Percentage Calculator - X% of Y, Reverse %, and Percent Change

A percentage calculator answers the six wordings people actually search, not a single vague “percent” box. Percent means “per hundred.” X% of Y is the portion (X/100)×Y. X as a percent of Y is (X/Y)×100. Reverse percentage recovers the whole when you already have a part and a rate. Percent change measures movement from A to B. Increase and decrease apply a rate to a starting number and return the new total - not only the portion.

The default on this page is the search people type most: what is 15 percent of 80? The answer is 12, because (15/100)×80 = 12. That is not the same as increasing 80 by 15% (which is 92), not the same as “12 is what percent of 80” (15%), and not the same as percent change from 80 to 12 (a 85% drop). Mixing those sentences is how discounts, tips, and exam scores get misquoted.

This free online percentage tool runs in your browser. Nothing is uploaded. Each mode prints the formula with your numbers substituted so you can copy the arithmetic into a notebook, not only the final figure. Y = 0 is rejected for “what percent of,” and A = 0 is rejected for percent change, because those formulas divide by the base.

Pick the wording that matches the question, then fill the two labeled fields:

1. What is X% of Y - portion only. Default 15 and 80 → 12.
2. X is what percent of Y - rate. Rejects Y = 0.
3. Y is X% of what number - reverse, recover the whole. Rejects X = 0.
4. Percentage change from A to B - ((B − A)/|A|)×100. Rejects A = 0.
5. Increase Y by X% - new total Y×(1 + X/100).
6. Decrease Y by X% - new total Y×(1 − X/100).

Note: results are IEEE floating-point, not exact cents in a particular currency rounding rule. For lab “how far from the true value,” use the percent error calculator, which divides by the accepted value rather than a starting amount. For a list mean rather than a percent of one number, use the average calculator.

15% means 15 per 100, which is the decimal 0.15. Then 0.15 × 80 = 12. You can also think of it as 15 × 80 / 100, same number. A 15% tip on an $80 bill is $12; sales tax at 15% on an $80 item (in a jurisdiction that works that way) is also $12 of tax, not a new total. The new total is the increase mode.

More worked portions:

• 20% of 45 = 0.20 × 45 = 9
• 8% of 250 = 0.08 × 250 = 20
• 150% of 40 = 1.5 × 40 = 60 (more than the whole)
• 0.5% of 200 = 0.005 × 200 = 1

X can be larger than 100. 200% of 50 is 100. X can be negative: −10% of 80 is −8, which is a signed portion, not a decrease-mode total. Decrease mode would return 80 × 0.9 = 72. If the homework said “take 10% off,” that is decrease, not “−10% of.”

12 is what percent of 80? (12/80)×100 = 15%. That inverts the default example. If 12 is 15% of some unknown whole, reverse: W = 12 × 100 / 15 = 80. Those two modes are inverses of “X% of Y” when the arithmetic is consistent.

Y = 0 is rejected for “what percent of” because you cannot divide by zero. “12 is what percent of 0” is not a percentage; it is undefined. X = 0 is rejected on reverse because “Y is 0% of what” would require dividing by zero. Zero percent of any finite whole is 0, which cannot uniquely recover W.

Exam scores: 42 points out of 50 is (42/50)×100 = 84%. That is not percent change and not percent error against a key. Discounts advertised as “was $80, now $68” are better as percent change (or as 68 is what percent of 80 = 85% of the original, a 15% decrease). Read the sentence before you pick the mode.

Percent change asks how far B moved relative to the starting size A. This page uses absolute value in the denominator so a negative starting value does not flip the sign of the change twice. From 50 to 75: (75 − 50) / 50 × 100 = +50%. From 80 to 12: (12 − 80) / 80 × 100 = −85%. From −20 to −10: (−10 − (−20)) / 20 × 100 = +50%.

A = 0 is rejected. Going from 0 to 10 is an infinite percent increase in the usual formula; people sometimes still want a sentence like “started at zero,” but that sentence is not a percentage. Report the absolute change (10 units) instead.

Percent change is not symmetric. +50% then −50% does not return to the start: 100 → 150 → 75. A drop of 85% followed by an 85% rise also does not undo. If you need a two-point comparison where neither value is a privileged start (two lab replicates, no “true” value), that is percent difference, not this mode and not percent error.

A 15% discount off $80 is decrease mode: $68. The $12 you save is “15% of 80.” Adding 15% tax on $80 is increase: $92. Successive discounts do not add. 20% off then 10% off is 80 × 0.8 × 0.9 = 57.6, not 30% off (which would be 56). This calculator applies one rate at a time; chain the output as the next Y if you have stacked discounts.

Treating “15% of 80” as the same as “increase 80 by 15%.” Dividing by the new number instead of the original in percent change (using B in the denominator). Adding successive percents (20% + 10% off) instead of compounding. Using percent error’s accepted-value denominator for a price change. Recovering a whole with reverse percentage after VAT when the tax was applied to a different base than you think - this tool only inverts (X/100)×W = Y; it does not model tax-inclusive versus tax-exclusive invoices beyond that algebra.

Percentages of percentages: 10% of 20% of 50 is 0.10 × 0.20 × 50 = 1, not 30% of 50. Run one mode, then feed the result into the next. Negative percents in increase mode: increasing by −15% is the same as decreasing by 15%. That is allowed mathematically; pick the wording your reader expects.

This calculator does not convert between percent, ppm, or basis points as named units, does not apply banker’s rounding to money, and does not compute compound interest over n periods (that is (1 + r)^n, not one multiply). It will happily compute 15% of −80 = −12; whether a negative whole makes sense is your problem statement. Stacked annual growth of 5% then 5% is 1.05 × 1.05 = 1.1025, a 10.25% two-year rise, not 10%. Type the first increase, copy the result into Y, then increase again - or compute 100 × (1.05^2 − 1) on a scientific calculator if you want the compound percent in one shot. This page stays one rate at a time so the formula on screen still matches a single homework sentence.

Rounding for money is a policy, not a math identity. 18% of $33.33 is 5.9994 before a cashier rounds to $6.00. IEEE will show 5.9994 or 6 depending on the inputs’ binary representation. For a gradebook that stores one decimal, round after you copy, using the syllabus rule, not this display’s twelve significant digits. Negative Y in decrease mode (decrease −50 by 10%) is −45, which is moving toward zero; that may or may not be the loss you meant.

Retail language collides with homework language. Markup is often (price − cost) / cost × 100, which is percent change from cost to price - this page’s change mode with A = cost and B = price. Margin is (price − cost) / price × 100, which is “the dollar profit is what percent of the selling price.” Those two percents are not interchangeable. A $40 cost sold at $50 is a 25% markup and a 20% margin. Using “what is X% of Y” on the selling price does not recover markup.

If a buyer says “give me 15% off the $50 ticket,” that is decrease mode: 50 × 0.85 = 42.50. If they say “what is 15% of $50?” they might only want the discount amount, $7.50. Ask which sentence they meant. Reverse percentage recovers a ticket price from a discounted total only when you know the rate: $42.50 is 85% of the original, so original = 42.50 × 100 / 85 = 50. That is reverse mode with X = 85 and Y = 42.50, not X = 15.

Basis points are 0.01 percent each: 25 bp = 0.25%. This calculator does not have a basis-point unit. Type 0.25 as X% if that is the rate. Percentage points are the subtraction of two percents (turnout went from 40% to 45%, a rise of 5 percentage points, which is a 12.5% percent change relative to 40). Mixing “points” and “percent change” is a classic news-story error.

Maya earns $2,400 and gets a 4% raise. Increase mode: 2400 × 1.04 = $2,496. The raise itself is 4% of 2400 = $96. After the raise, a 4% cut does not return to $2,400: 2496 × 0.96 = $2,396.16. Percent change from 2496 to 2396.16 is −4% relative to the new base, but the dollar path is not symmetric. Quote both dollars and percents when a contract is involved.

A restaurant bill is $64 before tip. 18% of 64 = 11.52 (portion). Increase 64 by 18% = 75.52 (what you pay if you tip on the pre-tax amount). If tax is already 8% on the $64, tax is 5.12 and the taxed bill is 69.12; tipping 18% on the post-tax total is 69.12 × 1.18 ≈ 81.56, which is a different custom. This tool will compute whichever pair you type; it will not read a receipt’s tax policy.

A quiz is 21 out of 25: 21 is what percent of 25 = 84%. If the syllabus says the quiz is 10% of the course, that 84% still has to be weighted 0.10 in an average - not multiplied by 10% a second time as if it were 8.4 course points unless your gradebook literally stores that. Weighted means belong on the average calculator. Reverse check: 84% of 25 should return 21, which is “what is X% of Y” with X = 84 and Y = 25.

Population 8,000 grows 12% then falls 12%: 8000 × 1.12 = 8960, then 8960 × 0.88 = 7884.80, below the start. Percent change from 8000 to 7884.80 is about −1.44%, not zero. Any “up X% then down X%” story that claims a wash is using the wrong base on the way down. The same pattern appears in sale-then-coupon stacking and in reversing a bonus that was later clawed back at the same advertised percent.

A part-to-whole that is already a fraction can be converted after you finish exact arithmetic. 5/6 of a class is (5/6)×100 ≈ 83.333% on this page’s IEEE preview. Keep 5/6 if the attendance sheet is 25 of 30 students; 25 is what percent of 30 is 83.333…%, and reverse 83.333…% of 30 will not land on an integer 25 if you paste a rounded 83.3. Prefer whole counts in the “X is what percent of Y” mode when you still have the counts.