Percentage Calculator

Percentage calculator at a glance#

A percentage calculator solves the three most common percent questions: what a percentage of a number is, what percentage one number is of another, and how much a value changed in percent. Each one is a single multiply or divide.

What is X% of Y? Multiply the number by the percentage written as a decimal: Y times X divided by 100. So 20% of 80 is 80 times 0.20, which is 16.

X is what percent of Y? Divide the part by the whole, then multiply by 100: X divided by Y times 100. So 30 is 25% of 120, because 30 divided by 120 is 0.25, times 100 is 25.

Percent change. Subtract the old value from the new value, divide by the old value, then multiply by 100: (new minus old) divided by old, times 100. Going from 40 to 50 is a 25% increase, because 50 minus 40 is 10, 10 divided by 40 is 0.25, times 100 is 25. A negative result means a decrease.

Enter your numbers in the calculator above for the exact result in any of these three modes. The math is exact, so any rounding you see is just the display trimming long decimals.

The three percent questions#

Most percentage work is one of three calculations, and each is a single multiply or divide. The calculator above does them instantly, but knowing the method lets you check the result.

Percent of a number#

Write the percentage as a decimal and multiply: Y times (X / 100). To find 20% of 80, multiply 80 by 0.20 to get 16. To find 7.5% of 240, multiply 240 by 0.075 to get 18.

What percent one number is of another#

Divide the part by the whole, then multiply by 100. If 30 out of 120 questions are correct, that is 30 / 120 = 0.25, times 100 = 25%. A score of 45 out of 50 is 45 / 50 = 0.90, or 90%.

Percent change#

Subtract the old value from the new value, divide by the old value, then multiply by 100. From 40 to 50 is (50 - 40) / 40 = 10 / 40 = 0.25, a 25% increase. From 200 to 150 is (150 - 200) / 200 = -0.25, a 25% decrease. A negative result is a drop.

Percent change vs percent difference#

These two sound alike but answer different questions. Percent change has a direction: it measures the move from a starting value to a later one, so it can be an increase or a decrease. Use it for prices, salaries, and growth over time.

Percent difference has no direction. It compares two values against their average: the absolute gap divided by the average of the two, times 100. For 40 and 50, the gap is 10 and the average is 45, so the difference is 10 / 45 = 0.222, about 22.2%. Use it when neither value is the "before", such as comparing two measurements.

Reading the result#

A percentage above 100% is normal: 150% of 80 is 120, because anything over 100% is more than the whole. A percent change can also pass 100% when a value more than doubles, so going from 20 to 50 is a 150% increase.

Do not confuse a percentage with a percentage point. If an interest rate rises from 4% to 5%, that is a 1 percentage point rise but a 25% increase relative to the starting rate. A basis point is one hundredth of a percentage point, so 25 basis points is 0.25 percentage points.

Percentage FAQ#

What is the difference between a percent and a percentage point?#

A percentage point is the plain gap between two percentages. Moving from 4% to 5% is a 1 percentage point change, but a 25% increase relative to 4%, since 1 / 4 = 0.25. Use percentage points when you compare two rates and percent change when you compare against a starting value.

How do I find a percentage of a number?#

Multiply the number by the percentage written as a decimal. For 15% of 60, multiply 60 by 0.15 to get 9. For 150% of 40, multiply 40 by 1.5 to get 60.

How do I work out a percentage without a calculator?#

Break it into round parts. 10% of any number is the number with the decimal moved one place left, so 10% of 250 is 25. Halve that for 5% (12.5), and add parts together for figures like 15% (25 + 12.5 = 37.5).

How do I calculate a percentage decrease?#

Subtract the new value from the old, divide by the old value, then multiply by 100. A price cut from 80 to 60 is (80 - 60) / 80 = 0.25, a 25% decrease. The same formula gives a negative number if you keep the new-minus-old order.

How do I work out a discount and the sale price?#

Multiply the original price by the discount as a decimal to get the amount off, then subtract. A 30% discount on 50 is 50 times 0.30 = 15 off, leaving a sale price of 35. A quicker route is to multiply by (1 - 0.30) = 0.70 to land on 35 directly.

What is a basis point?#

A basis point is one hundredth of a percentage point, or 0.01%. It is used in finance for small rate moves, so a shift of 50 basis points means 0.5 percentage points.