a
Mean (step deviation method)
x̄ = a + (Σfᵢuᵢ / Σfᵢ) × h, where uᵢ = (xᵢ − a)/h
Median
l + [(n/2 − cf) / f] × h
Mode
l + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h
Empirical relationship
3 Median ≈ Mode + 2 Mean (a useful check)
Chapter 14: Probability
Formula
Description
P(E) = favourable outcomes / total outcomes
Classical probability (equally likely outcomes)
P(E) + P(not E) = 1
Complementary events
0 ≤ P(E) ≤ 1
Range of a probability
P(sure event) = 1, P(impossible event) = 0
The two extremes
Chapter numbers follow the current NCERT Class 10 Mathematics textbook. Notes on what is and isn't assessed follow the CBSE 2026-27 syllabus; mark weights are from CBSE's 2026-27 course structure. State boards and ICSE differ, so check your own board's syllabus.
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It depends on how you count them. The formula-heavy chapters are Trigonometry (ratios, standard values and identities), Surface Areas and Volumes (a formula for every solid), Areas Related to Circles and Statistics. You don't need to memorise them blindly: understanding where a formula comes from helps you recall it in the exam.
Which chapter has the most formulas in Class 10 Maths?▾
Trigonometry, followed by Surface Areas and Volumes. In CBSE's 2026-27 course structure, Trigonometry carries 12 marks and Mensuration (Areas Related to Circles plus Surface Areas and Volumes) carries 10 of the 80 marks.
How do I memorise Maths formulas for board exams?▾
(1) Write each formula from memory daily for a week and check it. (2) Keep one formula sheet and revise it every morning. (3) Solve a few problems with each formula; using it beats rereading it. (4) Use memory aids for trigonometric values, such as the square-root pattern √0/2, √1/2, √2/2, √3/2, √4/2 for sin 0°, 30°, 45°, 60°, 90°. (5) Learn how formulas are derived so you can rebuild one you forget.
Are formulas given in the CBSE board exam?▾
No. CBSE does not provide a formula sheet in the board exam, so you need to know the formulas. A question may state a formula it wants you to use, but standard formulas for area, volume, trigonometry and coordinate geometry must be learnt.
Which formulas are most important for scoring in Class 10 Maths?▾
The ones you will use most: (1) the quadratic formula and discriminant, (2) the distance formula, (3) the section formula, (4) sin²θ + cos²θ = 1 and the other identities, (5) standard trigonometric values, (6) surface area and volume of cylinders, cones and spheres, (7) nth term and sum of an AP, (8) HCF × LCM = product of two numbers, (9) mean, median and mode of grouped data, (10) area of a sector and probability of an event.