How to calculate percentages
Every percentage question is one of three shapes. Once you can spot which one you are looking at, the arithmetic is always the same.
The one rule behind everything
Percent means “per hundred”. Writing 25% is the same as writing 25/100, or 0.25. Convert the percentage to a decimal first and the rest is ordinary multiplication.
That single move — divide by 100 — turns an intimidating word problem into one line of arithmetic.
The three question shapes
Shape one: what is X% of Y? Multiply. 15% of 200 is 0.15 × 200 = 30.
Shape two: X is what percent of Y? Divide, then multiply by 100. 45 out of 180 is 0.25, which is 25%.
Shape three: what changed? Take the difference, divide by the original, multiply by 100.
Mental shortcuts worth memorising
10% is the number with the decimal point moved one place left. From there, 5% is half, 20% is double and 30% is triple.
Percentages are reversible: 8% of 50 equals 50% of 8, which is 4. Flip the numbers whenever one side is easier.
1% is the decimal moved two places, which makes odd rates like 3% or 7% quick to build up.
Put it to work