The percentage calculator answers the three percentage questions people ask most often, from just two numbers. Enter a first value and a second value, press Calculate, and the calculator shows all three results at once, so you do not need to work out which formula to use or to run the same figures through three separate tools. Percentages appear everywhere: in shop discounts, in exam marks, in pay rises, in tax and tips, and in price changes. A percentage is simply a number out of one hundred, and once the base value is clear, the arithmetic is short. The difficulty is usually knowing which value is the base and which value is being compared with it, and this page keeps that distinction visible in every result.
What Is a Percentage?
A percentage means parts per hundred. The symbol % is a shorthand for dividing by 100, so 20% is 20 divided by 100, which is 0.20. To find a percentage of a value, multiply the value by the percentage as a decimal: 20% of 200 is 0.20 times 200, which is 40. To express one value as a percentage of another, divide the first value by the second and multiply by 100: 40 as a percentage of 200 is 40 divided by 200 times 100, which is 20%. Percentages above 100% are possible whenever the compared value is larger than the base: 250 as a percentage of 200 is 125%, because 250 is one and a quarter times 200. A percentage change can also be negative, which means a fall rather than a rise.
How to Use the Calculator
- Enter the first value (a): the value you want to compare, or the percentage figure in the second calculation, depending on the result you need.
- Enter the second value (b): the base value the first value is compared with.
- Press Calculate and read all three rows: the first value as a percent of the second, the percent of the second value, and the percentage change from the second value to the first.
- Change either figure and calculate again to test a different price, mark, or pay figure.
Worked Example
With the starting figures of 20 and 200, the three rows are easy to check by hand. First, 20 as a percentage of 200 is 20 divided by 200, which is 0.10, or 10%. Second, 20% of 200 is 0.20 times 200, which is 40. Third, the percentage change from 200 to 20 is 20 minus 200, which is minus 180, divided by 200, which is minus 90%. The minus sign matters: it shows that 20 is 90% lower than 200, not 90% higher. Try a rise instead: enter 220 as the first value and 200 as the second. The first value is then 110% of the second, 220% of 200 would be a different figure, and the change from 200 to 220 is a rise of 10%. Keeping the two input labels in mind stops the most common error, which is swapping the base and the compared value.
The Three Calculations Explained
The first row divides the first value by the second and multiplies by 100. Use it for questions such as: what percentage of the class passed, what share of a budget was spent, or what fraction of a target was reached? The second row treats the first value as a percentage and applies it to the second value. Use it for questions such as: what is 15% of a bill, what is a 20% tip on a meal, or what is a 5% fee on a payment? The third row subtracts the second value from the first, divides by the second value, and multiplies by 100. Use it for questions such as: by what percentage did a price rise, how much did a salary increase, or how far did a stock fall? Each row uses the same two inputs, but each answers a different question, so read the label beside each result before you use it.
Common Percentage Mistakes
Adding percentages that have different bases is the most frequent mistake. A 20% rise followed by a 20% fall does not return to the starting value: 100 rising by 20% becomes 120, and 120 falling by 20% becomes 96. Percentages also cannot be averaged by simply adding them and dividing, unless they share the same base. Another common error is confusing percentage points with percent: a rate rising from 10% to 12% has risen by 2 percentage points, which is a 20% relative increase. When a shop says an extra 10% off an already discounted price, the second discount applies to the reduced price, not the original price, so two 10% discounts are not the same as one 20% discount. This calculator shows the arithmetic for one step at a time, which makes each step easy to check.
Who Uses This Calculator
Shoppers use it to check discounts, sale prices, and value-added tax before paying. Students use it for marks, grades, and test scores, where a raw score only makes sense as a percentage of the total. Workers and managers use it for pay rises, targets, and performance changes, where the base year or the original salary must stay fixed. Sellers use it to set prices, work out margins, and compare offers on the same base. Anyone comparing two figures over time, such as household spending, savings, or a gold price, needs the percentage change row, because the raw difference alone does not show whether a change is large or small relative to where it started.
All Tools | Profit Margin Calculator
Frequently Asked Questions
How do I calculate a percentage of a number?
Multiply the number by the percentage divided by 100. For example, 20% of 200 is 200 times 0.20, which is 40. Enter 20 as the first value and 200 as the second value, and read the second result row.
How do I find what percentage one number is of another?
Divide the first number by the second number and multiply by 100. For example, 20 divided by 200 times 100 is 10%. Enter the compared value first and the base value second, and read the first result row.
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the original value, and multiply by 100. A positive answer is an increase and a negative answer is a decrease. Enter the new value first and the original value second, and read the third result row.
What is the difference between percent and percentage points?
A percentage point is the simple difference between two percentages, while a percent change is relative to the starting percentage. Moving from 10% to 12% is a rise of 2 percentage points, which is a 20% relative increase.
Can a percentage be more than 100%?
Yes. A percentage above 100% means the compared value is larger than the base value. For example, 250 is 125% of 200, and a value that doubles has increased by 100%.
What happens if the second value is zero?
A percentage of zero, or a change from zero, cannot be calculated by division, because division by zero has no result. The calculator will ask for a valid second value, so enter a non-zero base.
Does this calculator store my figures?
No. The calculation runs in your browser from the two numbers you enter, and nothing is sent to a server or stored. You can close the page and the figures are gone.