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Percentage Calculator

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Choose what you are looking for: a percent of a number, what percent one number is of another, the original whole, or the percent change from an old value to a new one. Enter the two numbers you know and the answer appears right away.

What do you want to find?

For example 15 for 15%.

The number that stands for 100%.

Use a period for decimals, like 12.5. Commas for thousands are fine. The result updates as you type.Decimals with a period, like 12.5

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Result: Result

30

15% of 200 is 30.

  • Total increased by this percent: 230
  • Total decreased by this percent: 170

Step by step

200 × 15 / 100 = 30

  1. You are looking for the part. You know the whole, 200, and the percent, 15.
  2. Multiply the whole by the percent and divide by 100: 200 × 15 / 100 = 30.
  3. Increased by this percent: 200 + 30 = 230. Decreased: 200 - 30 = 170.

Formula

part = whole × percent / 100
whole
the total, the number that is 100%
part
the portion of the whole
percent
the share in percent, such as 15 for 15%

How it works

Percent means “per hundred”, so 15% is 15/100 or 0.15. Every percentage problem has three numbers: the whole (the total, which is 100%), the part and the percent. Know two of them and you can find the third. To find a percent of a number, multiply the whole by the percent and divide by 100: 15% of 200 is 200 × 15 / 100 = 30.

To find what percent one number is of another, divide the part by the whole and multiply by 100: 30 out of 200 is 30 / 200 × 100 = 15%. To find the whole when you know a part and its percent, divide the part by the percent and multiply by 100: if 30 is 15% of something, that something is 30 × 100 / 15 = 200. This is how you get an original price back from a discount amount, for instance.

The percent change compares a new value with an old one: subtract the old value from the new value, divide by the old value and multiply by 100. A price that goes from $80 to $100 rose by (100 - 80) / 80 × 100 = 25%. A negative result means a decrease. The base is always the old value, which is why a 25% rise followed by a 20% drop brings you back where you started. For sales tax and discounts with dollar amounts, the steps below the calculator show each number.

The formula

All three main formulas are the same equation, part = whole × percent / 100, solved for a different unknown. A fast mental shortcut for the first one: move the decimal point. 10% of 250 is 25, so 5% is half of that, 12.5, and 15% is 25 + 12.5 = 37.5.

In the percent change formula the vertical bars mean the absolute value: the old value counts without its sign, so a change from -50 to -40 is an increase of 20%. A percent change from 0 cannot be calculated, because you cannot divide by zero.

Example

What is 15% of 200?

  1. You are looking for the part. The whole is 200 and the percent is 15.
  2. Apply the formula: 200 × 15 / 100 = 30.
  3. So 15% of 200 is 30. Increased by 15% the total becomes 230; decreased, it becomes 170.

15% of 200 is 30.

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Frequently asked questions

How do I find the percentage of a number?

Multiply the number by the percent and divide by 100, or multiply by the percent as a decimal. 20% of 50 is 50 × 20 / 100 = 10, or 50 × 0.20 = 10. For 7.5% of $40: 40 × 0.075 = $3.

How do I calculate what percent one number is of another?

Divide the part by the whole and multiply by 100. If you got 42 questions right out of 50, that is 42 / 50 × 100 = 84%. The whole is always the number that stands for 100%.

How do I calculate percent change between two numbers?

Subtract the old value from the new value, divide by the old value and multiply by 100. Rent going from $1,200 to $1,320 is (1,320 - 1,200) / 1,200 × 100 = 10% more. A result below zero is a decrease: $50 to $40 is -20%.

How do I find the original price before a discount?

Divide the sale price by what is left after the discount, as a decimal. A shirt costs $36 after 25% off: 36 / 0.75 = $48. In this calculator, use “The whole” mode with the part 36 and the percent 75.

What is the difference between percent and percentage points?

Percentage points measure the gap between two percentages. A rate that goes from 4% to 5% rises by 1 percentage point, but by 25% in relative terms, because 1 is a quarter of 4.

Why does a 50% drop need a 100% gain to recover?

Because each percent applies to a different base. $100 down 50% is $50. To get back to $100 the $50 has to double, which is a 100% increase. Losses and gains in percent are not symmetric.

Last updated: Responsible editor: Jared Alan
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