How to find the percentage increase of 2 numbers

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Knowing how to calculate percentage increase is useful in a variety of situations. For instance, even when watching the news, you'll often hear a change described in large numbers without any percentage to give them context. If you calculate the percentage increase and discover it's actually less than 1%, you'll know not to believe the scare stories. Calculating percentage increase is as simple as dividing the size of the increase by the original amount.

Practice Problems

1
Write down the starting value and end value. For example, let's say your auto insurance premium just went up. Write down these values:
- Your car insurance premium was $400 before the increase. This is the starting value.
- After the increase, it costs $450. This is the end value.
2
Find the size of the increase. Subtract the starting value from the end value to find the out how much it increased.[1] We're still working with ordinary numbers at this point, not percentages.
- In our example, $450 - $400 = a $50 increase.
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3
Divide the answer by the starting value.[2] A percentage is just a special kind of fraction. For example, "5% of doctors" is quick way to write "5 out of 100 doctors." By dividing the answer by the starting value, we turn it into a fraction that compares the two values.
- In our example, $50 / $400 = 0.125.
4
Multiply the result by 100. This converts your last result into a percentage.
- The final answer to our example is 0.125 x 100 = 12.5% increase in auto insurance premiums.

1
Write down the start value and end value. Let's start with a new example. The world population went from 5,300,000,000 people in 1990 to 7,400,000,000 in 2015.
- There's a trick to these problems with many zeroes. Instead of counting the zeroes each step of the way, we can rewrite these as 5.3 billion and 7.4 billion.
2
Divide the end value by the starting value. This will tell us how much bigger the end result is than the original.[3]
- 7.4 billion ÷ 5.3 billion = about 1.4.
- We've rounded to two significant digits because that's how many there were in the original problem.
3
Multiply by 100. This will tell you the percentage comparison between the two values. If the value increased (instead of decreasing), your answer should always be larger than 100.[4]
- 1.4 x 100 = 140%. This means the world population in 2015 is 140% the size of the population in 1990.
4
Subtract 100. In this kind of problem, "100%" is the size of the starting value. By subtracting this from our answer, we're left with just the percentage size of the increase.
- 140% - 100% = a 40% increase in population.
- This works because starting value + increase = end value. Rearrange the equation and we get increase = end value - starting value.

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Question
Why does my answer keep coming out wrong?

Grace Imson, MA
Math Instructor, City College of San Francisco
Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.

Math Instructor, City College of San Francisco
Expert Answer

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Make sure you're not using the wrong denominator to calculate the percentage increase. The original price, not the difference, should be the denominator when you're dividing. The difference should be the numerator.
Question
How can I learn to increase numbers by a certain percentage?

Convert the percentage to a decimal. Multiply the original number by that decimal. Add that product to the original number. The sum is the final number you're seeking.
Question
How do I determine the percentage between a product's yearly production increase?

Subtract the first year's production from the second year's production. Take that difference, and divide it by the first year's production. That's the percentage increase in production.

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The size of the increase is also called the absolute change, meaning the actual quantity described.[5] A $50 increase in the price of an egg and a $50 increase in the price of a house have the same absolute increase.
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The percentage increase tells you the relative change, meaning how much it increased in relation to the starting value. A $50 increase in the price of an egg is a huge relative increase. Adding $50 to the price of a house is a tiny relative increase.[6]
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You can calculate the percentage decrease with the exact same method. You'll end up with a negative number, showing that the amount became smaller.
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Article SummaryX

To calculate percentage increase, start by writing down the starting value and the current value. Then, subtract the starting value from the current value. Next, divide that number by the starting value. Finally, multiply the number you got by 100 to find out the percentage increase. If you want to learn how to find the percentage increase by dividing the start and end values, keep reading!

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