Shoppers
Shopping discount
A $150 jacket is marked 20% off. How much do you save, and what do you pay?
- Discount:
20% × $150 = $30 - Sale price:
$150 − $30 = $120
You save $30 and pay $120.
MathematicsFree online calculator
Percentage Calculator
Use this free percentage calculator to find percentages, percentage increases, decreases, changes and differences instantly. See clear results, formulas and step-by-step solutions.
Percentage Calculator
7 calculation types
What is P% of X?
Your result
Percentage of a number30
15% of 200 = 30
- Percentage as a decimal
- 0.15
- Remaining amount
- 170 (85%)
Formula with your values
Result = (15 ÷ 100) × 200
On this page
Guide
How to Use the Percentage Calculator
Each calculation type answers a different question, so start by choosing the one that matches yours.
Choose a calculation type
On a phone, use the Calculation type menu. On larger screens, pick Basic, Change or Increase / Decrease, then the specific calculation.
Enter your two values
The question above the fields updates as you type, so you can check it matches what you want to know. Decimals and negative numbers work where they make sense.
Read the result
It updates as soon as both values are valid. You can also press Calculate or Enter at any time.
See how it was worked out
Select Show steps to see the formula with your numbers substituted, one step at a time.
Copy, adjust or reset
Copy result puts the answer on your clipboard. Decimals switches between 2, 4 and 6 decimal places, and Reset restores the example values.
What Is a Percentage?
A percentage expresses a quantity as a number of parts out of 100. The word comes from the Latin per centum, “by the hundred”, and the % sign simply means “out of 100”. So 25% is 25 out of every 100: the same value as the fraction 25/100 and the decimal 0.25.
25%
= 1/4 = 0.25
a quarter
50%
= 1/2 = 0.5
one-half
75%
= 3/4 = 0.75
three-quarters
100%
= 1 = 1
the whole amount
Because every percentage is measured against 100, percentages make it easy to compare amounts of different sizes. Scoring 18 out of 24 and 45 out of 60 look like different results, but both are 75%.
To convert a percentage to a decimal, divide by 100 (12.5% = 0.125). To convert a decimal to a percentage, multiply by 100 (0.08 = 8%).
Percentage Formula
Almost every percentage problem comes from one relationship between a part, a whole and a percentage.
The basic percentage formula
Percentage = (Part ÷ Whole) × 100
- Part
- the amount you are measuring
- Whole
- the total or reference amount
- × 100
- turns the decimal into a percentage
Example: 21 of a class of 28 students passed: (21 ÷ 28) × 100 = 75%.
Rearranging the same formula lets you find whichever of the three values is missing:
| To find | Formula | Example |
|---|---|---|
| The percentage | Part ÷ Whole × 100 | 30 ÷ 200 × 100 = 15% |
| The part | Percentage ÷ 100 × Whole | 15 ÷ 100 × 200 = 30 |
| The whole | Part ÷ (Percentage ÷ 100) | 30 ÷ 0.15 = 200 |
How to Find a Percentage of a Number
Percentage of a number
Result = (Percentage ÷ 100) × Number
Example: 20% of 150 = 0.20 × 150 = 30
- Convert the percentage to a decimal by dividing by 100: 20% becomes 0.20.
- Multiply the decimal by the number: 0.20 × 150 = 30.
A handy property: x% of y always equals y% of x. That makes some problems much easier. 8% of 50 is hard to do in your head, but 50% of 8 is obviously 4, so both are 4.
How to Calculate Percentage Increase
Increase a value by a percentage
New value = Original × (1 + Percentage ÷ 100)
Example: $1,200 rent rising 5%: $1,200 × 1.05 = $1,260
You can work in two steps, finding the increase and adding it on ($1,200 × 0.05 = $60, then $1,200 + $60 = $1,260), or in one step with the multiplier 1.05. The multiplier is especially useful for repeated increases, such as several years of growth.
Increases can exceed 100%. Doubling a value is a 100% increase and tripling it is a 200% increase. To find the percentage increase between two numbers, use the percentage change formula below.
How to Calculate Percentage Decrease
Decrease a value by a percentage
New value = Original × (1 − Percentage ÷ 100)
Example: $80 shoes at 25% off: $80 × 0.75 = $60
Find the amount to remove ($80 × 0.25 = $20) and subtract it ($80 − $20 = $60), or multiply by what is left: paying 75% of the price after 25% off.
A 100% decrease brings a value to zero. Things that can’t go below zero, like prices, can’t fall by more than 100%, although a mathematical decrease of more than 100% simply produces a negative result.
Percentage Change vs. Percentage Difference
These two are often confused, but they answer different questions and can give different numbers for the same pair of values.
Percentage change
(New − Original) ÷ Original × 100
Measures movement from a starting value. It has a direction: positive for an increase, negative for a decrease. Use it when there is a clear before and after.
Example: 80 → 100: +25%
100 → 80: −20%
Percentage difference
|A − B| ÷ ((A + B) ÷ 2) × 100
Compares two values on equal terms, using their average as the reference. It has no direction and gives the same answer in either order.
Example: 80 and 100: 20 ÷ 90 × 100 ≈ 22.22%
100 and 80: ≈ 22.22%
Which one should you use?
- Percentage change for anything over time: price rises, sales growth, weight loss, a score before and after.
- Percentage difference when neither value is the baseline: two shops’ prices, two measurements of the same thing, or two products’ specifications.
Zero and negative starting values
Percentage change is undefined when the original value is 0, because the formula divides by it. When the original value is negative, this calculator divides by its absolute value so that the sign still shows the direction: a loss improving from −50 to −25 is shown as +50%. Other fields sometimes use different conventions, so state the method when you report such figures. Percentage difference is only calculated here for values of 0 or more.
How to Find the Original Number (Reverse Percentage)
Reverse percentage
Original = Known value ÷ (Percentage ÷ 100)
Example: 30 is 15% of what? 30 ÷ 0.15 = 200
Use this when you know a value after a percentage was applied and want the number you started with. If a sale price of $68 is after 15% off, it represents 85% of the original, so the original is $68 ÷ 0.85 = $80. If a 10% raise brought a salary to $55,000, the old salary was $55,000 ÷ 1.10 = $50,000.
Percentage Points vs. Percent Change
When the thing that changes is itself a percentage, there are two correct but very different ways to describe the change.
An interest rate rises from 20% to 25%.
Percentage-point change
5 points
25 − 20 = 5
Relative percent change
+25%
(25 − 20) ÷ 20 × 100 = 25
The percentage-point change is a simple subtraction of the two rates. The relative change compares the difference with the starting rate, exactly like any other percentage change. Both are correct; they answer different questions.
Saying the rate “went up 5%” is ambiguous, because it could mean either 25% or 21% (a 5% relative increase on 20%). That is why finance and news reporting use percentage points for differences between rates, and sometimes basis points, where 1 basis point is 0.01 percentage point.
Percentage Calculation Examples
Realistic problems, worked through. Select “Try this example” to load any of them into the calculator above.
Students
Exam score
You answer 45 of 60 questions correctly. What is your score as a percentage?
- Divide:
45 ÷ 60 = 0.75 - Convert:
0.75 × 100 = 75%
Your score is 75%.
- Divide:
Professionals
Salary increase
A monthly salary of $2,000 rises by 10%. What is the new salary?
- Raise:
10% × $2,000 = $200 - New salary:
$2,000 + $200 = $2,200
The new salary is $2,200 a month.
- Raise:
Business owners
Price reduction
A product that sells for $500 is reduced by 15% for a promotion.
- Reduction:
15% × $500 = $75 - New price:
$500 − $75 = $425
The promotional price is $425.
- Reduction:
Business owners
Sales growth
Weekly orders grow from 80 to 100. What is the percentage change?
- Difference:
100 − 80 = 20 - Relative to the start:
20 ÷ 80 × 100 = 25%
Orders grew by 25%.
- Difference:
Everyday
Find the price before a discount
You paid $68 for an item that was 15% off. What was the original price?
- You paid
100% − 15% = 85%of the original - Original:
$68 ÷ 0.85 = $80
The original price was $80.
- You paid
Shoppers
Adding sales tax
A $45 purchase has 8% sales tax added at the register.
- Tax:
8% × $45 = $3.60 - Total:
$45 + $3.60 = $48.60
You pay $48.60 in total.
- Tax:
Percentages in Everyday Life
The same handful of formulas covers a surprising range of decisions.
Students
Turn test results into scores, check how much a weighted assignment counts, and track attendance requirements.
Shoppers
Work out sale prices, compare discounts with coupons, add sales tax, and calculate tips.
Business owners
Measure month-over-month growth, set prices with markup, and compare profit margins between products.
Professionals
Evaluate a raise, compare interest rates, report budget variance, and track progress toward targets.
Everyday life
Read % Daily Value on nutrition labels, split shared costs fairly, and understand price rises in bills.
Common Percentage Mistakes
Most percentage errors come from using the wrong base value. These are the ones to watch for.
Expecting an increase and an equal decrease to cancel out
Raising 100 by 20% gives 120, but cutting 120 by 20% gives 96, not 100. The second change is taken from a larger base, so it removes more than the first one added.
Undoing a discount by adding the percentage back
If you paid $68 after 15% off, adding 15% to $68 gives $78.20, which is wrong. The $68 is 85% of the original price, so divide instead:
$68 ÷ 0.85 = $80.Adding successive discounts together
20% off followed by an extra 10% off is not 30% off. On $100:
$100 → $80 → $72, a total discount of 28%. Each discount applies to the already-reduced price.Measuring change against the wrong value
Percentage change is relative to the starting value. From 80 to 100 is a 25% increase (20 ÷ 80), not 20% (20 ÷ 100). Dividing by the new value is a different calculation.
Mixing up percentage points and percent
A rate moving from 4% to 5% has risen by 1 percentage point, but by 25% in relative terms. Saying it “rose 1%” is ambiguous and usually wrong.
Averaging percentages from groups of different sizes
If 90% of 10 people and 50% of 90 people agree, the overall figure is (9 + 45) ÷ 100 = 54%, not the simple average of 70%. Combine the underlying counts, not the percentages.
Forgetting to convert the percentage to a decimal
15% of 200 is
0.15 × 200 = 30. Multiplying by 15 instead of 0.15 gives 3,000, a result 100 times too large.
Frequently Asked Questions
What is a percentage?
A percentage is a number expressed as a part of 100. For example, 40% means 40 out of 100, which is 0.4 as a decimal or 2/5 as a fraction. Percentages put parts of differently sized wholes on the same scale, so they are easy to compare.
How do you calculate a percentage?
Divide the part by the whole, then multiply by 100. If 18 of 24 seats are taken: 18 ÷ 24 = 0.75 and 0.75 × 100 = 75%.
How do I find 20% of a number?
Multiply the number by 0.2, or divide it by 5. For example, 20% of 85 is 0.2 × 85 = 17. A mental shortcut: find 10% by moving the decimal point one place to the left (8.5), then double it (17).
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the original value, and multiply by 100. From 50 to 65: (65 − 50) ÷ 50 × 100 = 30%. To increase a number by a percentage instead, multiply it by (1 + percentage ÷ 100): 50 × 1.3 = 65.
How do I calculate percentage decrease?
Subtract the new value from the original, divide by the original, and multiply by 100. From 250 to 200: (250 − 200) ÷ 250 × 100 = 20%. To decrease a number by a percentage, multiply it by (1 − percentage ÷ 100): 250 × 0.8 = 200.
What is the difference between percentage change and percentage difference?
Percentage change measures movement from a starting value, so it has a direction: going from 80 to 100 is +25%, while going from 100 to 80 is −20%. Percentage difference compares two values without treating either as the starting point. It divides by their average, so the difference between 80 and 100 is about 22.22% whichever way round you put them.
Can percentages be greater than 100%?
Yes. A percentage is above 100% whenever the part is bigger than the whole you compare it with: 150 is 150% of 100, and growing from 40 to 100 is a 150% increase. A share of a fixed total, such as the percentage of a test answered correctly, can’t exceed 100%, and a price can’t be reduced by more than 100%.
Can a percentage be negative?
Yes. A negative percentage change means a decrease: going from 100 to 80 is a −20% change. Negative percentages also appear when the quantity itself can be negative, such as a profit that turns into a loss. A share of a total, like a test score, is normally between 0% and 100%.
What happens when the original value is zero?
Percentage change from zero is undefined, because the formula divides by the original value and you cannot divide by zero. Going from 0 to 25 is an increase of 25 units, but not of any finite percentage. In that case, report the absolute change or choose a different, non-zero baseline. For the same reason, “what percent of 0 is 5?” has no answer.
How do I calculate a percentage without a calculator?
Build it from easy benchmarks:
- 10%: move the decimal point one place left (10% of 64 = 6.4).
- 5%: half of 10%. 1%: move the decimal point two places left.
- 25%: divide by 4. 50%: divide by 2.
Then combine them: 15% of 60 is 10% (6) plus 5% (3), which is 9. You can also swap the numbers when that is easier, because x% of y = y% of x: 4% of 75 equals 75% of 4, which is 3.