Change the Subject of a Formula

In mathematics we will learn how to change the subject of a formula and find the value of the variable.

Change the Subject of a Formula

Subject of the formula:

It is a variable which is expressed in terms of other variables involved in the formula.

Formulas are written so that a single variable, the subject of the formula is on the L.H.S. of the equation. Everything else goes on the right side of the equation. We evaluate the formula by substituting for the literal numbers on the right hand side.

For example:

In the formula v = u + at, v is the subject.

To find v in the example, we substitute the values u, a and t in the R.H.S. of the equation.

Changing the subject of the formula:

To change the subject of a formula, begin with the variable to become the new subject, and apply inverse operation as for solving equations in the opposite order to the order conventions. 

1. To make ‘u’ the subject of the formula in v = u + at

v - at = u + a̶t̶ - a̶t̶   [subtract at from both sides]

v - at = u

or, u = v - at

2. To make ‘t’ the subject of the formula, v = u + at,

v - u = u̶ + at - u̶   [subtract u from both sides]

v - u = at

On dividing both sides by a we get;

(v - u)/a = a̶t/a̶

or, (v - u )/a = t

or, t = (v - u)/a

Change the Subject of a Formula

Solved examples to change the subject of a formula

1. The volume of a cuboid is the product of length and breadth of the cuboid.


If l, b, h are length, breadth and height of the cuboid.

Also, if the volume is denoted by v then

V = l × b × h

or, l = V/(b × h)   Here, the subject is l.

or, b = V/(l × h)   Here, the subject is b.

or, h = V/(l × b)   Here, the subject is h.

2. In the relation C/5 = make (F - 32)/9 make F as the subject.


C/5 = (F - 32)/9

⇒ 9C/5 = F - 32

⇒ 9C/5 + 32 = F

⇒ F = 9C/5 + 32

3. Make y the subject of the formula x = (y + z)/(y - z)


x = (y + z)/(y - z)

x (y - z) = y + z   [multiply both sides by (y - z)]

xy – xz = y + z

xy - y = z + zx

y (x - 1) = z (x + 1)

y = z(x + 1)/(x - 1)

More worked-out problems to change the subject of a formula

4. Write the formula for finding the area of the rectangle and indicate the subject in this formula. Also, make l as the subject. If A = 42 cm² and b = 6 cm, then find l.


If area is denoted by A, length by l and breadth by b,
then area of the rectangle is given by A = l × b

In this formula, A is the subject.

When we change the subject, i.e., make l as the subject then the formula becomes l = A/b

In order to find the value of l, substituting the value of A and b,

we get l = 4̶2̶/6̶ cm

Therefore, length (l) = 7 cm.

5. For a right angled triangle, square of the hypotenuse (h) is equal to the sum of squares of its other two sides (p, b).

  Frame the formula for the above statement and find out h if p = 4 and
     b = 3.

  Also, make ‘p’ the subject of the formula and find p if h = 10 and
     b = 8.


From the above statement,

h² = p² + b²

When p = 4 and b = 3

h² = 4² + 3²

    = 16 + 9

h² = 25

h² = 5²

Therefore, h = 5

Changing the subject,

p² = h² - b²

p = √(h² - b²)

  = √(10² - 8²)

  = √(100 - 64)

  = √36

  = 6   [when h = 10 and b = 8]

6. In the formula, l = a + (n - 1)d make d as the subject. Find d when
l = 10, a = 2, n = 5.


d = (l - a)/(n - 1) where d is the required subject

Now, substituting the values of l, a, n in the formula;
we get, d = (10 - 2)/(5 - 1)

                = 8/4 

                = 2.


Formula and Framing the Formula

Change the Subject of a Formula

Changing the Subject in an Equation or Formula

Practice Test on Framing the Formula

 Formula - Worksheets

Worksheet on Framing the Formula

Worksheet on Changing the Subject of a Formula

Worksheet on Changing the Subject in an Equation or Formula

7th Grade Math Problems

8th Grade Math Practice

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