Percentage Calculator
25% of 80 is 20, and 45 is 25% of 180. Use this percentage calculator when you need to solve the three percentage questions people ask most often: what is A% of B, A is what percent of B, and percent change from one value to another. Enter two numbers, pick the matching mode, and the tool returns the result without forcing you to rearrange formulas in your head. Percentage math shows up in discounts, tips, grades, survey results, price changes, and performance reports. The page explains each mode in plain language so you can tell when you need a part of a whole, when you need a ratio expressed as a percent, and when you need a growth or decline rate from an original value.
Quick answer
Use Percent Of when the percent is already known and you want the amount. A question like 18% of 250 fits this mode because the percent and base value are given upfront.
What this tells you
- •Use Percent Of when the percent is already known and you want the amount. A question like 18% of 250 fits this mode because the percent and base value are given upfront.
- •Use Is What Percent when you know the part and the whole. A question like 30 out of 120 asks for the share of the whole, so the answer needs to be converted into percent form.
- •Use Percent Change when you compare an old value with a new value. Positive results mean growth, while negative results mean the new value is lower than the starting value.
- •The formula tool rounds the displayed result to 4 decimal places, which is usually more than enough for school, shopping, budgeting, and quick business checks.
- •Percent change needs a non-zero starting value because the original value sits in the denominator. If the old value is 0, the growth rate is undefined in standard percentage math.
- •A percent is a rate out of 100. That is why moving between decimals and percentages often means multiplying or dividing by 100.
How to Use
- 1Choose the calculation mode that matches the wording of your question. Pick Percent Of for a portion, Is What Percent for a ratio, or Percent Change for movement from an old value to a new one.
- 2Enter A and B using the labels shown in the mode selector. In Percent Of mode, A is the percent and B is the base number. In Is What Percent mode, A is the part and B is the whole. In Percent Change mode, A is the old value and B is the new value.
- 3Click Calculate to generate the result. The tool applies the matching formula automatically, so you do not need to rewrite the numbers as fractions or decimals first.
- 4Read the sign of the answer carefully in Percent Change mode. A positive value means increase, while a negative value means decrease from the original amount.
- 5If you are using the answer for pricing, reporting, or homework, keep the raw numbers nearby and do a quick reasonableness check. For example, 10% of a number should be much smaller than the base value, and a drop from 240 to 198 should not come out as a positive change.
How It Works
Formula
Percent Of: (A/100) x B. Is What Percent: (A/B) x 100. Percent Change: ((B-A)/A) x 100Each mode answers a different percentage question. Percent Of converts the percent into a fraction of 100, then applies it to the base number. If A is 20 and B is 250, the math is (20/100) × 250 = 50. Is What Percent divides the part by the whole, then multiplies by 100 to express the ratio as a percent. If A is 45 and B is 180, the result is (45/180) × 100 = 25%. Percent Change compares the difference between the new value and the old value against the old value. If A is 80 and B is 100, the change is ((100 - 80)/80) × 100 = 25%. In this tool, A is the old value and B is the new value for percent change, so reversing them flips the sign and changes the meaning.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Find 20% of 250
Use Percent Of because the percent is already known. Divide 20 by 100 to get 0.2, then multiply by 250. The result is 50, which means 20% of 250 is 50.
Find what percent 45 is of 180
Use Is What Percent because 45 is the part and 180 is the whole. Divide 45 by 180 to get 0.25, then multiply by 100. The answer is 25%, so 45 represents one quarter of 180.
Measure an increase from 80 to 100
Use Percent Change with 80 as the old value and 100 as the new value. The difference is 20, and 20 divided by 80 is 0.25. Multiply by 100 to get 25%, which means the new value is 25% higher than the original.
Measure a decrease from 240 to 198
Use Percent Change again, but expect a negative result because the new value is smaller. The change is 198 - 240 = -42. Divide -42 by 240 to get -0.175, then multiply by 100. The result is -17.5%, which means a 17.5% decrease.
Calculate 12.5% of 64
Use Percent Of for a fractional percentage. Convert 12.5% to 0.125, then multiply by 64. The result is 8, which is a common mental-math checkpoint because 12.5% equals one eighth.
Three questions about one standing desk purchase
Maya finds a standing desk listed at $480 with a 15% coupon. Step 1 uses Percent Of: 15% of 480 is 72, so she pays 480 - 72 = $408. Step 2 reverses the check with Is What Percent: 408 is 85% of 480, which confirms the coupon took exactly 15% off. Step 3 uses Percent Change to compare the list price with last year's $450 tag: (480 - 450) / 450 x 100 = 6.6667%, so the desk cost about 6.7% more before the coupon than it did a year ago.
Fractions, decimals, and percents that come up constantly
The same value written three ways. Percent means per hundred, so the percent column is the decimal column multiplied by 100. Repeating decimals are shown rounded to 4 places, which is also how the calculator displays them.
| Fraction | Decimal | Percent | Quick check |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half. 50% of 80 is 40. |
| 1/3 | 0.3333 (the 3 repeats) | 33.3333% (repeating) | Entering 33.3333% of 80 returns 26.6666, while the exact third is 26.6667 |
| 2/3 | 0.6667 (0.6666 repeating, rounded) | 66.6667% (rounded) | Two thirds. 66.6667% of 80 returns 53.3334, the exact value is 53.3333. |
| 1/4 | 0.25 | 25% | A quarter. 25% of 80 is 20. |
| 3/4 | 0.75 | 75% | Three quarters. 75% of 80 is 60. |
| 1/5 | 0.2 | 20% | A common tip and discount rate. 20% of 80 is 16. |
| 1/8 | 0.125 | 12.5% | An eighth. 12.5% of 64 is 8. |
| 3/8 | 0.375 | 37.5% | Three eighths. 37.5% of 80 is 30. |
| 5/8 | 0.625 | 62.5% | Five eighths. 62.5% of 80 is 50. |
| 1/10 | 0.1 | 10% | Move the decimal point one place left. 10% of 80 is 8. |
| 1/12 | 0.0833 (the 3 repeats) | 8.3333% (repeating) | One month out of twelve |
| 1/16 | 0.0625 | 6.25% | A sixteenth. 6.25% of 80 is 5. |
Decimals and percents computed with the formula above and rounded to 4 places. Percent means per hundred, and the SI Brochure (BIPM, 9th edition) treats the symbol % as the number 0.01, so 25% of 80 is 0.25 x 80 = 20.
How to choose the right percentage formula
A lot of percentage mistakes start before the math starts. People often know the numbers but choose the wrong question type. If the sentence starts with a known percent, such as 30% of 90, use Percent Of. If the sentence asks how large one number is compared with another, such as 18 out of 60, use Is What Percent.
Percent Change is different because it cares about direction and order. The starting value matters. Going from 50 to 60 is a 20% increase, while going from 60 back to 50 is about a 16.6667% decrease. Those answers are not opposites because each one uses a different original value in the denominator.
It also helps to estimate before you calculate. Ten percent of 250 should be 25, so 20% should be about 50. If a sale price moves from 240 to 198, the drop should be less than 20% because 20% of 240 is 48 and the actual drop is 42. That kind of quick check catches swapped inputs and sign mistakes fast.
Percent and percentage points are different units of change. A rate that moves from 10% to 12% rose by 2 percentage points, but Percent Change mode with A = 10 and B = 12 reports a 20% increase, because 2 is one fifth of the starting 10. Both numbers are correct. They answer different questions, so say which one you mean when you report a result.
Rounding is the second thing to watch. Percent means per hundred, and the SI Brochure (BIPM, 9th edition) and NIST Special Publication 811 both treat the symbol % as the number 0.01, so 1/3 is 0.3333 repeating and never ends. This tool rounds every display to 4 decimal places, which is why 1 out of 3 shows as 33.3333% and why 33.3333% of 80 comes back as 26.6666 instead of the exact 26.6667. JavaScript also stores numbers as IEEE 754 double-precision values, so very long decimal inputs can carry tiny binary rounding effects before the display rounding is applied. For money or grades, round once at the end, not at every step.
Up and down moves do not cancel either. A price that rises 50% from 100 to 150 and then falls 50% does not return to 100. The second step takes 50% of 150, which is 75, so the price ends 25% below where it started. The same asymmetry means a 20% drop needs a 25% gain to recover. Always compute each step from its own starting value, and read the sign carefully in Percent Change mode.
Common mistakes
- Using Percent Of when the question is really asking for a ratio. If the wording says "is what percent," divide the part by the whole instead of multiplying a percent by the base.
- Swapping old and new values in Percent Change mode. The tool uses A as the old value and B as the new value, so reversing them changes an increase into a decrease or the other way around.
- Treating 15% like 15 in mental math. A percent must be converted into a rate out of 100, so 15% means 0.15, not 15.
- Ignoring the negative sign on percent change. A result like -17.5% is not a bad input. It means the new value is 17.5% lower than the original.
- Trying to divide by zero in ratio-based modes. Is What Percent cannot use a whole of 0, and Percent Change cannot use an old value of 0 in the standard formula.
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