Percentage Calculator
Type your numbers, pick a mode, and get the answer with every step shown. This percentage calculator handles three jobs: finding what X% of a number equals, working out what percent one number is of another, and measuring percent increase or decrease between two values.
Below you will find the formulas, dozens of solved examples using the exact numbers people search for, and quick reference tables you can scan in seconds.
How do you calculate a percentage?
A percentage is a number out of 100. To find a percentage of a value, divide the percent by 100 and multiply by the number. To turn a fraction into a percent, divide the top by the bottom and multiply by 100. Those two rules cover almost every percentage question you will ever face.
The calculator above does the arithmetic for you across three modes. Pick the one that matches your question, enter your figures, and read the worked steps it prints. The sections below explain each mode, then give you tables of solved answers so you can grab a result without typing anything.
What is X% of Y?
This is the most common percentage question. You have a percent and a number, and you want the portion. Discounts, tax, tips, commission, and interest all use it.
Result = (Percent ÷ 100) × Number
Say you want 8% of 1260. Divide 8 by 100 to get 0.08, then multiply by 1260.
8% of 1260 = 0.08 × 1260 = 100.8
A few more solved the same way:
15% of 42500 = 0.15 × 42500 = 6375
80% of 47.5 = 0.80 × 47.5 = 38
4.7% of 5000 = 0.047 × 5000 = 235
0.3% of 13750 = 0.003 × 13750 = 41.25
Percent of a number: quick reference
| Calculation | Answer |
|---|---|
| 8% of 1260 | 100.8 |
| 15% of 42500 | 6375 |
| 20% of 42500 | 8500 |
| 16.5% of 3250 | 536.25 |
| 13.5% of 3150 | 425.25 |
| 4.5% of 56000 | 2520 |
| 1.5% of 73000 | 1095 |
| 80% of 725000 | 580000 |
| 80% of 1185 | 948 |
| 60% of 1260 | 756 |
| 20% of 100 | 20 |
| 15% of 80 | 12 |
| 10% of 250 | 25 |
X is what percent of Y?
Here you have two numbers and want to know what percent the first is of the second. Grades, ratios, and progress checks use this one. Divide the part by the whole, then multiply by 100.
Percent = (Part ÷ Whole) × 100
For example, 45 out of 60:
45 ÷ 60 = 0.75, then 0.75 × 100 = 75%
How do you write a fraction like X out of Y as a percentage?
Divide the top number by the bottom number, then multiply by 100. For 756 out of 1000, that is 756 ÷ 1000 = 0.756, and 0.756 × 100 = 75.6%. The same method works for test scores, survey results, and any “so many out of so many” figure.
This is the exact question behind searches like “756 out of 1000 as a percentage” or “47.5 out of 50 as a percentage.” Use the second mode of the calculator (X is what % of Y), where the part is the top number and the whole is the bottom number. Here is a batch worked out:
| Fraction | As a percentage |
|---|---|
| 756 out of 1000 | 75.6% |
| 47.5 out of 50 | 95% |
| 4.17 out of 5 | 83.4% |
| 39 out of 41 | 95.12% |
| 53 out of 75 | 70.67% |
| 23.5 out of 30 | 78.33% |
| 156 out of 200 | 78% |
| 14.75 out of 20 | 73.75% |
| 29.5 out of 50 | 59% |
| 54 out of 70 | 77.14% |
| 46 out of 52 | 88.46% |
| 162 out of 206 | 78.64% |
| 18 out of 23 | 78.26% |
| 22 out of 23 | 95.65% |
| 15 out of 23 | 65.22% |
| 16 out of 23 | 69.57% |
| 20.5 out of 25 | 82% |
| 13.5 out of 15 | 90% |
| 28.5 out of 30 | 95% |
| 27.5 out of 30 | 91.67% |
| 21.5 out of 30 | 71.67% |
| 15.5 out of 20 | 77.5% |
When the top number is bigger than the bottom, the answer goes above 100%. For example, 65 out of 50 is 130%, and 127.5 out of 51 is 250%. That is normal and just means the part is larger than the whole.
How do you calculate percentage change, increase, or decrease?
Subtract the old value from the new value, divide by the old value, then multiply by 100. A positive answer is an increase, a negative answer is a decrease. From 50 to 65 the change is (65 − 50) ÷ 50 × 100 = 30% increase.
Change = ((New − Old) ÷ Old) × 100
Percentage increase examples
50 to 65 = (15 ÷ 50) × 100 = 30% increase
80 to 100 = (20 ÷ 80) × 100 = 25% increase
5000 to 6500 = (1500 ÷ 5000) × 100 = 30% increase
35 to 50 = (15 ÷ 35) × 100 = 42.86% increase
Percentage decrease examples
1000 to 850 = (−150 ÷ 1000) × 100 = 15% decrease
120 to 90 = (−30 ÷ 120) × 100 = 25% decrease
50000 to 42500 = (−7500 ÷ 50000) × 100 = 15% decrease
80 to 60 = (−20 ÷ 80) × 100 = 25% decrease
What is the difference between percentage change and percentage difference?
Percentage change compares a new value to a starting value and has a direction (up or down). Percentage difference compares two values with no starting point, using their average as the base, so it is always positive. If a price moves from 40 to 60, that is a 50% increase (change), but the percentage difference between 40 and 60 is 40%.
People mix these up constantly, so here is the split. Use percentage change when one value came first and you want to know how much it rose or fell. Use percentage difference when neither value is the “original” and you just want to know how far apart two numbers are.
Percentage difference = (|A − B| ÷ ((A + B) ÷ 2)) × 100
Difference between 40 and 60: |40 − 60| ÷ 50 × 100 = 40%
Difference between 50 and 70: |50 − 70| ÷ 60 × 100 = 33.33%
Difference between 20 and 30: |20 − 30| ÷ 25 × 100 = 40%
Notice that going from 40 to 60 is a 50% increase, but 60 to 40 is only a 33.33% decrease, even though it is the same pair of numbers. That is why direction matters for change and why difference (which uses the average) gives one steady figure both ways.
How do you increase or decrease a number by a percentage?
This is a different question from percent change. Here you start with one number and apply a percentage to it. To increase, multiply by (1 + percent as a decimal). To decrease, multiply by (1 − percent as a decimal).
Increase 200 by 15%: 200 × 1.15 = 230
A pay raise works exactly this way. To turn a percentage bump into your new salary in one step, use our pay raise calculator.
Decrease 52 by 7%: 52 × 0.93 = 48.36
Decrease 12 by 66.7%: 12 × 0.333 = 4 (approx)
To do this with the calculator, first find the percentage of your number using the top mode, then add it to (or subtract it from) the original value. If you track investment returns often, the ROI calculator handles profit and return figures directly.
How do you find the original number from a percentage? (Reverse percentage)
To find the whole when you know a part and its percentage, divide the part by the percentage written as a decimal. If 30 is 20% of a number, then 30 ÷ 0.20 = 150. This is called a reverse percentage, and it answers questions like “X is P% of what number?”
This comes up whenever you have a result but need the starting figure. Divide the known amount by the percent over 100.
Whole = Part ÷ (Percent ÷ 100)
30 is 20% of what? 30 ÷ 0.20 = 150
45 is 75% of what? 45 ÷ 0.75 = 60
12 is 8% of what? 12 ÷ 0.08 = 150
50 is 40% of what? 50 ÷ 0.40 = 125
Finding the price before a discount or markup
A slightly different reverse case is when a total already has a percentage baked in. To strip it out, divide by (1 plus the percent) for an increase, or (1 minus the percent) for a discount.
Price is $230 after a 15% markup: 230 ÷ 1.15 = $200 original
Price is $80 after 20% off: 80 ÷ 0.80 = $100 original
Total is $80 after a 25% increase: 80 ÷ 1.25 = $64 original
Everyday percentage examples
Most real percentage problems fall into a handful of shapes. Here is how each one works with actual numbers.
Discount on a price
A $100 item at 20% off: 20% of 100 is 20, so the price drops to $80 and you save $20.
Sales tax
8% tax on $250: 8% of 250 is 20, so the total is $270.
Tip at a restaurant
A 15% tip on an $80 bill: 15% of 80 is 12, so you pay $92 in total.
Test grade
Scoring 45 out of 60: 45 ÷ 60 × 100 = 75%. For full grade breakdowns, the test grade calculator converts scores to letter grades too.
Markup
Buying at $50 and selling at $65: the increase is 15, and 15 ÷ 50 × 100 = 30% markup.
Popular percentage calculations
These are the exact percentage problems people look up most often, solved and ready to copy.
| Question | Answer |
|---|---|
| What is 10% of 100? | 10 |
| What is 20% of 50? | 10 |
| What is 15% of 200? | 30 |
| What is 8% of 1260? | 100.8 |
| What is 60% of 1260? | 756 |
| 2 is what percent of 12? | 16.67% |
| 5 is what percent of 20? | 25% |
| 30 is what percent of 150? | 20% |
| Increase from 50 to 75? | 50% increase |
| Decrease from 80 to 60? | 25% decrease |
| Change from 4 to 7? | 75% increase |
| Change from 50 to 85? | 70% increase |
How do you turn a percentage into a decimal or fraction?
To convert a percent to a decimal, divide by 100 (move the point two places left). To convert to a fraction, put the percent over 100 and simplify, which also gives you the ratio between the part and the whole. To simplify, scale, or solve that ratio directly, use the ratio calculator. This table covers the values that come up most.
| Percentage | Decimal | Fraction |
|---|---|---|
| 5% | 0.05 | 1/20 |
| 10% | 0.10 | 1/10 |
| 20% | 0.20 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.33% | 0.3333 | 1/3 |
| 50% | 0.50 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.00 | 1/1 |
Common questions about percentages
What does percent actually mean?
Percent means “per hundred.” A percentage tells you how many parts out of 100 you have, which makes it easy to compare values on the same scale even when the totals differ.
Can a percentage be more than 100%?
Yes. Any time the part is larger than the whole, the percentage passes 100. Growth from 50 to 150 is a 200% increase, and 88.83 out of 21 works out to 423%.
How do I find the original number before a percentage was added?
If a total already includes a percentage, divide by (1 + the percent as a decimal). A price of $230 that included a 15% markup came from 230 ÷ 1.15 = $200.
Why does 2 out of 12 give a repeating decimal?
Because 2 ÷ 12 does not divide evenly. It equals 16.666…, which rounds to 16.67%. Most calculators, including this one, round to two decimal places for readability. If you are solving a proportion instead, the proportion calculator shows the cross-multiplication steps.
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