Calculate percent of a number, what percent X is of Y, and percentage change between two values.
20% of 150 equals 30.
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Pick "Percent of", "Is what percent of" or "Percent change" depending on the question. Each mode uses a different formula, so the mode you choose decides what your two inputs mean.
Type your first number. In "Percent of" this is the rate (e.g. 18 for 18%). In "Is what %" this is the part (e.g. 30). In "Percent change" this is the original value (e.g. 80).
Type your second number. In "Percent of" this is the base (e.g. 54). In "Is what %" this is the whole (e.g. 200). In "Percent change" this is the new value (e.g. 96).
The headline shows the answer to your specific question. The worked formula directly below it walks through the calculation so you can verify and learn the pattern for next time.
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A percentage is a number expressed as a fraction of 100. The word literally means "per hundred" (Latin: per centum). So 25% = 25/100 = 0.25 = one quarter. Percentages let us compare quantities of different sizes on a common scale — a $50 discount means very different things on a $100 item vs a $5,000 item, but "50% off" vs "1% off" tells you the relative weight instantly. This calculator handles the three universal percent operations: percent-of (multiplication), is-what-percent (division − percentage) and percent-change (difference — original — 100). All three are mathematically simple, but mixing them up is the most common percent mistake. Always identify which question you are answering before you compute.
"Percent of" multiplies a rate (as decimal) by a base value: 18% of 54 = 0.18 × 54 = 9.72. "Is what percent of" inverts: 30 out of 200 = 30/200 = 0.15 = 15%. Percent change measures direction and magnitude relative to the starting value: from 80 to 96 = (96−80)/80 = 0.20 = +20%. A positive percent change is an increase; a negative one is a decrease. The denominator is always the original (older) value.
Question: What is 18% of $54?
18% × $54 = 0.18 × 54 = $9.72
Your total bill is $54 + $9.72 = $63.72. If splitting between 3 people, each pays $63.72 — 3 = $21.24.
Question: $30 is what percent of $200?
(30 ÷ 200) × 100 = 0.15 — 100 = 15%
So the jacket is 15% off. To verify: 15% of $200 = 0.15 × $200 = $30 ?.
Question: What is the percent change from $80 to $96?
((96 - 80) ÷ 80) × 100 = (16 ÷ 80) × 100 = 0.20 × 100 = +20%
The stock gained 20%. Note that if it then fell from $96 back to $80, the percent change would be ((80 - 96) ÷ 96) × 100 = −16.67%. A 20% gain followed by a 16.67% loss puts you back to where you started — percent gains and losses are asymmetric.
Multiply the number by X/100 (or X as a decimal). 20% of 150 = 0.20 × 150 = 30. Quick trick: "X% of Y" equals "Y% of X" — so 20% of 150 is the same as 150% of 20 = 30. Use whichever direction is easier to do in your head.
They measure different things. If a tax rate goes from 10% to 12%: in percentage-point terms it rose by 2 points; in percent-change terms it rose by 20% ((12−10)/10). News headlines often mix these — be precise when it matters financially.
If a final price of $84 already includes a 20% markup, the original is 84 × 1.20 = $70. If $84 is what is left after a 20% discount, the original is 84 × 0.80 = $105. Always divide by the multiplier (1+rate or 1?rate), never subtract a percent of the final price.
Each discount applies to the already-reduced price. 20% off then 10% off = 0.80 × 0.90 = 0.72 = 28% off the original — not 30%. For three stacked discounts (e.g. 10/20/30), the combined rate is 1 ≈ 0.90 × 0.80 × 0.70 = 1 − 0.504 = 49.6% off — not 60%.
It is always larger than the loss. If you lose 20%, you need 25% to recover (because 0.80 × 1.25 = 1.0). Formula: required gain = loss / (1 − loss). A 50% loss needs a 100% gain. A 90% loss needs a 900% gain. This is "asymmetric loss math" and is critical in investing.
Divide top by bottom, multiply by 100. 3/4 = 0.75 × 100 = 75%. Quick checks: 1/2 = 50%, 1/3 = 33.3%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, 1/10 = 10%.
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