Percentage Calculator

Percentage calculator at a glance#

How do you calculate a percentage of a number?#

Convert the percentage to a decimal and then multiply. 22% is 0.22, so 22% of 3,500 is 3,500 × 0.22 = 770. With the calculator above, you can select either Common Phrases or Simple Percentage, input the percentage and the number, and then hit Calculate.

What is 30% of 9,700?#

30% of 9,700 is 2,910. You multiply 9,700 by 0.30, or determine 10% of 9,700, which is 970, and then multiply that by 3.

How do you calculate a percentage change?#

First, subtract the old value from the new one, then divide by the old value and multiply by 100. If there is an increase from 3,500 to 4,270, the change is 770, and 770 ÷ 3,500 × 100 results in 22%. This is a 22% increase. The Percentage Difference mode in the calculator gives you this figure along with the percentage difference.

What a percentage means#

A percent is a ratio with a denominator of 100, as defined by the OpenStax Prealgebra 2e textbook. So 22% means 22 out of every 100. It can be expressed as the fraction 22/100 or as the decimal 0.22. Every percentage problem involves three numbers: the whole, the part, and the percentage.

The formula is: part = percentage ÷ 100 × whole

Here, the whole is 3,500, the percentage is 22%, and the part is 770. Each question below begins with two of these numbers and helps you find the third one.

The three percentage questions#

The Common Phrases mode in the calculator has a row for each of these queries. Fill in only the row you need.

Finding a percentage of a number#

To find a percentage of a number, multiply the number by the percentage expressed as a decimal: 22% of 3,500 equals 0.22 times 3,500, resulting in 770. This process is what the Simple Percentage mode follows.

Finding what percent one number is of another#

You calculate what percent one number is of another by dividing the part by the whole and then multiplying by 100: 770 divided by 3,500 and then multiplied by 100 gives you 22%. This is similar to how a test score turns into a percentage, so 45 out of 50 is 45 divided by 50 times 100, resulting in 90%. If you want to combine several scores into a weighted result, use the grade calculator.

Finding the whole from a part and a percentage#

This task involves dividing the part by the percentage written as a decimal: 770 divided by 0.22 results in 3,500. This method is used when you know a part and its percentage but not the total amount, like when 770 people responded to a survey, which was 22% of everyone you approached.

Percentage increase and decrease#

In the Percentage Change mode, you apply a percentage to a number. To increase 3,500 by 22%, multiply it by 1.22: 3,500 times 1.22 is 4,270. To decrease a number, multiply by 1 minus the percentage written as a decimal. Decreasing 9,700 by 35% is 9,700 × 0.65 = 6,305.

To determine the percentage change between two values, use the Percentage Difference mode. It calculates the change by dividing by the first value, or the original, which is the method the OpenStax textbook uses to find a percent increase or decrease. From 3,500 to 4,270, the change is 770, and 770 divided by 3,500 times 100 equals 22%, indicating an increase.

If you return to the original number, the calculation changes. Moving from 4,270 to 3,500, the change remains 770, but since the original is now 4,270, the decrease is 770 divided by 4,270 times 100, resulting in 18.03%. The same difference represents a smaller portion of the larger number.

This is also why a 22% increase followed by a 22% decrease doesn't return you to the starting point. Increasing 3,500 by 22% results in 4,270, while decreasing 4,270 by 22% leads to 3,330.60, which is 169.40 below where you started.

To reverse a percentage increase, divide by the multiplier rather than subtracting the percentage: 4,270 divided by 1.22 equals 3,500. In the calculator, if you enter 4,270 is 122% of what in the third Common Phrases row, you get the same outcome.

Percentage difference#

Percentage difference compares two values when neither serves as the starting point, like the same item having different prices at two stores. The calculator divides the gap by the average of the two values and multiplies by 100. For 3,500 and 4,270 the average is 3,885, so the difference is 770 ÷ 3,885 × 100 = 19.82%. This result falls between the 22% increase and the 18.03% decrease, since the average lies between the two values.

Percentage points and a percent of a percent#

When numbers are already percentages, a change can be described in two ways. If an interest rate moves from 4% to 5%, it rose by 1 percentage point, and it also increased by 25% in relative terms, because 1 is 25% of 4. Both statements are accurate, so it's useful to specify which one you mean.

Calculating a percent of a percent is straightforward multiplication. 20% of 30% is 0.20 × 30% = 6%. Enter 20 and 30 in the first Common Phrases row and read the result of 6 as 6%.

Where percentages come up#

• Discounts: 20% off an $80 item is $16 off, meaning you pay $64.
• Tips: a 20% tip is calculated by multiplying the bill by 0.20. The tip calculator adds this amount and splits the total among people.
• Test scores: 45 out of 50 equals 90%.
• Conversions: 0.22 converts to 22%, and 22% is represented as 11/50 in fraction form. The decimal to percent calculator and the percent to fraction calculator handle these conversions.

Common percentage values#

The first table shows common percentages of 3,500 and 9,700, which are used in the calculator's Percentage Change examples. Every value is exact.

The second table converts scores and other X out of Y results into percentages, rounded to two decimal places when necessary.

Sources#

• OpenStax, Prealgebra 2e, section 6.1: Understand Percent
• OpenStax, Prealgebra 2e, section 6.2: Solve General Applications of Percent

Frequently asked questions#

How do you find what percent one number is of another?#

Divide the first number by the second and multiply by 100. So, 15 out of 25 is 15 ÷ 25 × 100 = 60%, and 10 out of 45 equals 22.22%, rounded to two decimal places.

What is the formula for percentage change?#

The formula for percentage change is (new value − old value) ÷ old value × 100. A positive result indicates an increase and a negative one a decrease. From 3,500 to 4,270 the change is a 22% increase, and from 4,270 to 3,500 it's an 18.03% decrease.

How do you work out a percentage without a percent key?#

Shift the decimal point two places to the left and multiply. 30% becomes 0.30. Therefore, 30% of 9,700 is 9,700 × 0.30 = 2,910.

How do you reverse a percentage increase?#

Divide by 1 plus the percentage expressed as a decimal. If a price increased 22% to 4,270, the original was 4,270 ÷ 1.22 = 3,500. Subtracting 22% of 4,270 gives an incorrect result, 3,330.60.

What is the difference between percentage change and percentage difference?#

Percentage change is calculated against a starting value, so direction matters. Percentage difference uses the average of two values, making the order irrelevant. For 3,500 and 4,270, the change is a 22% increase or an 18.03% decrease depending on direction, while the difference is 19.82% regardless.

What is 200% of a number?#

It's double the number. 200% of 3,500 is 2 × 3,500 = 7,000. Percentages over 100% are common for growth, and when a value doubles, it has grown by 100%.