List of Math Formulas (Basic & Important for Every Student) - BYJUS

# Math Formulas

Math as a subject in school has been made more friendly to students with the use of formulas. Any mathematical expression with numbers and letters, exponents, fractions and a whole lot of mathematically relevant terms help students to solve problems with ease. We’re on a quest to make formulas available to all students! ...Read MoreRead Less

## Basic Math Formulas

In addition to the list of formulas that have been mentioned so far, there are other formulas that are frequently used by a student in either geometry or algebra.

1. Surface Area of a sphere $$=4\pi r^2$$ where r is the radius of the sphere – We’re getting back to the characteristics of a sphere and finding the surface area with the formula that has been mentioned.
2. Slope-intercept form: $$y=mx+b$$, m is the   and b is the y-intercept.  – Having already observed the point slope equation for a straight line, another popular formula is the slope intercept form in which all straight lines have an equation linked to them, $$y=mx+b$$!
3. $$(a+b)^2=a^2+2ab+b^2$$ – This is probably iconic, and one of the fundamental formulas in algebra, which is the square of two variables added together!

## Important Math Formulas

When we talk about formulas, we expect complex expressions and numbers and exponents! Formulas actually make it easier for students to solve and understand the concepts of mathematics usually introduced to them from lower. Here is a list of a few important formulas that students from different grades apply in the classroom.

1. Volume of Sphere $$=\frac{4}{3}\pi r^3$$, r is the radius – A formula that is applied to calculate the volume of a sphere, a three dimensional, circular solid.
2. Area of a Circle $$=\pi r^2$$, r is the radius – If we cut a sphere in exactly two halves, we get a circle at the surface of one of the halves, and the area of the circle is calculated with the given formula.
3. Perimeter of a Rectangle $$=2(l+b)$$, l is the length and b is the breadth. – Now that we see the area of a circle, the perimeter is a different concept in relation to geometric shapes. The perimeter of a rectangle introduces us to the length of the boundary of a geometric shape.
4. Pythagoras Theorem, $$c^2=a^2+b^2$$ where c is the length of the hypotenuse, a and b are the lengths of the other two sides of the right triangle. – Created by the great Pythagoras, a Greek mathematician, this formula mentions the relationship between the hypotenuse, the longest side of a right angled triangle, and the lengths of the other two sides.
5. Sum of interior angles of a polygon $$:(n-2)\times 180^{\circ}$$, where n is the number of sides. – The previous formula spoke of a right angled triangle, which is a polygon. In fact all closed shapes with three or more than three sides are polygons. And the sum of the interior angles of a polygon is calculated with the formula given.
6. Point slope form: $$y-y_1=m(x-x_1)$$, where m is the slope and $$(x_1,~y_1)$$ are the coordinates of the point passing through the line. – Polygons are made up of straight lines and when we speak of lines, there is a way to represent a straight line in the form of one of mainly four types of equations, and this equation represents the slope, and one point on the line.
7. Exponents: $$a\times a\times a\times a\ldots(n~times)=a^n$$ – Moving away from geometry we have a formula that prevents us from repeated multiplication. Representing an expression that indicates repeated multiplication makes life easier for a lot of students.
8. Simple Interest: $$I=Prt$$ where P is the principal amount, r is the rate of interest (in decimal form), and t is the time period. – While on the topic of increasing a number exponentially, we can also look at making money grow with the application of simple interest.
9. $$\text{Mean}=\frac{\text{Sum of all data values}}{\text{Number of data values}}$$ – And when we need to calculate the mean of a set of numbers or values, we just need the sum of all the values and divide it by the number of values. This formula is definitely of statistical significance!
10. Dilation: On dilation, the coordinates of the figure $$(x,~y)$$ become $$(kx,~ky)$$, where k is the scale factor. – Of importance in coordinate geometry the concept of dilation is to either increase or decrease the size of a geometric shape by a given scale factor.

## Benefits of Math Formulas

• Mathematics as a subject is not isolated from a lot of other subjects. In fact, math is linked to branches of science such as physics, chemistry and biology. Not only does math help support theories in these subjects, the projections made by researchers and scientists are based on mathematical models.

• Talking about mathematical models, many real life scenarios are solved using rules and symbols. All these rules and symbols combine to give us formulas. There is a transition in learning equations and formulas, from learning one and one gives two, to, “x” subtracted from “y” giving us “z”.

• The difference here is that as a student progresses from one grade to the next, the complexity of the formulas a student learns gradually increases. It’s the lessons in class and the formulas in math that are introduced in greater numbers that allows a students to decode the reality around them.

• Formulas make math convenient to learn, and so does practice. A constant interaction with the formulas on our website is bound to make students sharper and more focused on everything that they do on a day to day basis.

• Fluency in terms of recalling formulas is sure to help students in higher grades and college. As the formulas introduced in school are the foundations for more complex ones in higher grades and college.

• From college to a career, definitely has formulas linked to them. Not simple ones like the area of a square or finding the speed of a car, but ones that could man on Mars, or building the next tallest building, or even exploring the deepest parts of the ocean!

Formulas provide a method of solving problems and they also make a student sharp, focused and ready to face real world problems.

Sure, math problems can be solved without formulas. However, the process of obtaining the solution to a problem may involve many more steps when compared to the application of a formula to the same problem, and solving it in fewer steps.

Even though math started with counting numbers, complex formulas were known to many ancient civilizations as they needed to build monuments, measure land, keep a track of commerce and so on. However, Pythagoras and his formula for the hypotenuse or even Euclid are a couple of Greek mathematicians whose formulas have become famous!

Whether it is algebra, geometry or arithmetic, there are formulas for all these branches of mathematics.

The method to get those formulas ingrained is to understand a concept, and understand why the final form of the formula is the way it is written. Adding to the clarity about the why and how a formula is expressed, practice, the golden rule, is always the best option to remember a formula.

It’s common to find formulas in the textbook that are the backbones of different math concepts. There is also a possibility of deriving or simply arriving at a formula from known information, especially in algebra and geometry.

The most famous of mathematical relationships is the $$E=mc^2$$, which was proposed by Einstein. Euclid, Euler and Pythagoras are other mathematicians who have formulas named after them.

Formulas provide a direct way of solving problems and are not shortcuts. Even though there could be alternate methods of solving problems, using a formula and substituting the values in the expression, could be a quicker and a more efficient way to obtain the solution.

There is no fixed number of formulas for every grade as the number of formulas may vary according to the math concepts related to a particular grade, starting from the grade four.

The application of formulas starts from grade 4 as in the lower grades an introduction to formulas with unknowns may seem difficult to process by the student.