Percentage Calculator

This calculator handles common percentage questions. It allows you to calculate the percent of a number, find the percent change between two numbers, measure the percent difference between two numbers or apply two percentages one after another. Select a mode, enter the known values and let the calculator fill in the desired fields.

What is a percentage?

A percentage is a fraction with a denominator of 100. The word "percent" comes from the Latin per centum, which means "per hundred". So 25% represents a quantity of 25 units (each unit being 1/100), or the fraction 25/100, or the decimal number 0.25. Since a percentage is a ratio, it has no unit and can therefore be used in many fields such as finance, grades, statistics, and science.

Percentages allow things to be compared on the same scale. For example, 27 points out of 30 and 195 points out of 250 are hard to compare at a glance, but 90% and 78% make it clear which is higher.

Percentage of a number:

This is the typical "What is P percent of X?" calculation. Multiply this number by the percentage expressed as a decimal, with a denominator of 100.

For example, if you apply 15% to 200, this is how it works out:

If you rephrase this relationship, two other problems can be solved as well. If another field is left blank, the calculation tool will calculate the value of that field.

Percentage change

Percentage change measures how much a value has changed relative to an original amount. It is directional and requires both an initial (old) value and a final (new) value.

For an increase from 50 to 75 the change is (75 - 50) / 50, multiplied by 100, which results in a 50% increase. Since a positive result indicates an increase and a negative result indicates a decrease, the same formula can be used for both cases. To increase 500 by 10%, multiply 500 by 1.10, which equals 550. To decrease 500 by 10%, multiply 500 by 0.90, which equals 450.

Percentage difference

The percentage difference is used to compare two values when neither of them is a reference value. As the difference is divided by the average of the two values and not by a starting value, the result is symmetric.

For 5 and 7 the difference is calculated as absolute difference 2, divided by the average 6, multiplied by 100, which gives approximately 33.33%. Swapping the two numbers still results in the same answer of 33.33%, regardless of order.

Percentage change or percentage difference?

Because they answer different questions, the results are usually not the same. A percentage change has a reference value and indicates direction, so an increase from 5 to 7 is expressed as 40%. A percentage difference has no reference value or direction, so 5 and 7 have the same difference regardless of order, which is 33.33%. Use percentage change when one value represents a previous or reference value; use percentage difference when two values are just two measurements. Note: There's not a single, universal formula for percentage difference. This tool uses the most common convention, which is to average the two numbers as the denominator.

Percentage of percentages

Sometimes a second percentage is applied to a result that has already had a percentage applied to it. For example, if you want to take the 20% share and split it further by 10%, then do this calculation:

Thus, applying 20% to 10% on 1000 is done by multiplying 1000 by 0.20 and then multiplying the result by 0.10, which gives a result of 20. In practice, these two percentages can be combined into one single percentage. Applying 20% to 10% is equivalent to applying 2% overall. This differs from adding percentages together, and is often the source of errors when discounts or fees are applied in layers.

Percentages and percentage points

Confusing the two terms is the most common mistake made when dealing with percentages. A percentage point is the direct arithmetic difference between two percentage values, while a percentage change is relative. If a value goes from 10% to 12%, it has increased by 2 percentage points but also by 20%. 2 is 20% of the original value, which was 10. Both representations are correct and describe the same change, so it's good practice to clarify what type of value you're referring to.

Applications of percentages

Percentages are used in all areas of daily life. Stores advertise discounts of 25%, restaurants suggest tipping at 18%, and sales tax is added as a percentage to the gross price. Banks quote interest rates or yields as annual percentages, while polling agencies report results with margins of error of several percentage points. Mobile phones also show battery charge levels as a percentage of full capacity. The reverse calculation is just as useful: to find out what an item cost before a 10% discount was applied, divide the sale price by 0.90; and to find out what it cost before a 10% increase, divide by 1.10.