 Subject of a Formula: A formula is a rule or a fact written with mathematical symbols. In mathematics, students find many formulas for various concepts. The main objective of the formula is to solve the problem easily & quickly. We think you all may have an idea about establishing an equation if not, look at our previous article.

The subject of a formula is the part of Changing the subject of a formula concept. Students who are looking to learn about the subject of formula and how to change it can refer to this article without any delay.

It completely helps you to understand what is meant by the subject of the formula and how to make something the subject of a formula. So, jump into the below sections and gain proper knowledge.

What is the Subject of a Formula?

A linear equation which is stated in variables and literals with mathematical operators is known as a formula. Hence, the variable that we need to calculate & discover as per the given context hints is called the Subject of the Formula.

For instance, let’s assume Newton’s law of motion as an equation ie., v²-u² = 2as

Here, v, u, a, and s are the variables such as final velocity, initial velocity, acceleration, and displacement of the particle respectively.

This equation can be rearranged as:

s = $$\frac { v²-u² } { 2a }$$, s become the subject of the formula.

OR

a = $$\frac { v²-u² }{ 2s }$$, a become the subject of the formula.

How to make the subject of the formula?

The steps that are involved in making one variable as a subject of the formula are as given.

• First, Isolate the variable by adding or subtracting terms near to the variable, eliminating any fractions, dividing by the coefficient of the variable, and removing a root or power of both sides of the equation.
• Rearrange the equation and the subject variable should be on the left side of the equal sign.
• In case, the same subject variable contains in multiple terms, then perform factorization or any other related operation to make an end result as a single variable left as a subject of the formula on the left side of the equal sign.

Subject of a Formula Questions | Examples on Change the Subject of the Formula

Example 1:
If z is the subject of a formula, it expresses the product of x and y. Find x as the subject of the formula?

Solution:
Given formula as per the context is z = xy
Now, we have to find out the x as a subject of the formula.
z = xy
Divide y on both sides ie., (÷)y
$$\frac { z} { y }$$ = $$\frac { xy } { y }$$
$$\frac { z } { y }$$ = x
Hence, x = $$\frac { z } { y }$$.

Example 2:
Change the subject of the equation in terms of p: z = x² + 2y +p

Solution:
Given equation is z = x² + 2y +p
We have to change the subject of an equation in terms of p:
z = x² + 2y +p
After applying the steps of how to subject the formula, we get the result as
p = z – x² – 2y

Example 3:
Make ‘x’ the subject of the formula, s = x + bt

Solutions:
Given expression is s = x + bt
x is added to the bt.
Firstly, subtract bt on both sides.
s – bt = x + bt – bt
s – bt = x, Hence, the subject x = s – bt.

FAQs on Rearrange Formulas or Equations

1. How to find the subject of the formula in x = 6a + 2b?

The variable that expresses in other variables is known as the subject of a formula. In the given formula, the x variable is the subject of the formula.

2. What happens when a positive variable moves to the other side of an equal sign?

When the positive variable moves to the other side of the equal sign it changes to a negative variable or subtracts.

3. What is changing the subject of the formula?

Changing the subject of the formula is nothing but rearranging the formula and getting the different subject as per the given hints in the problem.