Percentages Explained: Every Formula You Actually Need
Published · 3 min read · By The Samsung Calculator editorial team
The five formulas
Percent of a number: part = percent ÷ 100 × whole. 15% of 240 is 36.
What percent is X of Y: percent = part ÷ whole × 100. 45 out of 180 is 25%.
Percentage change: change = (new − old) ÷ old × 100. From 80 to 100 is +25%.
Increase or decrease by a percentage: multiply by (1 ± percent/100). Adding 8% means multiplying by 1.08; removing 8% means multiplying by 0.92.
Reverse a percentage: original = final ÷ (1 ± percent/100). If a price is £60 after 20% off, the original was 60 ÷ 0.8 = £75.
The reverse case, worked properly
A jacket costs £60 in a 20% sale. The wrong answer is to add 20% back: 60 × 1.2 = £72. The right answer is to divide: the sale price is 80% of the original, so the original is 60 ÷ 0.8 = £75.
The difference — £3, or 4% — happens because the two percentages are taken from different bases. This is the single most common percentage error in retail, tax and invoicing, and it always favours whoever is holding the money.
Four traps
Stacked discounts do not add. 20% off then a further 10% off is 0.8 × 0.9 = 28% off, not 30%.
Percentage points are not percent. An interest rate moving from 4% to 6% is a rise of two percentage points and a 50% increase. Both are true; only one sounds dramatic, and it is the one that appears in headlines.
Falls and rises are asymmetric. A 50% loss needs a 100% gain to recover, because the base shrank.
Averaging percentages is usually wrong. Two shops with 50% and 10% margins do not average 30% unless they sell identical volumes. Weight by the base.
A sanity check that always works
Ask whether the answer should be bigger or smaller than what you started with, and roughly by how much. 15% is about a seventh; 33% is a third. If the calculator disagrees with the estimate, you divided where you should have multiplied.
Run your own numbers
The percentage calculator handles all five cases in one place, and the increase, decrease and percent-of variants each have their own page if you want the specific one.
Questions this answers
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Run your own numbers
Every common percentage question in one place: percent of a number, percent change, increase, decrease and reverse percentages.
About this article
Written and reviewed by The Samsung Calculator editorial team. Every calculator is written against a published formula, reviewed against at least one independent reference implementation, and dated when it changes. Last updated July 28, 2026. Spotted an error? Tell us.