Percentage Calculator
A free percentage calculator that solves every common percent question in one place. Calculate the percentage of a number, use it as a find percent calculator to work out what percent X is of Y, run a percentage increase or percentage change calculation between two values, calculate a decrease percentage, or use percent off mode to find a discounted sale price. Numbers update as you type, and each mode shows the percentage formula behind the result.
Common percentage values
Quick mental references for the percentages people use most often.
| Percentage | As a fraction | As a decimal | Common use |
|---|---|---|---|
| 1% | 1/100 | 0.01 | Sales commission, interest |
| 5% | 1/20 | 0.05 | Salary raise, sales tax |
| 10% | 1/10 | 0.10 | Tip on bill, small discount |
| 15% | 3/20 | 0.15 | Standard restaurant tip (US) |
| 20% | 1/5 | 0.20 | Good tip, common discount |
| 25% | 1/4 | 0.25 | Quarter, sale discount |
| 33.33% | 1/3 | 0.3333 | One-third split |
| 50% | 1/2 | 0.50 | Half off, half a value |
| 75% | 3/4 | 0.75 | Three-quarters complete |
| 100% | 1 | 1.00 | Full amount, total |
What this calculator does
4 calculation modes
Find X% of Y, find what % X is of Y, calculate change, and compute discounts.
Instant results
Numbers update as you type. No "Calculate" button to slow you down.
Discount mode
Enter original price and discount percent. See sale price and amount saved.
Percentage change
Find percent increase or decrease between any two values.
100% private
All math runs in your browser. Nothing stored, nothing sent anywhere.
Mobile friendly
Big touch targets and large numbers, even on a phone.
When you need a percentage calculator
Restaurant tips
Quickly calculate a 15% or 20% tip. Enter the bill, choose the percentage, and see the total tip in cents.
Shopping discounts
See exactly how much you save and pay when a store offers 25% off, 40% off, or any other discount.
Grade calculations
Find your percentage on any test or assignment. Enter marks obtained and total marks.
Salary increases
See what a 5% or 10% raise actually means in your monthly pay. Useful for negotiation.
Sales and growth metrics
Calculate month-over-month or year-over-year growth percentages for business reports.
Tax and tip on bills
Add sales tax or service charge as a percentage of any base amount.
How percentage math works
What is a percentage?
Percent comes from the Latin "per centum," meaning "per hundred." A percentage is a number that expresses a portion as a fraction of 100. So 25% means 25 out of 100, which is the same as one-quarter (1/4), or 0.25 as a decimal. Any fraction or ratio can be expressed as a percentage by multiplying by 100.
Three conversions tie the idea together. To turn a percentage into a decimal, divide by 100, so 8% becomes 0.08. To turn a decimal into a percentage, multiply by 100, so 0.4 becomes 40%. To turn a fraction into a percentage, divide the top by the bottom and multiply by 100, so 3/8 becomes 37.5%. Once a value is in decimal form, every percentage calculation is just multiplication or division.
The percentage formula and how to use it
The core percentage formula is part divided by whole, times 100, which gives the percent. Rearranged, the same formula answers the other two common questions: part equals percent times whole divided by 100, and whole equals part divided by percent times 100. Those three forms cover almost everything: finding a percent of a number, finding what percent one number is of another, and working backward from a known percentage to the original total.
How to calculate the percentage of a number
To calculate a percentage of a number, multiply the number by the percent, then divide by 100. Or, equivalently, multiply the number by the decimal form of the percent, so 15% becomes 0.15. To find 15% of 200, you can do (15 x 200) / 100 = 30, or 0.15 x 200 = 30. Both give the same answer. The decimal method is faster on a calculator, while the divide-by-100 method is easier in your head when the numbers are clean.
How to find what percent one number is of another
This is the find-percent question: X is what percent of Y. Divide X by Y, then multiply by 100. For example, 25 out of 200 is 25 / 200 = 0.125, which is 12.5%. This is exactly how grade percentages, conversion rates, and completion progress are worked out. A find-percent calculator removes the guesswork: enter the part and the whole, and the percentage appears as you type.
Percentage increase and percentage decrease
A percentage increase measures how much a value has grown relative to where it started. The percentage increase formula is new value minus old value, divided by the old value, times 100. Going from 80 to 100 is (100 - 80) / 80 = 0.25, which is a 25% increase. A percentage decrease uses the same formula and simply produces a negative result, or you can read the drop directly: from 200 down to 150 is (200 - 150) / 200 = 0.25, a 25% decrease.
To increase a number by a percentage, multiply it by one plus the decimal form of the percent. To increase 60 by 25%, multiply by 1.25 to get 75. To decrease by a percentage, multiply by one minus the decimal, so 60 reduced by 25% is 60 x 0.75 = 45. This shortcut is faster than calculating the change and adding it back on.
How to calculate percentage change between two numbers
Percentage change is the general term that covers both increase and decrease, and it is the calculation behind stock moves, price swings, weight loss, exam improvement, and revenue growth. Subtract the old value from the new value, divide that difference by the old value, then multiply by 100. A positive result is an increase and a negative result is a decrease. The percentage change calculator mode does this in one step, which is useful for month-over-month and year-over-year reporting.
Percentage difference vs percentage change
Percentage change and percentage difference are not the same calculation. Percentage change has a clear start and end value, so it divides by the original. Percentage difference compares two values where neither is a baseline, so the percent difference formula divides the absolute difference by the average of the two numbers, then multiplies by 100. Comparing 40 and 60, the difference is 20 and the average is 50, so the percentage difference is 40%. Use change when something moved over time, and use difference when you are comparing two independent measurements.
How to calculate percent off and discounts
Percent off is the discount question shoppers ask most. Multiply the original price by the discount percentage divided by 100 to get the amount saved, then subtract that from the original price for the sale price. A 30% discount on an $80 item is 80 x 0.30 = $24 saved, and the sale price is $80 - $24 = $56. A faster route is to multiply the price by one minus the decimal discount: 80 x 0.70 = $56 straight to the final price. The percent off calculator mode shows both the amount saved and the price you pay.
How to calculate a percentage of a percentage
A percentage of a percentage is solved by multiplying the two decimal forms together. To find 20% of 50%, convert both to decimals, multiply 0.20 by 0.50 to get 0.10, and that is 10%. This comes up with stacked discounts and compounded rates: an extra 10% off an item already marked 25% off does not equal 35% off. Instead the price is multiplied by 0.75 and then by 0.90, giving 0.675, so the shopper pays 67.5% of the original and saves 32.5%, not 35%.
Mental math shortcuts for tips and discounts
To find 10% of any number, move the decimal one place left. So 10% of $43.50 is $4.35. For 15%, find 10% and add half of that: $4.35 + $2.18 = $6.53. For 20%, just double the 10% value: $8.70. For 5%, take half of the 10% value: $2.18. These tricks work because a percentage is just division by 100, and they make tip and discount math quick even without a calculator.
One more shortcut is the reversal rule: X percent of Y always equals Y percent of X. Finding 16% of 25 looks awkward, but 25% of 16 is obviously 4, and the answer is the same. Swapping the numbers often turns a hard percentage into an easy one.
Using this as a find percent calculator
A find percent calculator answers the question "X is what percent of Y," and it is one of the most searched percentage problems. The method is always the same: divide the part by the whole, then multiply by 100. If 18 questions out of 24 are correct, the score is 18 / 24 = 0.75, which is 75%. If a project is 140 hours into a 200 hour estimate, it is 140 / 200 = 0.70, so 70% complete. Enter the part and the whole in the calculator above and the percentage appears instantly, no formula recall needed.
The find-percent calculation is the engine behind conversion rates, test scores, survey results, and progress bars. It also reverses cleanly: if you know the percentage and the whole, multiply them to recover the part, and if you know the percentage and the part, divide to recover the whole. Those three rearrangements of one formula handle nearly every percentage question you will meet.
How to calculate a decrease percentage
To calculate a decrease percentage, subtract the new value from the old value, divide that drop by the old value, then multiply by 100. A price falling from $250 to $200 is a drop of $50, and $50 / $250 = 0.20, so a 20% decrease. A decrease percentage is always measured against the starting value, not the ending value, which is a common point of confusion. The same $50 drop expressed against the new $200 price would be 25%, but that is not the decrease percentage.
Decrease percentage shows up in price cuts, weight loss, falling test scores, budget reductions, and shrinking sales. It is the mirror image of percentage increase and uses an identical formula, just producing a negative or smaller result. The percentage change mode in the calculator above reports a decrease automatically when the new value is lower than the old one, so you do not have to decide which direction to subtract.
Percent change in business and finance reporting
Percent change is the standard way to summarize movement in a number over time, and it appears constantly in business and finance. Revenue up from $1.2M to $1.5M is a percent change of (1.5 - 1.2) / 1.2 = 0.25, a 25% gain. A stock falling from $40 to $34 is a percent change of (34 - 40) / 40 = -0.15, a 15% loss. Because percent change normalizes for the size of the starting figure, it lets you compare growth across products, regions, or quarters that have very different absolute values.
Two reporting habits keep percent change accurate. First, always divide by the earlier value, the baseline, not the later one. Second, be careful with figures that cross zero or start near zero, because dividing by a tiny baseline produces huge, misleading percentages. For month-over-month and year-over-year tracking, the percentage change mode above gives a consistent, signed result you can drop straight into a report.
Worked percentage examples for everyday situations
A few worked examples show the formulas in action. Tip: a 20% tip on a $54.50 dinner bill is 54.50 x 0.20 = $10.90, for a total of $65.40. Sales tax: an 8.25% tax on a $120 purchase is 120 x 0.0825 = $9.90, so the final cost is $129.90. Grade: scoring 68 out of 75 on an exam is 68 / 75 = 0.9067, which rounds to 90.7%. Raise: a 4.5% raise on a $62,000 salary adds 62,000 x 0.045 = $2,790, lifting pay to $64,790.
Discounts and growth follow the same pattern. A 35% off coupon on a $89 jacket saves 89 x 0.35 = $31.15, so you pay $57.85. A subscriber base growing from 4,200 to 5,460 is a percentage increase of (5,460 - 4,200) / 4,200 = 0.30, a 30% gain. Each of these is one entry in the calculator above, and the mode you pick shows the exact formula it applied so you can verify the result.
To find X% of Y, multiply Y by X then divide by 100. For example, 15% of 200 is (200 x 15) / 100 = 30. Our calculator does this instantly with three other percentage modes too.
Subtract the old value from the new value, divide by the old value, then multiply by 100. Example: going from 80 to 100. (100 - 80) / 80 = 0.25. Multiply by 100 to get 25% increase.
Multiply the original price by the discount percentage, then divide by 100 to get the amount saved. Subtract that from the original price to get the sale price. Example: 30% off a $50 item = $15 saved, so the sale price is $35.
20% of 150 is 30. The calculation is (20 x 150) / 100 = 30.
Divide the first number by the second, then multiply by 100. Example: 25 is what percent of 200? 25 / 200 = 0.125. Multiply by 100 to get 12.5%.
15% of 60 is 9. Useful for tips: a 15% tip on a $60 bill is $9, making the total $69.
Divide marks obtained by total marks, then multiply by 100. For example, 425 marks out of 500: (425 / 500) x 100 = 85%.
Subtract the new value from the old value, divide by the old value, multiply by 100. The result is the percentage decrease. Example: from 200 to 150. (200 - 150) / 200 = 0.25. So 25% decrease.
Percentage is a portion out of 100 (90% means 90 out of 100). Percentile means rank within a group (90th percentile means scoring better than 90% of the group). These are different concepts even though they both use the word "percent."
For a 15% tip, multiply the bill by 0.15. For 20%, multiply by 0.20. Quick mental method: take 10% of the bill (move decimal one place left), then add half of that for 15%, or double it for 20%.
The percentage increase formula is new value minus old value, divided by the old value, then multiplied by 100. For example, going from 80 to 100 is (100 - 80) / 80 = 0.25, which is a 25% increase. If the result is negative, the value went down, so it is a percentage decrease instead.
Multiply the number by one plus the decimal form of the percentage. To increase 60 by 25%, multiply 60 by 1.25 to get 75. To go the other way and decrease a number by a percent, multiply by one minus the decimal, so 60 reduced by 25% is 60 x 0.75 = 45. This is faster than finding the change and adding it back on.
Percentage change has a clear starting value and ending value, so it divides the difference by the original value. Percentage difference compares two values where neither is a baseline, so it divides the absolute difference by the average of the two numbers. Use change when a value moved over time, and use difference when comparing two independent measurements.
The percent difference formula is the absolute difference between two numbers, divided by their average, then multiplied by 100. For example, comparing 40 and 60, the difference is 20 and the average is 50, so the percentage difference is (20 / 50) x 100 = 40%. It is symmetric, meaning the order of the two numbers does not change the result.
Multiply the original price by the discount percentage divided by 100 to find the amount saved, then subtract it from the original price. A 30% discount on an $80 item saves $24, leaving a sale price of $56. A quicker route is to multiply the price by one minus the decimal discount: $80 x 0.70 = $56 straight to the final price.
Convert both percentages to decimals and multiply them together. To find 20% of 50%, multiply 0.20 by 0.50 to get 0.10, which is 10%. This matters for stacked discounts: an extra 10% off an item already 25% off gives 0.75 x 0.90 = 0.675, so you pay 67.5% and save 32.5%, not 35%.
Multiply the number by the percentage and divide by 100, or multiply by the decimal form of the percent. To find 15% of 200, do (15 x 200) / 100 = 30, or 0.15 x 200 = 30. A useful shortcut is that X% of Y always equals Y% of X, so a hard percentage can often be swapped into an easy one.
The basic percentage formula is part divided by whole, multiplied by 100, which gives the percent. The same formula rearranges two ways: part equals percent times whole divided by 100, and whole equals part divided by percent times 100. These three forms cover finding a percent, finding what percent one number is of another, and working back to the original total.
A find percent calculator answers "X is what percent of Y" by dividing the part by the whole and multiplying by 100. For example, 18 correct answers out of 24 is 18 / 24 = 0.75, which is 75%. Enter the part and the whole in the find percent mode above and the percentage updates instantly as you type.
Subtract the new value from the old value, divide that drop by the old value, then multiply by 100. A price falling from $250 to $200 is a drop of $50, and $50 / $250 = 0.20, so a 20% decrease. A decrease percentage is always measured against the starting value, not the ending value, which is a common source of error.
Percent change measures how much a number moved over time, in either direction. Subtract the old value from the new value, divide by the old value, then multiply by 100; a positive result is an increase and a negative result is a decrease. Always divide by the earlier baseline value, and be cautious when the starting figure is near zero because it can produce misleadingly large percentages.
Both use the same formula: new value minus old value, divided by the old value, times 100. A percentage increase produces a positive result because the value grew, while a percentage decrease produces a negative result because the value fell. The percentage change mode in the calculator above reports the correct direction automatically based on which value is larger.
Multiply the number by one plus the decimal form of the percentage. To increase $80 by 8.25% sales tax, multiply 80 by 1.0825 to get $86.60. This one-step method is faster than calculating the added amount separately and then adding it back to the original number.