Percentage Calculator

The Four Percentage Questions You Actually Face

A percentage is a part out of one hundred, and most real problems come down to four shapes: finding the percent of a number, working out what percent one number is of another, measuring a percentage change up or down, and running a reverse percentage to recover an original amount. Once you know which shape you have, the math is short and always the same.

Students, shoppers, and finance staff use these daily. A teacher turns a raw score into a grade. A shopper checks that a coupon is as good as it claims. An analyst reports how sales moved between two quarters. A cook scales a recipe. Each is one of the four shapes below.

How Each Type Is Calculated

• Percent of a number: divide the percent by 100, then multiply by the number. So 20% of 150 is 0.20 times 150, which is 30.
• What percent one number is of another: divide the part by the whole, then multiply by 100. So 30 out of 150 is 30 divided by 150, times 100, which is 20%.
• Percentage increase or decrease: subtract the old value from the new value, divide by the old value, then multiply by 100. From 80 to 100 is 20 divided by 80, times 100, a 25% increase.
• Reverse percentage: to find the original before an increase, divide the final by 1 plus the rate as a decimal. If a price is 120 after a 20% rise, divide 120 by 1.20 to get 100.

Worked Example

A jacket rings up at 96 after a 20% markdown, and you want the pre-sale price. This is a reverse percentage on a decrease, so divide by 1 minus the rate. That is 96 divided by 0.80, which is 120. To check, take 20% of 120, which is 24, and 120 minus 24 is 96. The numbers agree.

Common Percentages at a Glance

Handy shortcut: 10% of any number is that number with the decimal point moved one place left, so 10% of 340 is 34. Halve that for 5%, and double it for 20%.

Benefits and Limits

Percentages let you compare things of different sizes on a fair scale, which is why they show up in grades, taxes, interest, and discounts. The limit is that a percent alone hides the base number. A 50% rise sounds big, but 50% of two dollars is only one dollar. Always ask "percent of what" before you act on the figure.

Common Mistakes

• Adding percentages that sit on different bases, such as treating a 20% then 10% discount as 30% off when it is really 28% off.
• Reversing a percentage change by subtracting the same percent, which does not return the original because the base changed.
• Confusing percentage points with percent, so a move from 10% to 15% is 5 points but a 50% relative increase.

Tips

• For a fast tip, use 10% as an anchor, then adjust up or down. A tip calculator handles the split.
• For a sale price, run the percent off, then subtract. A discount calculator does both steps at once.

People Also Ask

How do I find the percentage of a number?

Divide the percent by 100 and multiply by the number. For example, 15% of 240 is 0.15 times 240, which is 36.

How do I calculate percentage increase?

Subtract the old value from the new value, divide by the old value, then multiply by 100. Going from 40 to 50 is a 25% increase.

What is a reverse percentage?

It works backward from a final amount to the original. To undo a 25% increase, divide the final by 1.25. To undo a 25% decrease, divide by 0.75.

What is the difference between percent and percentage points?

Percentage points measure the gap between two percentages, while percent measures relative change. Moving from 20% to 25% is a 5-point rise and a 25% relative increase.

How do I turn a fraction into a percentage?

Divide the top number by the bottom number and multiply by 100. So 7 out of 20 is 0.35 times 100, which is 35%.

How do I work out percentage change between two numbers?

Take the new minus the old, divide by the old, and multiply by 100. A positive result is an increase and a negative result is a decrease.

Why can't I add two percentage discounts together?

Each discount applies to a smaller base than the last, so they multiply rather than add. A 20% then 10% off equals 28% off, not 30%.