Percent Change

Percent change measures how much a value has increased or decreased relative to its original value, expressed as a percentage.

What Is Percent Change?

Percent change tells you how much something grew or shrank compared to the original.

\%\text{ change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100

Positive result = increase. Negative result = decrease.

A plant was 20 cm tall. It grew to 25 cm.

$\%\text{ increase} = \frac{25 - 20}{20} \times 100 = \frac{5}{20} \times 100 = 25\%$

A shirt cost €40. It is now €28.

$\%\text{ decrease} = \frac{40 - 28}{40} \times 100 = \frac{12}{40} \times 100 = 30\%$

Warning Always divide by the original value, not the new one.

If you know the percent change, you can find the new value directly:

$\text{New} = \text{Old} \times (1 \pm \frac{P}{100})$

A store raises a €45 item by 8%. What is the new price?

$\text{New price} = 45 \times 1.08 = 48.60\text{ EUR}$

Real world: smartphone price drop

A phone that cost €500 is now selling for €425.

$\% \text{ decrease} = \frac{500 - 425}{500} \times 100 = \frac{75}{500} \times 100 = 15\%$

Shoppers use this calculation to judge whether a "sale" is a genuine deal or just clever marketing.

Real world: town population growth

A town's population grows from 20,000 to 23,000.

$\% \text{ increase} = \frac{23\,000 - 20\,000}{20\,000} \times 100 = \frac{3\,000}{20\,000} \times 100 = 15\%$

Local councils use percentage growth figures to plan new schools, roads, and housing.

Real world: pay rise

A worker's hourly wage rises from €8.00 to €9.20.

$\% \text{ increase} = \frac{9.20 - 8.00}{8.00} \times 100 = \frac{1.20}{8.00} \times 100 = 15\%$

Pay negotiations, employment contracts, and tax forms all express wage changes as percentages.

A temperature rose from 10°C to 14°C. What is the percent increase?

Show answer

(14 − 10) / 10 × 100 = 40%.

After a 25% discount, a game costs €30. What was the original price?

Show answer

30 / 0.75 = €40.