The percentage calculator: every % problem, one blackboard.
Five ways people actually use percentages — type your numbers into the sentence and read the answer off the board.
Percent of a number
= 30
Reverse: what percent?
= 15%
Percentage change
= +25% increase
Increase / decrease by %
= 204
Find the whole
= 200
The five formulas, with real examples
Percent of a number
result = number × percent ÷ 100
15% of €200 restaurant bill as a tip → €30.
What percent is X of Y
percent = part ÷ whole × 100
450 points out of 625 in the Leaving Cert → 72%.
Percentage change
change = (new − old) ÷ old × 100
Rent going from €1,600 to €1,800 → +12.5%.
Increase / decrease by percent
result = number × (1 ± percent ÷ 100)
€59.99 jacket at 25% off → €44.99.
Find the whole (reverse)
whole = part ÷ (percent ÷ 100)
€46 VAT at 23% means the net price was €200.
Quick mental shortcuts
No board handy? Chain these and you can do most percentages in your head.
10%
move the decimal one place left: 10% of €84 is €8.40
5%
half of 10%: 5% of €84 is €4.20
1%
move the decimal two places: 1% of €84 is €0.84
15%
10% + 5%: 15% of €84 is €12.60
20%
double 10%: 20% of €84 is €16.80
25%
divide by 4: 25% of €84 is €21
33%
divide by 3 (near enough): a third of €84 is €28
50%
halve it: 50% of €84 is €42
Questions people ask
Multiply the number by the percentage and divide by 100. For example, 15% of 200 is 200 × 15 ÷ 100 = 30. Or move the decimal: 10% of 200 is 20, 5% is 10, so 15% is 30.
Divide the part by the whole and multiply by 100. If you got 30 marks out of 200, that’s 30 ÷ 200 × 100 = 15%.
Take the difference between the new and old value, divide it by the old value, then multiply by 100. Going from €80 to €100 is (100 − 80) ÷ 80 × 100 = +25%. Going from €100 to €80 is −20% — the change is measured from where you started, which is why the two answers differ.
Multiply the price by (100 − discount) ÷ 100. A €59.99 jacket at 25% off is 59.99 × 0.75 = €44.99. Use the "decrease by %" card above and it’s done for you.
It’s working backwards: you know the final amount and the percentage, and you want the original. If a price of €138 already includes a 15% increase, the original was 138 ÷ 1.15 = €120 — dividing, not subtracting 15%, is the key step people get wrong.
Because the base changes. €100 increased by 50% is €150, but €150 decreased by 50% is €75, not €100. Percentage changes always apply to the current value, not the original one.