Math Formula Chart: All Maths Formulas For Class 8 To 12

Q: What is the formula for the area of a circle in Hindi?

वृत्त का क्षेत्रफल = π r^2, where r is the त्रिज्या (radius). Its परिधि (circumference) is 2π r.

Q: What is the difference between a formula and an equation?

A formula is a general rule connecting quantities, such as V = lbh. An equation states that two expressions are equal and is usually solved for an unknown, such as 2x + 3 = 9, which gives x = 3.

A math formula is a short rule, written with letters and symbols, that turns the numbers you know into the one you need, like $A = \pi r^2$ for the area of a circle. This page collects the maths formulas of class 8 to 12 in one chart, grouped by topic, so you can find any formula in seconds.

Each block lists the core formulas with one line on what the letters mean, then links to the page that explains that topic with worked examples and common mistakes. There is a basic math formulas section for quick revision, a class-wise guide, and the Hindi names for every topic. You can also download the formula sheet PDF below, which gathers the key formulas of every page on this site.

Key formulas

Quadratic formula
$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
a plus b whole square
$(a + b)^2 = a^2 + 2ab + b^2$
Area and circumference of a circle
$A = \pi r^2,\quad C = 2\pi r$
Pythagoras theorem
$\text{hypotenuse}^2 = \text{base}^2 + \text{perpendicular}^2$
Heron's formula
$A = \sqrt{s(s-a)(s-b)(s-c)}$
Volume of a cylinder
$V = \pi r^2 h$
Trigonometric identity
$\sin^2\theta + \cos^2\theta = 1$
Distance formula
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Mean
$\bar{x} = \dfrac{\sum x}{n}$
Compound interest amount
$A = P\left(1 + \dfrac{r}{100}\right)^n$
rate r% a year, compounded yearly for n years
Power rule of differentiation
$\dfrac{d}{dx}\,x^n = n x^{n-1}$
Power rule of integration
$\int x^n\,dx = \dfrac{x^{n+1}}{n+1} + C,\ n \neq -1$

How to use this math formula chart

The blocks below follow the order of the school syllabus: algebra, geometry and mensuration, trigonometry, coordinate geometry, statistics, calculus and commercial maths. Every block is a summary. When you need the full story (the derivation, solved examples, the traps examiners set), follow the link at the end of the block.

Three habits help when you revise from any formula chart:

Say what each letter means. A formula you cannot read aloud in words is a formula you will misuse. "A equals pi r squared" should come with "r is the radius, not the diameter".
Check the units. Lengths are in cm or m, areas in square units, volumes in cubic units. If your answer for a volume comes out in cm², a step is wrong.
Test with an easy number. Unsure whether the sum 1 + 2 + ... + n is $\tfrac{n(n+1)}{2}$ ? Put n = 3: the sum is 6, and $\tfrac{3 \times 4}{2} = 6$ as well.

Math equations and formulas are not quite the same thing. An equation, such as $3x + 2 = 11$ , is true for a particular value of x. A formula is a general rule that holds whenever its conditions are met, and an identity holds whatever values the letters take. Every mathematics formula on this page is one of these general rules.

Basic math formulas chart

These are the building blocks used in every later chapter. Most of them are taught by class 6 to 8, and they still decide marks in class 12 because a single arithmetic slip spoils a long answer.

Idea	Rule
Order of operations (BODMAS)	Brackets, Orders (powers and roots), Division and Multiplication left to right, then Addition and Subtraction left to right
Adding fractions	$\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{ad + bc}{bd}$
Dividing fractions	$\dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a}{b} \times \dfrac{d}{c}$
HCF and LCM of two numbers	$\text{HCF} \times \text{LCM} = a \times b$
Square and cube	$a^2 = a \times a,\ a^3 = a \times a \times a$
Average	sum of values divided by the number of values

A few definitions students look up often. A product is the result of multiplying; the product of 6 and 7 is 42. A factor of a number divides it exactly, so the factors of 12 are 1, 2, 3, 4, 6 and 12. A constant is a quantity that does not change, like 5 or $\pi$ , while a variable can take different values. In geometry, a point marks a position and has no size, and a line is a straight path of points that extends without end in both directions; a line segment has two end points and a ray has one. The four mathematical operations are addition, subtraction, multiplication and division, and simplification (sarlikaran) questions test exactly these with BODMAS.

Algebra formulas

Algebra is where most of the "remember this" formulas live. The core identities:

\begin{aligned} (a + b)^2 &= a^2 + 2ab + b^2 \\ (a - b)^2 &= a^2 - 2ab + b^2 \\ a^2 - b^2 &= (a + b)(a - b) \\ (a + b)^3 &= a^3 + b^3 + 3ab(a + b) \\ a^3 + b^3 &= (a + b)(a^2 - ab + b^2) \end{aligned}

The cube formula maths students search most is that last pair, along with $a^3 - b^3$ and the three letter result $a^3 + b^3 + c^3 = 3abc$ when $a + b + c = 0$ . Exponent laws ( $a^m a^n = a^{m+n}$ ) and log laws ( $\log mn = \log m + \log n$ ) sit in the same family. The complete list with solved examples is on algebra formulas.

Quadratic equations and progressions

For $ax^2 + bx + c = 0$ the roots come from the formula at the top of this page, and the discriminant $D = b^2 - 4ac$ tells you whether they are real. Sum of roots is $-\tfrac{b}{a}$ , product is $\tfrac{c}{a}$ . The full method, with complex roots and graphs, is on the quadratic formula home page.

Arithmetic progressions (class 10) use two formulas: the nth term $a_n = a + (n - 1)d$ and the sum $S_n = \tfrac{n}{2}[2a + (n - 1)d]$ . In the AP 3, 7, 11, and so on, the 20th term is $3 + 19 \times 4 = 79$ , and the first 20 terms add to 820.

Geometry and mensuration formulas

Mensuration means measuring: perimeter (the boundary), area (the flat surface inside) and volume (the space a solid fills). NCERT questions usually take $\pi = \tfrac{22}{7}$ unless they say 3.14.

Perimeter and area of plane figures

Shape	Perimeter	Area
Square, side a	$4a$	$a^2$
Rectangle, l by b	$2(l + b)$	$lb$
Circle, radius r	$2\pi r$	$\pi r^2$
Parallelogram, base b, height h	sum of sides	$bh$
Trapezium (trapezoid), parallel sides a and b, height h	sum of sides	$\tfrac{1}{2}(a + b)h$
Rhombus, side a, diagonals $d_1, d_2$	$4a$	$\tfrac{1}{2}d_1 d_2$

A circle of radius 7 cm has area $\tfrac{22}{7} \times 49 = 154$ cm² and circumference 44 cm. More shapes, sectors and segments are on area formulas and perimeter formulas.

Triangle formulas

Area is $\tfrac{1}{2} \times \text{base} \times \text{height}$ . When you know only the three sides, use Heron's formula with $s = \tfrac{a + b + c}{2}$ ; see Heron's formula. An equilateral triangle of side a has area $\tfrac{\sqrt{3}}{4}a^2$ . In a right triangle, Pythagoras gives the third side, and the angles of any triangle add to 180°.

Volumes and surface areas of solids

Solid	Volume	Surface area
Cube, side a	$a^3$	$6a^2$
Cuboid	$lbh$	$2(lb + bh + hl)$
Cylinder	$\pi r^2 h$	curved $2\pi rh$ , total $2\pi r(r + h)$
Cone, slant height l	$\tfrac{1}{3}\pi r^2 h$	curved $\pi r l$
Sphere	$\tfrac{4}{3}\pi r^3$	$4\pi r^2$
Hemisphere	$\tfrac{2}{3}\pi r^3$	total $3\pi r^2$

A cylinder with radius 7 cm and height 10 cm holds 1540 cm³. Combined solids and conversions between shapes are covered on volume and surface area formulas.

Trigonometry formulas

For an acute angle $\theta$ in a right triangle, $\sin\theta = \tfrac{\text{perpendicular}}{\text{hypotenuse}}$ , $\cos\theta = \tfrac{\text{base}}{\text{hypotenuse}}$ and $\tan\theta = \tfrac{\sin\theta}{\cos\theta}$ . The other three ratios are their reciprocals: cosec, sec and cot.

\sin^2\theta + \cos^2\theta = 1,\qquad 1 + \tan^2\theta = \sec^2\theta,\qquad 1 + \cot^2\theta = \operatorname{cosec}^2\theta

Class 10 adds the values at 0°, 30°, 45°, 60° and 90°, such as $\sin 30^\circ = \tfrac{1}{2}$ and $\tan 45^\circ = 1$ , plus heights and distances. Class 11 brings compound angles, $\sin(A + B) = \sin A\cos B + \cos A\sin B$ , and the double angle results $\sin 2A = 2\sin A\cos A$ and $\cos 2A = \cos^2 A - \sin^2 A$ . The full table of identities, triple angles and the standard value chart is on trigonometry formulas.

Coordinate geometry formulas

Coordinate geometry places shapes on the x and y axes so that lengths and areas become arithmetic. For points $(x_1, y_1)$ and $(x_2, y_2)$ :

Distance: $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ . From $(1, 2)$ to $(4, 6)$ it is $\sqrt{9 + 16} = 5$ .
Midpoint: $\left(\tfrac{x_1 + x_2}{2}, \tfrac{y_1 + y_2}{2}\right)$ .
Section formula, ratio m : n inside: $\left(\tfrac{mx_2 + nx_1}{m + n}, \tfrac{my_2 + ny_1}{m + n}\right)$ .
Slope: $m = \tfrac{y_2 - y_1}{x_2 - x_1}$ , and a line is $y = mx + c$ .
Area of a triangle with three vertices: $\tfrac{1}{2}\left|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)\right|$ . For $(1, 2)$ , $(4, 6)$ , $(3, 8)$ it gives 5 square units.

Proofs and worked problems are on the distance and section formula page.

Statistics and probability formulas

Statistics turns a list of numbers into one or two summary values.

Mean of raw data: total divided by count. The mean of 4, 8, 9, 11 and 13 is $\tfrac{45}{5} = 9$ . For grouped data, $\bar{x} = \tfrac{\sum f_i x_i}{\sum f_i}$ .
Median of grouped data: $l + \left(\tfrac{\tfrac{n}{2} - cf}{f}\right)h$ .
Mode of grouped data: $l + \left(\tfrac{f_1 - f_0}{2f_1 - f_0 - f_2}\right)h$ .
Empirical relation: $3\,\text{median} = \text{mode} + 2\,\text{mean}$ .
Standard deviation: $\sigma = \sqrt{\tfrac{\sum (x - \bar{x})^2}{n}}$ .
Probability of an event: favourable outcomes divided by total equally likely outcomes, always from 0 to 1.

The meaning of l, cf, f and h, and solved tables for class 10, are on mean, median and mode. Variance and the shortcut methods are on standard deviation.

Calculus and class 12 math formula sheet

Calculus starts in class 11 with limits and derivatives and fills most of class 12. The two power rules in the key box are used more than anything else. A short list of standard results:

Function	Derivative	Integral
$x^n$	$nx^{n-1}$	$\tfrac{x^{n+1}}{n+1} + C,\ n \neq -1$
$\sin x$	$\cos x$	$-\cos x + C$
$\cos x$	$-\sin x$	$\sin x + C$
$e^x$	$e^x$	$e^x + C$
$\tfrac{1}{x}$	$-\tfrac{1}{x^2}$	$\ln\lvert x\rvert + C$

The product rule $(uv)' = u'v + uv'$ and the chain rule handle combinations. Rules, the quotient rule and many examples are on differentiation formulas; substitution, by parts and definite integrals are on integration formulas.

Class 12 also has vectors. The vector formula you will use most is the dot product, $\vec{a}\cdot\vec{b} = |\vec{a}||\vec{b}|\cos\theta$ , where $\theta$ is the angle between the two vectors, with the cross product giving $|\vec{a}||\vec{b}|\sin\theta$ as its magnitude.

Commercial maths: percentage, profit and interest

These formulas are short but carry many marks in class 8 and in competitive exam aptitude papers.

Percentage: $x\% \text{ of } y = \tfrac{x}{100} \times y$ . So 18% of 250 is 45.
Profit % $= \tfrac{\text{profit}}{\text{cost price}} \times 100$ and loss % uses loss in the same way. Discount % is worked out on the marked price.
Simple interest: $SI = \tfrac{P \times R \times T}{100}$ .
Compound interest: $A = P\left(1 + \tfrac{r}{100}\right)^n$ and $CI = A - P$ .

On a principal of ₹10,000 at 10% a year for 2 years, simple interest is ₹2,000 while compound interest is ₹2,100, because the second year earns interest on the first year's interest too. Half-yearly and quarterly cases are on interest formulas, and increase, decrease and successive change are on percentage formula.

Maths formulas class wise: class 8, 9, 10, 11 and 12

If you only need your own year, use this guide to pick the right blocks above. Topics for class 8 depend on the edition of your book, so check its contents page.

Class	Formula topics
Class 8	Exponents, squares and cubes, basic identities, area of trapezium and polygons, surface area and volume of cube, cuboid and cylinder, compound interest, percentage and profit
Class 9	Polynomials with cube identities, Heron's formula, surface areas and volumes including cone and sphere, statistics, coordinate plane basics
Class 10	Real numbers (HCF and LCM), quadratic equations, AP, triangles and similarity, coordinate geometry, trigonometry and heights and distances, areas related to circles, surface areas and volumes, statistics, probability
Class 11	Trigonometric functions, complex numbers, permutations and combinations, binomial theorem, sequences, straight lines, conic sections, limits and derivatives, statistics
Class 12	Matrices and determinants, continuity and differentiability, applications of derivatives, integrals, differential equations, vectors, 3D geometry, probability

For maths formulas for class 10 all chapters, remember that in the latest NCERT edition Surface Areas and Volumes is chapter 12 and Areas Related to Circles is chapter 11. Those two chapters use the mensuration block and are among the most formula heavy in the book.

Math formula in Hindi

Students in Hindi medium schools often search "math ka formula" or "math ke sare formulae". The formulas themselves are the same in every language; only the names change. Use this table to match the Hindi word in your book with the English heading on this page.

English	Hindi
Math formula	गणित सूत्र
Area, perimeter	क्षेत्रफल, परिमाप
Volume, surface area	आयतन, पृष्ठीय क्षेत्रफल
Square, cube	वर्ग, घन
Radius, diameter	त्रिज्या, व्यास
Trigonometry	त्रिकोणमिति
Mean, median, mode	माध्य, माध्यक, बहुलक
Simple interest, compound interest	साधारण ब्याज, चक्रवृद्धि ब्याज
Simplification	सरलीकरण
Differentiation, integration	अवकलन, समाकलन

Triangle formulas in Hindi

Hindi name	Formula
त्रिभुज का क्षेत्रफल	$\tfrac{1}{2} \times \text{base} \times \text{height}$
पाइथागोरस प्रमेय	$\text{hypotenuse}^2 = \text{base}^2 + \text{perpendicular}^2$
हीरोन का सूत्र	$\sqrt{s(s-a)(s-b)(s-c)}$

In Hindi books the three sides of a right triangle are called कर्ण (hypotenuse), आधार (base) and लंब (perpendicular).

If you came here for a math all formula PDF download in Hindi, note that the sheet on this page is in English, because the symbols are what you write in the exam; keep this table beside it to read it in Hindi. "Math sutra" and "mathematics sutro" simply mean maths formulas, and if your book is in Gujarati or Odia the same symbols apply too.

Common mistakes when using any formula

Read the question twice. Most formula errors are not about the formula at all. Students use the diameter where the radius was needed, or forget to convert minutes to hours.

Mixing units: convert every length to the same unit before you substitute.
Confusing curved and total surface area of a cylinder or cone.
Using degrees in a calculus formula that expects radians.
Writing $(a + b)^2 = a^2 + b^2$ , the most common algebra slip of all.
Forgetting $+ C$ in an indefinite integral.
Rounding too early: keep full values until the last line, then round.

One last tip: write the formula first, then the substitution, then the answer with its unit. Examiners give step marks for the first two lines even if the arithmetic goes wrong.

Download the PDF

Questions students ask

What are the basic math formulas every student should know?

Start with BODMAS, fractions, percentage, the area and perimeter of a square, rectangle, triangle and circle, the identity $(a + b)^2 = a^2 + 2ab + b^2$ , Pythagoras theorem, simple interest and the mean. Almost every later formula builds on these.

How many formulas are there in class 10 maths?

There is no fixed count, but a complete class 10 sheet has roughly 80 to 100 formulas across algebra, AP, coordinate geometry, trigonometry, mensuration and statistics. Lists that promise 100 maths formulas cover about the same ground as the blocks above.

Is there a PDF of all maths formulas?

Yes. The full formula sheet PDF on this page gathers the key formulas of every topic page on the site, on A4 so you can print it. Each topic page also has its own one-page sheet.

What is the formula for the area of a circle in Hindi?

वृत्त का क्षेत्रफल $= \pi r^2$ , where r is the त्रिज्या (radius). Its परिधि (circumference) is $2\pi r$ .

What is the difference between a formula and an equation?

A formula is a general rule connecting quantities, such as $V = lbh$ . An equation states that two expressions are equal and is usually solved for an unknown, such as $2x + 3 = 9$ , which gives $x = 3$ .

How should I memorise maths formulas before an exam?

Write each formula by hand, say what every letter means, and solve one short example with it. Revise from one sheet in the last week, and group related formulas (all the circle ones together, all the cone ones together) so that one reminds you of the next.