1. What Is P% of a Number?
Convert the percentage to a decimal, then multiply it by the number.
15% of 800 = 0.15 × 800 = 120
Percentage Calculator
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Calculate percentages, increases, decreases, differences, discounts, reverse percentages, and marks percentage. See the result, formula, and calculation steps instantly. All processing happens locally in your browser.
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What Is a Percentage?
A percentage expresses a number as parts out of 100. The word “percent” means “per hundred,” so 25% means 25 out of every 100, which is the same as the fraction 25/100 or the decimal 0.25.
Percentages make values with different totals easier to compare. A score of 45 marks is difficult to judge without knowing the maximum marks, but 45 out of 50 can immediately be expressed as 90%.
This calculator handles common percentage questions, but the guide below also explains how to calculate each result manually and how to use quick mental-math shortcuts when a calculator is not available.
The Three Basic Percentage Questions
Most percentage problems are variations of three basic questions: finding the part, finding the percentage, or finding the whole.
2. One Number Is What Percent of Another?
Divide the part by the whole, then multiply the result by 100.
120 ÷ 800 × 100 = 15%
3. Find the Whole
Divide the known part by the percentage written as a decimal.
120 ÷ 0.30 = 400
How to Calculate a Percentage Manually
To find a percentage of any number by hand, first convert the percentage to decimal form. You do this by dividing the percentage by 100 or moving the decimal point two places to the left.
Basic formula
Percentage amount = Number × Percentage ÷ 100
Example: Find 18% of 750.
-
Write the percentage as a fraction over 100.
18% = 18 ÷ 100 -
Multiply by the number.
750 × 18 ÷ 100 -
Simplify the calculation.
750 ÷ 100 = 7.5 -
Multiply by 18.
7.5 × 18 = 135
Answer:
18% of 750 is 135.
Quick Percentage Shortcuts for Mental Math
You do not always need to use the full formula. Many common percentages can be calculated quickly by finding 10%, 1%, one-half, one-quarter, or another simple fraction.
10%: Move the decimal one place left
10% of 480 is 48. For whole numbers, you can also divide by 10.
1%: Divide by 100
1% of 480 is 4.8. Move the decimal point two places left.
5%: Find 10%, then halve it
10% of 480 is 48, so 5% is 24.
20%: Find 10%, then double it
10% of 350 is 35, so 20% is 70.
25%: Divide by 4
25% is one-quarter. Therefore, 25% of 360 is 90.
50%: Divide by 2
50% is one-half. Therefore, 50% of 86 is 43.
75%: Find three-quarters
Divide by 4 and multiply by 3. For 200: 200 ÷ 4 × 3 = 150.
12.5%: Divide by 8
12.5% is one-eighth. Therefore, 12.5% of 240 is 30.
Use the Percentage-Swap Shortcut
A useful mental shortcut is that X% of Y gives the same result as Y% of X. You can swap the numbers when the second version is easier to calculate.
Example
18% of 50 = 50% of 18 = 9
Calculating 18% of 50 directly may take several steps, but finding half of 18 is immediate. This shortcut works because multiplication can be rearranged:
18 ÷ 100 × 50 = 50 ÷ 100 × 18
How to Calculate Percentage Increase or Decrease
Percentage change compares a new value with a specific original value. The original value is the base of the calculation, so the order of the numbers matters.
Percentage change formula
((New value − Original value) ÷ |Original value|) × 100
Example: A price increases from 500 to 650.
- Find the change:
650 − 500 = 150. - Divide by the original value:
150 ÷ 500 = 0.30. - Multiply by 100:
0.30 × 100 = 30%.
The result is a 30% increase.
Shortcut:
To increase a number by P%, multiply it by
1 + P/100. To decrease it by P%, multiply it by 1 − P/100.
For example:
- Increase 800 by 20%:
800 × 1.20 = 960. - Decrease 800 by 20%:
800 × 0.80 = 640.
How Reverse Percentage Works
A reverse percentage calculation finds the original value before an increase or decrease was applied. You cannot reverse a 20% increase by subtracting 20% from the final amount because the second percentage uses a different base.
Original Before an Increase
Original = Final ÷ (1 + P/100)
120 after a 20% increase:120 ÷ 1.20 = 100
Original Before a Decrease
Original = Final ÷ (1 − P/100)
80 after a 20% decrease:80 ÷ 0.80 = 100
Why Simple Reversal Fails
Add 20% to 100 and you get 120. Subtracting 20% from 120 gives 96 because 20% is now calculated from 120.
Percentage Change, Difference, and Percentage Points
These three measurements are related but answer different questions.
| Measurement | When to Use It | Formula | Example |
|---|---|---|---|
| Percentage Change | When one value is the original and the other is the new value. | (New − Original) ÷ |Original| × 100 |
80 to 100 is a 25% increase. |
| Percentage Difference | When neither value is the starting point and you want a direction-free comparison. | |A − B| ÷ ((|A| + |B|) ÷ 2) × 100 |
The difference between 80 and 100 is 22.22%. |
| Percentage Points | When comparing two values that are already percentages. | New percentage − Old percentage |
20% to 25% is an increase of 5 percentage points. |
Do not confuse percentage points with relative percentage change.
Moving from 20% to 25% is a rise of 5 percentage points, but the relative increase is 25%.
Discount, Tax, and Final-Price Shortcuts
For shopping calculations, you can calculate the amount saved first or go directly to the final price using the remaining percentage.
Discount Amount
Original price × Discount ÷ 100
30% of 2,000 is 600.
Price After Discount
Original price × (100 − Discount)%
2,000 × 70% = 1,400.
Price After Tax or Markup
Original price × (100 + Rate)%
1,000 plus 18% = 1,180.
Mental shortcut: For a 30% discount, you pay 70% of the original price. Instead of calculating the discount and subtracting it, multiply the price directly by 0.70.
How to Calculate Marks Percentage
To calculate an exam or test percentage, divide the marks obtained by the maximum marks and multiply by 100.
Marks percentage formula
(Marks obtained ÷ Total marks) × 100
Example: 438 marks out of 500.
438 ÷ 500 × 100 = 87.6%
A quick shortcut is available when the total is a convenient number. If the total is 500, divide the marks by 5 to convert them to a percentage:
438 ÷ 5 = 87.6%
Common Percentage Mistakes
- Using the wrong base: percentage change must use the original value as the denominator.
- Confusing part and whole: in
part ÷ whole × 100, the total must be in the denominator. - Reversing by subtraction: subtracting the same percentage after an increase does not restore the original number.
- Confusing difference with change: percentage difference is direction-free, while percentage change has an original value.
- Ignoring zero: standard percentage change is undefined when the original value is zero.
- Rounding too early: keep full precision during the calculation and round only the final result.
- Averaging unrelated percentages: percentages based on different group sizes may require a weighted average.
- Adding repeated percentages directly: two successive 10% increases produce a 21% total increase, not 20%.
Percentage Formula Quick Reference
| Question | Formula |
|---|---|
| What is P% of N? | N × P ÷ 100 |
| A is what percent of B? | A ÷ B × 100 |
| Find the whole when A is P% | A × 100 ÷ P |
| Add P% to N | N × (1 + P/100) |
| Subtract P% from N | N × (1 − P/100) |
| Percentage change | (New − Original) ÷ |Original| × 100 |
| Percentage difference | |A − B| ÷ ((|A| + |B|) ÷ 2) × 100 |
| Original before increase | Final ÷ (1 + P/100) |
| Original before decrease | Final ÷ (1 − P/100) |
Browser Processing and Calculation Data
The percentage calculation logic is designed to run in the browser. Numbers entered into the calculator, calculated prices, marks, discounts, and result history should not be included in analytics events.
Calculator results are useful for checking everyday calculations, but important academic, financial, tax, legal, or business figures should also be verified against their original documents and applicable rules.
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Frequently Asked Questions
What does percent mean?
Percent means per hundred. For example, 25% means 25 out of 100, which is equal to the fraction 25/100 and the decimal 0.25.
How do I calculate a percentage of a number manually?
Divide the percentage by 100 and multiply by the number. For example, 15% of 800 is calculated as 15 ÷ 100 × 800 = 120.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by 100. For example, 120 is 15% of 800 because 120 ÷ 800 × 100 = 15%.
How do I find the total when I know the part and percentage?
Divide the known part by the percentage written as a decimal. If 120 is 30% of the total, calculate 120 ÷ 0.30 = 400.
What is the fastest way to calculate 10%?
Move the decimal point one place to the left or divide the number by 10. For example, 10% of 480 is 48.
How can I calculate 5% quickly?
First calculate 10%, then divide that result by two. Since 10% of 480 is 48, 5% of 480 is 24.
How can I calculate 25% quickly?
Because 25% is one-quarter, divide the number by four. For example, 25% of 360 is 90.
Why is 18% of 50 equal to 50% of 18?
A percentage-of calculation is multiplication, so the values can be swapped. Both calculations equal 18 × 50 ÷ 100, which is 9.
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the absolute original value, and multiply by 100. An increase from 500 to 650 is 30%.
How do I calculate percentage decrease?
Subtract the new value from the original value, divide by the original value, and multiply by 100. A decrease from 500 to 400 is 20%.
How do I add a percentage to a number?
Multiply the number by 1 plus the percentage written as a decimal. To add 18% to 1000, calculate 1000 × 1.18 = 1180.
How do I subtract a percentage from a number?
Multiply the number by 1 minus the percentage written as a decimal. To subtract 25% from 800, calculate 800 × 0.75 = 600.
How do I calculate the original value before a percentage increase?
Divide the final value by 1 plus the percentage written as a decimal. If 120 is the value after a 20% increase, the original is 120 ÷ 1.20 = 100.
Why does subtracting 20% not reverse a 20% increase?
The increase and decrease use different base values. Adding 20% to 100 gives 120, while subtracting 20% from 120 gives 96 because the second calculation uses 120 as its base.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with a specific original value. Percentage difference compares two values relative to their average when neither is treated as the starting point.
What is the difference between percent and percentage points?
Percentage points measure the arithmetic difference between percentages. A change from 20% to 25% is 5 percentage points, but it is a 25% relative increase.
How do I calculate a discount quickly?
Subtract the discount rate from 100% and multiply the price by the remaining percentage. For a 30% discount, multiply the original price by 70% or 0.70.
How do I calculate marks percentage?
Divide marks obtained by total marks and multiply by 100. For example, 438 out of 500 is 438 ÷ 500 × 100 = 87.6%.
Can a percentage be greater than 100?
Yes. A percentage above 100 means the amount is larger than the reference value. For example, 150% of 20 is 30.
Why is percentage change undefined when the original value is zero?
The standard percentage-change formula divides by the original value. Division by zero is undefined, so a normal percentage-change result cannot be calculated.
Should I round during the calculation?
Keep full precision during intermediate calculations and round only the final displayed result. Rounding too early can introduce avoidable errors.
Are the numbers I enter sent to analytics?
Entered numbers, prices, marks, calculated results, and calculation history should not be included in analytics events.