Rearranging Formulae
• Introduction

Sometimes you are given a formula that will need to be manipulated to be useful to you.  You may have to rearrange the formula to make a different letter the subject.

Use the rules of equations (i.e. do the same to both sides) to achieve this.

Example

The formula for finding a temperature in degrees Centigrade from one in Fahrenheit is shown below.  Rearrange the formula to make F the subject.

Our aim is to get F on its own on the left hand side.

• Question 1

Rearrange the following formula to make w the subject.

v = lwh

l = vwh

w = vlh

w = v/lh

w = v/l/h

• Question 2

Rearrange the following formula to make u the subject.

v = u + at

u = v + at

u = v - at

u = v/at

u = vat

• Question 3

Rearrange the following formula to make a the subject.

v = u + at

a = v + ut

a = v - ut

a = (v - u)t

a = (v - u)/t

• Question 4

Rearrange the following formula to make c2 the subject.

a2 = b2 + c2

c² = a² + b²

c² = a² - b²

c² = b² - a²

c² = a² - b²

• Question 5

Rearrange the following formula to make c the subject.

a2 = b2 + c2

c² = a² + b²

c = √a² - b²

c = √(b² - a²)

c = √(a² - b²)

• Question 6

Rearrange the following formula to make h the subject.

A = ½bh

h = ½Ab

h = 2A/b

h = ½A/b

h = 2Ab

• Question 7

Rearrange the following formula to make h the subject.

P = 2(b + h)

h = ½Pb

h = 2P/b

h = ½P - b

h = 2P - b

• Question 8

Rearrange the following formula to make u the subject.

s = ut + ½at2

u = (s - ½at²)/t

u = v - at

u = st - 2at²

u = 2t² - ½at

• Question 9

Rearrange the following formula to make a the subject.

s = ut + ½at2

a = (s - ½at²)/t

a = sut²

a = st - 2ut²

a = 2(s - ut)/t²

• Question 10

Rearrange the following formula to make r the subject.

A = 4πr2

r = 4π/A

r = ½√π/A

r = √(A/4π)

r = √(4π/A)

Progress