Percentages trip people up not because the math is hard, but because "percent" shows up in three different questions that each need a slightly different formula. Once you can spot which case you're in, the rest is easy. Here are the three — with the formula and a worked example for each.
Case 1: What is X% of a number?
This is the classic "how much is the tip / the discount / the tax" question.
Formula: (percent ÷ 100) × number
Example — 15% of 80:
(15 ÷ 100) × 80 = 0.15 × 80 = 12
So 15% of 80 is 12.
Case 2: What percent is one number of another?
Use this when you have a part and a whole and want the percentage — like a test score or a completion rate.
Formula: (part ÷ whole) × 100
Example — 18 out of 24:
(18 ÷ 24) × 100 = 0.75 × 100 = 75%
So 18 is 75% of 24.
Case 3: Percentage increase or decrease
This is the "how much did it change" question — prices, weights, followers, anything that went up or down.
Formula: ((new − old) ÷ old) × 100
Example — price rose from 50 to 65:
((65 − 50) ÷ 50) × 100 = (15 ÷ 50) × 100 = 30%
So that's a 30% increase. A negative result means a decrease.
A quick sanity check
Percentages are reversible, which makes them easy to verify:
- 15% of 80 is 12 → and 12 is 15% of 80. ✓
- A 30% increase on 50 gives 65 → and 65 is 130% of 50. ✓
One thing to watch: a 50% drop followed by a 50% rise does not bring you back to the start. Fall from 100 to 50 (−50%), then rise 50% of 50 (+25), and you land on 75, not 100. Percentages always apply to whatever the current value is.
Skip the mental math
Once you know which case you're in, the Percentage Calculator handles all three instantly — just type the numbers. For shopping math specifically, the Discount Calculator and Sales Tax Calculator are purpose-built for those exact questions.