Rearranging Formulae

Spec reference: Algebra - Notation, vocabulary and manipulation
Key idea: Change the subject of a formula using inverse operations.

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Changing the subject

The subject of a formula is the letter on its own on one side. To change it, use inverse operations - the same as solving an equation.

Example

Make $r$ the subject of $A=\pi r^2$

$$\frac{A}{\pi }=r^2$$$$r=\sqrt{\frac{A}{\pi }}$$

Example

Make $u$ the subject of $v=u+at$

$$u=v-at$$

Example

Make $x$ the subject of $y={\displaystyle \frac{3x+1}{x-2}}$

$$y(x-2)=3x+1$$$$xy-2y=3x+1$$$$xy-3x=2y+1$$$$x(y-3)=2y+1$$$$x=\frac{2y+1}{y-3}$$

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Common physics formulae to rearrange

Formula	Variables
$v=u+at$	velocity, initial velocity, acceleration, time
$F=ma$	force, mass, acceleration
$P=IV$	power, current, voltage
$s=\frac{d}{t}$	speed, distance, time

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Test Yourself

Question 1 of 5

Make $r$ the subject of $C = 2\pi r$