How to Calculate Percentage Increase

Two Methods:Calculating Percentage IncreaseAlternate Method

Knowing how to calculate percentage increase is useful in a variety of situations. 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 only 2%, you'll know not to believe the scare stories.

Method 1
Calculating Percentage Increase

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    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.
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    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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    Divide the answer by the starting value. 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.
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    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.

Method 2
Alternate Method

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    Write down the start value and end value. Let's start with a new example. The world population went from 5,300,000,00 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.
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    Divide the end value by the starting value. This will tell us how much bigger the end result is than the original.[2]
    • 7.4 billion รท 5.3 billion = about 1.4.
    • We've rounded to two significant digits because that's how many there were in the original problem.
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    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.
    • 1.4 x 100 = 140%. This means the world population in 2015 is 140% the size of the population in 1990.
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    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.

Tips

  • 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.
  • 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.
  • The size of the increase is also called the absolute change, meaning the actual quantity described.[3] A $50 increase in the price of an egg and a $50 increase in the price of a house have the same absolute increase.

Article Info

Categories: Mathematics | Learning Techniques and Student Skills