1
What is 15% of 200?
Find a percentage of a number
(percentage / 100) x number(15 / 100) x 200 = 30
15% of 200 is 30.Percentage guide
How to Calculate Percentages
A percentage is simply an amount out of 100. The calculation becomes much easier once you identify what you know, what you need to find, and which number should be the base.
Start with the question
Choose the percentage formula that fits
The word percentage does not always describe the same calculation. Match your question to one of these four patterns first.
2
12 is what percent of 60?
Turn a part into a percentage
(part / total) x 100(12 / 60) x 100 = 20%
12 is 20% of 60.3
What is 20% of 50%?
Find a percentage of a percentage
(first percentage / 100) x second percentage(20 / 100) x 50% = 10%
20% of 50% is 10%.4
How much did 100 change to 125?
Measure an old-to-new change
((new - old) / old) x 100((125 - 100) / 100) x 100 = 25%
The value increased by 25%.Method 1
How to find a percentage of a number
Divide the percentage by 100 to turn it into a decimal, then multiply that decimal by the number. This is the method to use when the question already gives you the percentage, as in "What is 15% of 200?"
- Convert 15% to a decimal: 15 / 100 = 0.15.
- Multiply by the number: 0.15 x 200 = 30.
- State the result: 15% of 200 is 30.
A useful sense check is that 15% is less than one fifth, so the answer should be less than 40. That catches common errors such as multiplying 200 by 15 instead of 0.15.
Method 2
How to find what percent one number is of another
When you know the part and the total, divide the part by the total and multiply by 100. In "12 is what percent of 60?", 12 is the part and 60 is the total.
12/60x100=20%
The total cannot be zero because division by zero is undefined. If the part is larger than the total, the answer can validly be more than 100%.
Method 3
How to calculate a percentage of a percentage
Treat the first percentage as the share. Convert it to a decimal, then multiply it by the second percentage. For 20% of 50%, turn 20% into 0.20 and calculate 0.20 x 50%.
0.20 x 50%10%
This is not the same as adding 20 percentage points to 50%. "20% of 50%" equals 10%, while "50% plus 20 percentage points" equals 70%.
Choose the right comparison
Increase, change, or difference?
These terms sound similar, but the base of the calculation changes. Use the starting value for an increase or change. Use the average of both values when neither value is the starting point.
Percentage increase
A value moved upward from an original amount.
- Calculation base
- The original value
Percentage change
A value moved up or down from an old amount.
- Calculation base
- The old value
Percentage difference
You are comparing two values and neither is the starting point.
- Calculation base
- The average of both values
Adjust a value
How to add or subtract a percentage
To add 20% to 80, first find 20% of 80, which is 16, then add it to the original: 80 + 16 = 96. The one-step formula is 80 x 1.20 = 96.
To subtract 20%, multiply by what remains: 100% - 20% = 80%, so 80 x 0.80 = 64. For a price reduction, the percent off calculator shows both the amount saved and the final price.
Keep this handy
Percentage formula reference
Use this table when you know the type of question and only need the matching formula.
| What you need | Formula | Example |
|---|---|---|
| Find a percent of a number | (percentage / 100) x number | 15% of 200 = 30 |
| Find what percent one number is of another | (part / total) x 100 | 12 out of 60 = 20% |
| Find a percentage of a percentage | (first percentage / 100) x second percentage | 20% of 50% = 10% |
| Find percentage change | ((new - old) / old) x 100 | 100 to 125 = 25% increase |
| Increase a number by a percentage | number x (1 + percentage / 100) | 80 plus 20% = 96 |
| Decrease a number by a percentage | number x (1 - percentage / 100) | 80 minus 20% = 64 |
Without a calculator
Useful mental percentage shortcuts
You can combine these pieces to figure out a percentage quickly. For example, 15% of 200 is 10% (20) plus 5% (10), giving 30.
Check your working
Common percentage mistakes
Using the percentage as a whole number
15% means 15 out of 100, so use 0.15 when multiplying. Multiplying by 15 makes the answer 100 times too large.
Dividing the numbers in the wrong order
For "12 is what percent of 60?", 12 is the part and 60 is the total. The calculation starts with 12 / 60, not 60 / 12.
Using the wrong comparison formula
Change uses the original value as its base. Difference uses the average of both values. They answer different questions and can give different results.
Rounding before the final step
Keep the full decimal while you work, then round the final answer. Early rounding can noticeably change percentages with several decimal places.
Check a result
Use the calculator that matches the question
Use the broad tool for percent of a number, part of a total, percentage of a percentage, and mixed everyday questions.
Use this focused tool when a value has gone up from an original amount.
Use this when you are comparing two values without calling either one the original.
Use this for an old-to-new increase, decrease, or unchanged value.
Use this to find the discount amount and final sale price.
FAQ
Percentage questions, answered
What is the easiest way to calculate a percentage?
First decide what the question is asking. To find a percentage of a number, divide the percentage by 100 and multiply by the number. To find what percent one number is of another, divide the part by the total and multiply by 100.
What is the basic percentage formula?
The basic formula for finding what percentage a part is of a total is (part / total) x 100. To find a stated percentage of a number, use (percentage / 100) x number.
How do I work out a percentage without a calculator?
Break the percentage into easy pieces. Find 10% by dividing by 10, find 1% by dividing by 100, and combine those pieces. For example, 15% is 10% plus 5%.
How do I turn a decimal into a percentage?
Multiply the decimal by 100 and add the percent sign. For example, 0.35 x 100 = 35%.
How do I turn a fraction into a percentage?
Divide the numerator by the denominator, then multiply by 100. For example, 3 / 4 = 0.75, and 0.75 x 100 = 75%.
Why are percentage change and percentage difference not the same?
Percentage change compares a new value with an original value and uses the original as the base. Percentage difference compares two values without a starting point and uses their average as the base.