Convert 90° to radians

Step by step

The question

Question: change 90° to radians.

1 Write the rule

Radians are another way to measure an angle.

A half turn is 180°.

In radians, a half turn is π.

So 180° = π.

We divide both sides by 180.

One degree is π/180.

Careful!

To get radians, π must end up in the answer.

So π goes on top.

2 Multiply

90° is 90 times one degree.

So we multiply 90 by π/180.

Top times top: 90π.

The bottom stays 180.

3 Make it simpler

90 and 180 can both be divided by 90.

It is the biggest number that goes into both.

90 ÷ 90 is 1.

180 ÷ 90 is 2.

So 90° = π/2 radians.

4 Check

Let's check: go back to degrees.

Times 180° over π: the πs cancel.

We get 90° again: the angle we started with.

So it is right!

Let's look back.

First: write the rule.

Then: multiply.

Then: make it simpler.

Last: check.