In mathematics, the concept of "percentage change" is used to describe the relationship between a new and a previous value. Specifically, the percentage change expresses the difference between the new and the old value as a percentage of the second. Use the equation ((V2 - V1) / V1) × 100, where V1 represents the initial value and V.2 the present value. If the number is positive, it indicates a percentage increase; if it is negative, a reduction. You can also use a modified formula to calculate a percentage reduction without working with negative numbers.
Steps
Method 1 of 2: Using the Standard Equation
Step 1. Subtract the original value from the new one
When you calculate a percentage increase, the smallest number is the original (or old) number and the largest is the new (or final) value. The opposite is true for percentage reductions. You can use this formula for both increases and decreases. If the result is a negative number, you know that the percentage change is a reduction.
- For example, imagine you want to find out how much your salary has increased from last year to the next. If you earned € 37,000 last year and € 45,000 this year, subtract 37,000 from 45,000 and you get 8,000.
- Alternatively, in the retail world, when a product receives a discount, it is often expressed as "x% less", which is a percentage reduction. If some pants cost € 50 and now you can buy them for € 30, € 50 is the initial value and € 30 the new one. To start with, subtract € 50 from € 30 and you get -20 €.
Advise:
when dealing with variables with more than one change in value, find the percentage change of just the two values you want to compare.
Step 2. Divide the result by the original value
Once you find the difference between the digits, divide that number by the original value - the smallest for a percentage increase or the largest for a percentage decrease.
- Going back to the previous example, divide 8,000 (the difference between the two salaries) by 37,000 (the original value) and you will get 0, 216.
- Alternatively, dividing the difference (-20 €) by the old value (50 €) you get -0.4. Another way to understand this result is to consider that the variation of 20 € is equal to 40% of the starting value of 50 € and that was negative.
Step 3. Multiply the result by 100
To convert the result into a percentage, simply multiply it by 100.
- Take 0, 216 and multiply that by 100. In this case the result is 21.6, so your income has increased by 21.6%.
- In the other case, multiply the decimal result (-0, 4) by 100 to get the final percentage. -0, 4 × 100 = -40%. This means that the new price of € 30 is discounted by 40% compared to the old one of € 50. Another way to understand this result is to consider that the price difference of € 20 is equal to 40% of the initial price of € 50. Since the change leads to a lower final price, it has a negative sign.
Method 2 of 2: Calculate Percentage Reductions Differently
Step 1. Subtract the new value from the original one
To calculate the percentage reduction using this formula, subtract the smallest number (the new or final value) from the largest number (the original or old value). Note that this step is the reverse of the one described in the previous method.
For example, imagine you want to calculate the change in the number of people enrolled in a school over the years. If the number of subscribers this year is 12,125, while the previous year was 13,500, subtract 12,125 from 13,500 to get 1,375
Step 2. Divide the answer by the original value
Remember that when determining percentage reductions, the original value is the largest number.
In this case, divide 1,375 (the difference between the numbers) by 13,500 (the original value), resulting in 0.1019
Step 3. Multiply the result by 100
It's easy to convert the result from decimal to percentage - just multiply it by 100.
Multiply 0, 1019 by 100 and you will get 10, 19. In this case, therefore, the number of subscribers has dropped by 10, 19%
Advise:
if using this equation you get a negative change, you are dealing with a percentage increase.
