# 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.

## Steps

### Method 1 Calculating Percentage Increase

- 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.

- Your car insurance premium was
- 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**.

- In our example, $450 - $400 =
- 3
**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**.

- In our example,
- 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**.

- The final answer to our example is 0.125 x 100 =

### Method 2 Alternate Method

- 1
**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**.

- 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
- 2
**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.

- 7.4 billion รท 5.3 billion = about
- 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.- 1.4 x 100 =
**140%**. This means the world population in 2015 is 140% the size of the population in 1990.

- 1.4 x 100 =
- 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.

- 140% - 100% =

## 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