How to calculate percentages

Almost every percentage problem you’ll ever meet is one of three questions in disguise: what is X% of a number, what percent is one number of another, and how much did something change by. Spot which one you’re facing and the calculation is a single step. The confusion people run into isn’t the maths — it’s not knowing which of the three questions they’re actually being asked.

What is X% of a number

Divide the percentage by 100, then multiply by the number. 20% of 150 means 20 ÷ 100 = 0.2, and 0.2 × 150 = 30. The division turns the percentage into a plain multiplier — a fraction of one — and the multiplication applies that fraction to whatever you’re measuring.

Nothing stops the percentage from passing 100. 150% of 40 works exactly the same way: 150 ÷ 100 = 1.5, and 1.5 × 40 = 60. A percentage above 100 just means “more than the whole thing” — 150% of a number is that number plus half of it again. This is the same step you’d use for a tip, a tax, or a discount rate; only the label on the answer changes.

What percent is A of B

This is the reverse question: instead of being given a percentage and a number, you’re given two numbers and asked how one relates to the other as a percentage. Divide A by B, then multiply by 100. Thirty is what percent of 150? 30 ÷ 150 = 0.2, and 0.2 × 100 = 20%.

The part that trips people up isn’t the division — it’s deciding which number is B. B is always the whole, the total, the starting point: the thing everything else is measured against. Ask “of what?” before you calculate anything. Thirty as a percentage of 150 is 20%, but thirty as a percentage of a different total would give a completely different answer. The denominator is the choice that decides the result; get it wrong and the arithmetic that follows is correct but meaningless.

Adding and removing a percentage

To increase a number by a percentage, add that percentage’s value to the original. 200 increased by 15% is 230: 15% of 200 is 30, and 200 + 30 = 230. To decrease, subtract instead: 200 decreased by 15% is 170, because you take that same 30 away.

Here’s the honest warning: removing a percentage is not the mirror image of adding it. Increasing 200 by 15% gets you to 230 — but decreasing 230 by 15% does not bring you back to 200. Each percentage change is calculated on whatever number you’re currently standing on, not on the original figure, so a rise and a fall of the same percentage never fully cancel out. Working backwards from a changed figure to the number it started from is a different calculation, built around this same asymmetry.

Doing them in your head

Most percentages you meet day to day can be built from three moves, without a calculator.

• 10%: move the decimal point one place left. 10% of 200 is 20.
• 5%: take your 10% figure and halve it. 5% of 200 is 10.
• 1%: move the decimal point two places left — a hundredth of the number. 1% of 200 is 2.

Once you have those three, almost any percentage is addition. Need 15%? That’s 10% plus 5%. Need 20%? Double your 10%. Need 3%? Triple your 1%. The percentages themselves stay fixed — 10%, 5%, 1% — but combining them covers the great majority of everyday calculations without reaching for anything more than the number you started with.

These are the same mechanics behind fractions and decimals, percentage change, and the percentage calculator: one core operation, applied to whichever of the three questions you’re actually answering.