5. Formulas and Literal Equations

It is very common in science and engineering to have a formula that needs re-arranging so that a variable that is originally on the right hand side becomes the subject of the formula, on the left.

In this section, we need to find an expression (involving letters and numbers) which is equal to a particular given letter. [Hence "literal" equation].

This is an important skill - you'll use it all the time in math and science (and engineering, too).

We simply solve the equation like we did in the previous Solving Equations section, by balancing both sides.

Example 1

We recall the area of a rectangle with width w and height h.

A = w × h

formula for area of a rectangle, A = wh

Express the formula in terms of the height.

Example 2

The area of a circle is given by

A = π r2

Solve for r.

Example 3

The formula for the area of a trapezoid is given by:


where h is the height of the trapezoid and x1, x2 are the lengths of the parallel sides.

Solve the formula for x1.

Example 4

The pressure in an airtight container is given by the following formula. Solve for P1:

P = 0.05(P2 P1)

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