Find a Scale Factor Between Shapes

Find the corresponding sides

To find a scale factor between two shapes, first identify which sides match each other. The shapes must be the same type and in the same orientation, so each side in one shape has a corresponding side in the other.

Compare lengths

Write the lengths of a pair of corresponding sides as a ratio. The scale factor is the number that shows how one shape is enlarged or reduced from the other.

• If you are going from the first shape to the second, use: scale factor = second length ÷ first length
• If you are going the other way, reverse the division.

Simplify the ratio

Reduce your answer to simplest form. If the lengths are whole numbers, divide both by the same number when possible. If the ratio is a fraction, simplify it just like any other fraction.

Check your answer

Use another pair of corresponding sides to see whether you get the same scale factor. If the ratio is not the same, the sides may not match correctly.

Quick example method

1. Match a side in the first shape with a side in the second.
2. Divide the second length by the first length.
3. Simplify the result.
4. Confirm with another pair of sides.

A correct scale factor should be consistent for all corresponding sides.