What is Formula in Maths? Definition with Examples

What is Formula in Math?

The formula is a fact or a rule written with mathematical symbols. It usually connects two or more quantities with an equal sign. When you know the value of one quantity, you can find the value of the other using the formula. It helps to solve the questions quickly. In algebra, geometry and other topics, formulas are used to simplify the process of reaching the answer and saving time. 

Simple Formulas in Math

Pythagorean Theorem is one of the examples of formula in math. Besides this, there are so many other formulas in math. Some of the mostly used formulas in math are listed below:

Basic Formulas in Geometry

Geometry is a branch of mathematics that is connected to the shapes, size, space occupied, and relative position of objects. In geometry, we use formulas to find the dimensions, perimeter, area, surface area, volume, etc., of the different shapes. The 2D shapes are flat and have only two dimensions, length, and width. Some basic 2D formulas for listed below:

Basic Geometry Formula for 2D Shapes
Pythagorean Theorem

The 3D objects are solid objects with three dimensions, length, width, and height or depth. For example, cube, cuboid, sphere, cylinder, and cone. Formulas for volumes of basic 3D Shapes are listed below:

Basic Formula for 3D Shapes

Basic Algebraic Formula

Algebraic formulas build foundation for various topics of mathematics like equation, polynomials, trigonometry etc. Here are some most commonly used algebraic formulas.

  • a2 – b2 = (a – b)(a + b)
  • (a + b)2 = a2 + 2ab + b2
  • (a – b)2 = a2 – 2ab + b2
  • a0 = 1
  • (am)(an) = am + n
  • ($\frac{a}{b}$)n $=$ $\frac{a^n}{b^n}$
  • (ab)n = anbn
  • (am)n = amn
  • x-n = 1/xn
  • $\frac{x^m}{x^n}$ = xm-n

Arithmetic Mean Formula

Arithmetic mean (average) = $\frac{Sum of values}{Number of values}$

Real-Life Applications of Math Formulas

It is important to understand that math formulas are part of every area of your life. The meaning of formula in math is to express information symbolically concisely, and they are derived after several decades of research. We use them widely in construction, architecture, engineering and more. Whether you realize it or not, we use algebraic formulas to plan our schedule and do our tasks simply. Geometry formulas like area, perimeter and the Pythagorean theorem is commonly used in the construction of different types of structures or buildings. We use algebraic formulas in the areas of financial planning and in fields of computer science. Formulas of algebra are used in medicine to measure drug dosage depending on the age and weight of an individual. In real life, we need formulas to solve most of our calculation-based problems. 

Solved Examples

Example 1: Find the perimeter of a square with a side of 5 units.

Solution: Perimeter of a square = 4 × side = 4 × 5 = 20 units.

Example 2: Find the value of n, when 3-7 × 3n = 32

Solution: Using the laws of exponents, we get

3-7 × 3n = 32

3-7+n = 32

Since the bases are the same and equating the powers, we get -7 + n = 2

Therefore, n must be 2 + 7 or 9.

Example 3: Find the area of a square with a perimeter of 28 cm.

Solution: Perimeter of the square = 28 cmSo, the length of each side must be 28 ÷ 4 or 7 cm. Therefore, Area of square = 72 = 49 cm2.

Practice Problems

What is Formula in Maths? Meaning, Definition, Examples

Attend this quiz & test your knowledge.

1What is the perimeter of the square that has an area of $4a^2cm^2$?

$2a cm$
$4a cm$
$8a cm$
$16a cm$
Correct answer is: $8a cm$
Area of square is $4a^2cm^2$. So, the side of the square must be $\sqrt{4a^2} or $2a cm$.Therefore, the perimeter must be 4 × 2$a$ or 8$a cm$.

2Each side of a cube is 5 cm long. What is its volume?

$25 cm^3$
$50 cm^3$
$125 cm^3$
$250 cm^3$
Correct answer is: $125 cm^3$
Each side of the cube is $5 cm$ long. So, volume of the cube must be 5 × 5 × 5 or 125 $cm^3$.

3Which of the following is the area of the circle with a diameter of 4 cm?

$π cm^2$
$2π cm^2$
$3π cm^2$
$4π cm^2$
Correct answer is: $4π cm^2$
Diameter is 4 cm. So the radius of the circle is 2 cm. The area of the circle must be πr2 or $4π cm^2$.

4Find the value of n, when 49 = 7$^{3+n}$

Correct answer is: -1
7$^{3+n}$ = 49 = 72. By equating the powers, we get 3 + n = 2 or n = -1

Frequently Asked Questions

The formula is a fact or rule written with mathematical symbols. It usually connects two or more quantities with an equal sign. Math formulas are derived to solve a problem with speed and accuracy. It makes finding a solution much more manageable than attempting it from scratch. When you know the value of one quantity, you can find the value of the other using the formula.

Area of a triangle = ½ (b × h) [b = base length, h = height]

The first formula was invented between 1800 and 1600 BC. You find them not just in mathematics but in fields of construction, architecture, engineering, and medicine. We use them to help us solve problems easier and faster.