Percentage FAQs
The questions that actually come up — formulas, the change/difference/points tangle, discounts, negative numbers, and how this calculator rounds. Every answer matches what the calculator does.
All questions
How do I calculate a percentage of a number?
Multiply and divide by 100: 15% of 200 = 200 × 15 ÷ 100 = 30. Or move the decimal — 15% is the same as multiplying by 0.15. For mental math, build from 10%: take a tenth, then scale (15% = 10% + half of 10%).
How do I express one number as a percentage of another?
Divide the part by the whole, then multiply by 100. Scoring 30 out of 150 is 30 ÷ 150 × 100 = 20%. The number after "of" goes in the denominator — swapping them is the most common slip, and it produces 500% instead of 20%.
What is the formula for a percentage increase?
Multiply by (1 + percent ÷ 100): increasing 120 by 25% is 120 × 1.25 = 150. To find an increase between two known values instead, use (new − old) ÷ old × 100. The percentage increase calculator does both.
What is the difference between percentage change and percentage difference?
Change is directional and measured against the starting value: 50 → 70 is +40%. Difference is symmetric and measured against the average of the two values: 50 vs. 70 is 33.33% either way. Use change when time flows between the numbers, difference when neither is the baseline.
What is the difference between a percent and a percentage point?
Percentage points measure the absolute gap between two percentages; percent change measures the relative one. An approval rating going 40% → 45% rose 5 percentage points but 12.5 percent. Whenever both numbers already wear a % sign, "points" is the unambiguous unit.
Can a percentage be more than 100?
Yes. 250% of 40 is 100 — percentages above 100 just mean "more than the whole." Growth above 100% means more than doubling. The only true cap is on decreases of quantities that can't go negative: a price can fall at most 100%.
How do I decrease a number by a percentage?
Multiply by (1 − percent ÷ 100): 200 decreased 15% is 200 × 0.85 = 170. Reading "15% off" as "keep 85%" turns every discount into one multiplication and makes stacked discounts impossible to get wrong.
How do I find the original number after a percentage was applied?
Divide by the multiplier that was applied. If 36 is 24% of something: 36 ÷ 24 × 100 = 150. If $54 includes 8% tax: 54 ÷ 1.08 = $50. Subtracting the percentage instead of dividing is the classic error — it uses the wrong base. The reverse percentage calculator handles both shapes.
Why doesn't a 50% gain undo a 50% loss?
The two percentages act on different bases. Lose 50% of 200 and you hold 100; gaining 50% of 100 only returns 150. Recovering a 50% loss takes a 100% gain, because the required gain is loss ÷ (1 − loss). Small losses hide this (−5% needs +5.26%); big ones make it brutal.
How do stacked discounts combine?
Multiply the pay-multipliers: 20% off then 30% off is × 0.8 × 0.7 = × 0.56, i.e. 44% off — not 50%. Shoppers reliably add sequential discounts instead, an error documented experimentally by Chen & Rao (2007); the full story is in the double-discount trap.
How do I convert a fraction or decimal to a percentage?
Multiply by 100. The decimal 0.35 is 35%; the fraction 3/8 is 3 ÷ 8 × 100 = 37.5%. Going the other way, divide by 100: 62% is 0.62. The % sign literally means "÷ 100," which is why the conversions are this clean.
How does this calculator round results?
Exact results are shown exactly — 16.5% of 3 displays 0.495, never 0.49500000000000005. Repeating decimals round half away from zero, by default at 2 places (33.33 for thirds); the .0← / .00→ buttons set a fixed precision from 0 to 8, re-rendered from the exact value so error never accumulates. One rounding step, at the very end.
Is my data private? Does the calculator work without a connection?
The math runs entirely in your browser — numbers you type never leave your device, and there are no accounts or cookies required to use it. Once a page has loaded it keeps working if your connection drops (it isn't an installable offline app; it just doesn't need the network to calculate). Details in the privacy policy.
How are negative numbers handled?
They work in every row, with one documented convention: percentage change divides by the absolute value of the start, so −50 → −25 reads +50% — the sign tracks the direction the value actually moved. Percentage difference declines opposite-sign pairs (the average base loses meaning) and points you to percentage change instead.
How accurate are the results?
Exact, up to your chosen display precision. The engine computes with exact rational arithmetic — no binary floating point ever touches a result — and a golden-value test suite locks the behavior, including the classic float traps. The methodology page describes the engine and its tests.