How to Calculate Percentages: The Only 3 Formulas You Need

Percentages show up everywhere — discounts, tips, taxes, pay rises, statistics — yet most of us only half-remember the rules from school. The good news: every percentage problem you'll ever meet is one of just three types. Master these and you're done.

Formula 1: What is X% of a number?

Multiply the number by the percentage divided by 100.

What is 15% of 80? 80 × (15 ÷ 100) = 80 × 0.15 = 12

This is the one you use for tips, discounts, and taxes. A €60 dinner with a 15% tip? 60 × 0.15 = €9. A quick mental shortcut: find 10% (move the decimal one place left), then scale. 10% of 80 is 8, half of that is 4, so 15% is 8 + 4 = 12.

Formula 2: Percentage change (increase or decrease)

Divide the difference by the original value, then multiply by 100.

Your rent went from €800 to €920. (920 − 800) ÷ 800 × 100 = 120 ÷ 800 × 100 = 15% increase

The classic mistake is dividing by the new value instead of the original — that would give 13%, which is wrong. The original value is always the reference point.

Watch out for the asymmetry this creates: if a stock drops 50% and then rises 50%, you are not back where you started. €100 → €50 → €75. A 50% loss needs a 100% gain to undo. This trips up even experienced investors.

Formula 3: Reverse percentages (finding the original)

Divide the final amount by (1 + rate) for increases, or (1 − rate) for decreases.

A jacket costs €68 after a 15% discount. What was the original price? 68 ÷ (1 − 0.15) = 68 ÷ 0.85 = €80

The trap here is adding 15% back to €68 — that gives €78.20, not €80, because the 15% was taken from the original price, not the discounted one. Reverse percentages are exactly how you extract the pre-tax price from a receipt: a €121 total with 21% VAT was 121 ÷ 1.21 = €100 before tax — our VAT calculator does this in both directions.

Percentage points vs percentages

If interest rates go from 2% to 3%, that's a rise of 1 percentage point but a 50% increase. News headlines regularly blur this distinction, which makes changes sound bigger or smaller than they are. When someone quotes a percentage change of a percentage, always check which one they mean.

Skip the mental math

All three formulas (and a few more, like "X is what percent of Y") are built into our percentage calculator. For shopping specifically, the discount calculator stacks coupon-style discounts correctly, and if you're working with fractions or ratios instead, the fraction calculator and ratio calculator convert between all three forms.

Quick reference

Bookmark this, and the next sale rack or restaurant bill will never slow you down again.