Solve the three most common percent problems instantly, right in your browser
In plain terms: it answers the three percent questions people ask most. What is X% of a number? (a tip, a discount, a tax amount). What percent is one number of another? (a test score, a share of a budget). And what is the percentage increase or decrease between two values (this month versus last, a price rise or a markdown). Type your numbers into the matching box and read the answer instantly. Everything runs in your browser — nothing you type is uploaded or stored.
Percentage calculator solves the three most common percent questions instantly — percent of a number, percent change, and what percent one number is of another. Whether you are working out a discount at the checkout, adding sales tax, checking a test score, or comparing this month's revenue to last month's, the underlying math is always the same handful of formulas. This page gives you a fast tool for each of those problems and then explains exactly how each one works, so you can also do the calculation by hand or in your head when you need to.
The word "percent" literally means "per hundred", so a percentage is simply a way of expressing a fraction with a denominator of 100. When you say 25%, you are saying 25 out of every 100, which is the same as the fraction 25/100 or the decimal 0.25. Almost every percentage problem reduces to a single core relationship: the part divided by the whole, multiplied by 100. Once that idea clicks, every other percentage question becomes a rearrangement of the same equation.
The foundation of all percentage math is: percentage = (part ÷ whole) × 100. From this one relationship you can derive everything else. If you know the whole and the percentage and want the part, you rearrange to get part = (percentage ÷ 100) × whole. If you know the part and the whole and want the percentage, you use the formula as written. And if you want to compare two values to see how much one grew or shrank relative to the other, you treat the change as the part and the original value as the whole.
The calculator above is split into three mini tools because, in practice, nearly every real-world percentage question is one of these three shapes. Understanding which shape you are facing is half the battle; once you recognize it, the formula is automatic.
Problem 1 — What is X% of Y? This is the "find the part" problem. You know a percentage and a total, and you want the amount that percentage represents. The formula is (X ÷ 100) × Y. For example, to find 20% of 150 you compute (20 ÷ 100) × 150 = 0.20 × 150 = 30. This is the calculation behind tips, discounts, tax amounts, and commission. If a restaurant bill is $84 and you want to leave an 18% tip, you compute (18 ÷ 100) × 84 = $15.12.
Problem 2 — X is what percent of Y? This is the "find the percentage" problem. You have two raw numbers and you want to express one as a percentage of the other. The formula is (X ÷ Y) × 100. If you answered 45 questions correctly out of 60, your score is (45 ÷ 60) × 100 = 75%. If your team closed 12 of 40 leads, that is (12 ÷ 40) × 100 = 30%. The key is identifying which number is the part and which is the whole — the whole is the total or reference amount, and the part is the piece you are measuring against it.
Problem 3 — Percentage increase or decrease. This is the "find the change" problem, and it trips people up more often than the first two. You have an original value and a new value, and you want to know how much it changed in relative terms. The formula is ((new − old) ÷ |old|) × 100. A positive answer is an increase; a negative answer is a decrease. If a stock moves from $80 to $100, the change is ((100 − 80) ÷ 80) × 100 = 25% increase. If it later falls from $100 back to $80, the change is ((80 − 100) ÷ 100) × 100 = −20%, a 20% decrease. Notice that a 25% rise followed by a 20% fall returns you to the start — the percentages differ because they are measured against different starting points.
One of the most counter-intuitive things about percentages is that increases and decreases of the "same size" are rarely symmetrical. The reason is that the percentage is always measured relative to the starting value, and the starting value changes. The table below shows several price movements and the resulting percentage change so you can see the asymmetry directly.
| Original Value | New Value | Absolute Change | Percentage Change | Direction |
|---|---|---|---|---|
| $80 | $100 | +$20 | +25% | Increase |
| $100 | $80 | −$20 | −20% | Decrease |
| $50 | $75 | +$25 | +50% | Increase |
| $200 | $150 | −$50 | −25% | Decrease |
| $40 | $40 | $0 | 0% | No change |
| $120 | $240 | +$120 | +100% | Doubled |
The first two rows tell the whole story: the same $20 swing between $80 and $100 is a 25% increase going up but only a 20% decrease coming down, because on the way up the base is 80 and on the way down the base is 100. Whenever you read that something "recovered its losses", remember that the recovery percentage must be larger than the loss percentage to get back to even.
A frequent source of confusion — especially in news and finance — is the difference between a "percentage point" and a "percent". A percentage point is the simple arithmetic gap between two percentages. A percent change is the relative difference between them. These are not the same number, and mixing them up can make a small change sound dramatic or a large change sound trivial.
Suppose an interest rate rises from 4% to 5%. The plain difference is 5 − 4 = 1 percentage point. But the relative change is ((5 − 4) ÷ 4) × 100 = 25 percent. Both statements are correct, and both describe the same event, but they mean very different things. When a headline says a rate "rose 25%", it may mean it went from 4% to 5% (a relative rise) rather than from 4% to 29% (an absolute rise of 25 points). Whenever precision matters, state explicitly whether you mean points or percent.
| Old Rate | New Rate | Change in Percentage Points | Percent (Relative) Change |
|---|---|---|---|
| 4% | 5% | +1 point | +25% |
| 10% | 12% | +2 points | +20% |
| 50% | 45% | −5 points | −10% |
| 2% | 3% | +1 point | +50% |
Percentages show up constantly in daily life, and being quick with them saves both money and mistakes. Here are some of the most common situations where these three calculators apply:
Reversing a percentage — finding the original value before an increase or decrease was applied — is where many people slip up. The instinctive move is to subtract the same percentage back, but that gives the wrong answer because the percentage was applied to a different base than the one you now have.
Suppose a receipt total of $120 already includes 20% tax and you want the pre-tax price. The wrong approach is to take 20% off $120 (which gives $96). The correct approach is to divide by the multiplier: since the total is 120% of the original, the original is 120 ÷ 1.20 = $100. To check: 20% of $100 is $20, and $100 + $20 = $120. It works.
The same logic reverses discounts. If a jacket is on sale for $75 after a 25% discount, it originally sold for 75 ÷ 0.75 = $100, because the sale price is 75% of the original. The general rule is: to undo an increase of p%, divide by (1 + p ÷ 100); to undo a decrease of p%, divide by (1 − p ÷ 100). Whenever you need the "before" number and you only have the "after" number, reach for division rather than subtraction.
You do not always need a calculator. A few mental shortcuts cover most everyday cases. To find 10% of anything, move the decimal point one place to the left — 10% of 240 is 24. From there you can build almost any percentage: 5% is half of 10%, 20% is double 10%, and 15% is 10% plus half of 10%. To find 1%, move the decimal two places left. Combining these, 17% of 300 is 10% (30) + 5% (15) + 2% (6) = 51. With a little practice these steps become fast enough to do while standing at a register or reading a report.
Each of the three mini-calculators answers a different question, so read its result in the shape of that question:
A common trap is confusing a change in percentage points with a change in percent. If a rate moves from 4% to 5%, that is a rise of one percentage point but a 25% relative increase. When the numbers you are comparing are themselves percentages, say explicitly which one you mean. And when you only have the "after" number and need the "before" — a pre-tax price, or an original price behind a sale tag — reverse the percentage by dividing rather than subtracting (see the worked examples below).
Here is one fully worked example of each problem type, plus a reverse-percentage example that trips many people up.
These three calculators cover almost every percentage you meet in daily life. A few of the most common:
A quick reference for the terms used on this page:
Each tool uses a standard percentage formula computed directly in your browser: (X ÷ 100) × Y for percent of a number, (part ÷ whole) × 100 for what percent one number is of another, and ((new − old) ÷ |old|) × 100 for percentage change. Division by zero is blocked (the whole and the original value cannot be zero), and results are rounded to at most four decimal places with trailing zeros trimmed for readability. The math is exact within normal floating-point precision, and nothing you enter is sent to a server or stored.
Formulas and guidance last reviewed July 2026. The percentage formulas used here are standard arithmetic and do not change over time.
Working with percentages often leads to a money question. These free, private calculators pair naturally with percentage math:
A percentage expresses a part out of one hundred. To find what percent one number is of another, divide the part by the whole and multiply by 100: (part ÷ whole) × 100. For example, 30 out of 120 is (30 ÷ 120) × 100 = 25%. To go the other way and find a part from a percent, divide the percent by 100 and multiply by the whole: (percent ÷ 100) × whole. These two formulas cover almost every everyday percentage problem.
Convert the percent to a decimal by dividing by 100, then multiply by the number. The formula is (X ÷ 100) × Y. For example, 20% of 150 is (20 ÷ 100) × 150 = 0.20 × 150 = 30. A quick mental shortcut for 10% is to move the decimal one place left (10% of 150 = 15), then scale up or down from there — 20% is double that, and 5% is half.
Divide the first number (the part) by the second number (the whole), then multiply by 100. The formula is (part ÷ whole) × 100. For example, if you scored 45 out of 60 on a test, that is (45 ÷ 60) × 100 = 75%. If you spent $18 out of a $200 budget, that is (18 ÷ 200) × 100 = 9%. Make sure the whole is not zero, because dividing by zero is undefined.
Subtract the original value from the new value, divide by the original value, and multiply by 100. The formula is ((new − old) ÷ |old|) × 100. A positive result is an increase and a negative result is a decrease. For example, a price rising from $80 to $100 is ((100 − 80) ÷ 80) × 100 = 25% increase. A price falling from $100 to $80 is ((80 − 100) ÷ 100) × 100 = −20%, a 20% decrease. Note that the same dollar change gives a different percentage depending on the starting value.
A percentage point is the plain arithmetic difference between two percentages, while a percent change describes the relative difference. If an interest rate rises from 4% to 5%, that is an increase of 1 percentage point, but it is a 25% increase in relative terms ((5 − 4) ÷ 4 × 100). Confusing the two is one of the most common mistakes in news reports and financial writing, so it is worth stating explicitly which one you mean.
To add a percentage, multiply the number by (1 + percent ÷ 100). To subtract, multiply by (1 − percent ÷ 100). For example, adding 15% tax to $40 gives 40 × 1.15 = $46. Taking 25% off a $60 item gives 60 × 0.75 = $45. This single-step multiplier method is faster and less error-prone than calculating the percentage separately and then adding or subtracting it.
If a value already includes an added percentage, divide by (1 + percent ÷ 100) to recover the original. For example, if a total of $120 already includes 20% tax, the pre-tax amount is 120 ÷ 1.20 = $100. To reverse a discount, divide by (1 − percent ÷ 100): a sale price of $75 after a 25% discount came from 75 ÷ 0.75 = $100. A common mistake is subtracting the same percentage back, which does not return the original because the percentage was applied to a different base.
Yes. The calculator uses the standard percentage formulas — (X ÷ 100) × Y, (part ÷ whole) × 100, and ((new − old) ÷ |old|) × 100 — and computes them directly in your browser using JavaScript. Results are rounded to a sensible number of decimal places with trailing zeros trimmed for readability, but the underlying math is exact within normal floating-point precision. Nothing is sent to a server, so your numbers stay private on your device.
Divide by the multiplier rather than subtracting the percentage back. If a value already includes an increase of p%, the original is the current value divided by (1 + p ÷ 100); if it reflects a decrease of p%, divide by (1 − p ÷ 100). For example, an item that costs $80 after a 20% discount originally sold for 80 ÷ (1 − 0.20) = 80 ÷ 0.80 = $100, and a $120 total that already includes 20% tax came from 120 ÷ 1.20 = $100. Subtracting the same percentage from the "after" number gives the wrong answer, because that percentage was applied to a different, larger base.
A percentage point is the plain arithmetic difference between two percentages, while a percent change is the relative difference between them. If an interest rate rises from 4% to 5%, that is an increase of 1 percentage point, but a 25% increase in relative terms, because ((5 − 4) ÷ 4) × 100 = 25%. The two are easy to confuse and can make a change sound larger or smaller than it is, so when both numbers are themselves percentages, state explicitly whether you mean points or percent.
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