How to calculate percentages

A percentage is a fraction out of 100. Saying 25% is the same as saying 25 out of every 100, or 0.25 as a decimal. Every percentage problem is some version of comparing a part to a whole.

Keeping the three pieces straight — the part, the whole and the percentage — makes most problems easy. If you know any two, you can find the third.

Divide the part by the whole and multiply by 100. If 25 of your 200 customers renewed, the renewal rate is 25 ÷ 200 × 100 = 12.5%.

The part can be larger than the whole. 300 out of 200 is 150%, which simply means the part is one and a half times the whole.

Convert the percentage to a decimal and multiply. 15% of 80 is 0.15 × 80 = 12. This is the calculation behind discounts, tips and sales tax.

To add a percentage, multiply by 1 plus the decimal: a price of 80 with 15% added is 80 × 1.15 = 92. To subtract it, multiply by 1 minus the decimal: 80 × 0.85 = 68.

Percentage change is (new − old) ÷ old × 100. Going from 50 to 65 is a 30% increase. Going from 65 back to 50 is only a 23.1% decrease, because the base is different.

Do not add or subtract percentages that apply to different bases. A 20% discount followed by another 20% discount is 36% off in total, not 40%, because the second discount applies to the already reduced price.