Knowing how to calculate a percentage increase can be useful in several situations. Often when you watch the news, you hear about changes in prices or values described by very large numbers, but without any percentage reference that defines the context. It can often happen that by calculating the percentage of the variation in question it turns out to be very modest (for example 1 or 2%), which would make the alarmist tone of the information sources much calmer.
Steps
Method 1 of 2: Calculate a Percentage Increase
Step 1. Take note of the initial and final value of the quantity in question
For example, let's say we want to calculate the percentage increase in the cost of insurance for your car. Start by noting the following values:
- The cost of insurance before the increase was 400 €. This is therefore our initial value.
- After applying the increase, the new price is 450 €. This represents the final value.
Step 2. Calculate the size of the increment
To do this, subtract the initial value from the final one. In this step we are still working with simple numbers and not with percentages.
In our example we will get: € 450 - € 400 = € 50. We therefore have a increase of 50 €.
Step 3. Divide the result by the initial value
A percentage simply represents a relationship between two values. For example, the expression "5% of doctors" is a quick way to describe the relationship "5 out of 100 doctors". By dividing the result obtained by the initial value, we transform it into a fraction that describes the relationship between the two values.
In our example we will get: 50 € / 400 € = 0, 125.
Step 4. Multiply the result by 100
This operation transforms the coefficient calculated in the previous step into a percentage.
The final result of our example is 0, 125 x 100 = 12.5% increase in the cost of your car insurance.
Method 2 of 2: Alternative Calculation
Step 1. Take note of the initial and final value of the quantity in question
For example, let's assume that the total population of the earth went from 5,300,000,000 people in 1990 to 7,400,000,000 in 2015.
When we have to deal with numbers with so many zeros, we can simplify the calculations by rewriting the digits in play as follows: 5, 3 bln And 7, 4 bln.
Step 2. Divide the final value by the initial value
The result of this operation shows by how much the final figure has increased compared to the initial one.
- 7.4 billion ÷ 5.3 billion = 1, 4 (approximately).
- We have rounded the result to the two most significant digits. This is because the original data in our example has only two significant digits (the rest are all zeros).
Step 3. Multiply the result by 100
This data shows the percentage variation existing between the two values we compared. If the value was increased (rather than decreased), we would always get a percentage greater than 100.
1, 4 x 100 = 140%. This means that the world population, in 2015, represented 140% of that present in 1990.
Step 4. Subtract 100 from the calculated percentage
In this type of calculations, 100% represents the starting value. Then, by subtracting 100 from the calculated percentage, we find the absolute percentage change of the initial value.
- 140% - 100% = 40%. The world population has increased by 40% in 25 years.
- This calculation method is correct because the following equality starting value + increment = ending value is true. Solving the equation based on the increment we will get the following: increment = final value - initial value.
Advice
- The magnitude of the increment is also called absolute value, that is, the real quantity described by that quantity. A 50 € increase on the price of an egg and a 50 € increase on the price of a house, have the same absolute value.
- Using the exact same method described in the guide you can also calculate the percentage decrease of a value. As a result, however, you will get a negative number, which shows by how much the original value must be decreased.
- The percentage increase shows the variation relative, that is, by how much the original value must be increased. For example, a $ 50 increase in the price of an egg is a very large relative change. Conversely, the € 50 increase on the price of a property is a very small relative change.
