In mathematics, the concept of percent change is used to describe the relationship between a past and a present value. Specifically, the percentage change represents the difference between a past value and a present one in terms of a percentage of the past value. The equation to use is **((V _{2} - V_{1}) / V_{1}) × 100** in which V

_{1}represents the past or initial value and V

_{2}represents the present or final value. If the number is positive, then there is a percentage increase. If it is negative, there is a percentage decrease or decrease. If you prefer to avoid working with negative numbers, you can use a modified formula to determine the percentage decrease.

## Steps

### Method 1 of 2: Use the Standard Equation

#### Step 1. Subtract the original value from the new value

When a percentage increase is to be calculated, the smallest number is the original (or past) and the largest is the new (or present). If it is a decrease, it is just the opposite. This formula can be used to calculate both a percentage increase and decrease. If the answer is a negative number instead of a positive one, then the percentage change is a decrease.

- For example, suppose you want to determine how much your income has increased from year to year. If you earned $ 37,000 last year and this year $ 45,000, then subtract 37,000 from 45,000. The result is 8,000.
- Another example. In the world of retail sales, when a product is discounted, it is typically expressed as "X% off." This represents a percentage decrease. If pants used to cost $ 50 and now $ 30, then $ 50 is the original value and $ 30 is the new one. To get started, subtract $ 50 from $ 30. The result is - $ 20.

#### Tip:

If you are going to work with variables whose values have undergone more than one variation, find only the percentage variation of those two values that you want to compare.

#### Step 2. Divide the answer by the original value

After finding the difference between the numbers, divide that number by the original value which is the smallest number if it is a percentage increase or the largest number if it is a decrease.

- Continuing with the example, divide 8,000 (difference between income) by 37,000 (original value). The answer is 0, 216.
- In the second case, by dividing the difference (- $ 20) by the original value ($ 50) you will obtain -0.40. Another way of looking at it is considering the variation of $ 20 as 0.40 from the original point whose value underwent a variation in the sense negative.

#### Step 3. Multiply the answer by 100

To convert the answer to a percentage, all you have to do is multiply it by 100.

- Take the 0.216 and multiply it by 100. In this case, the answer is 21.6 so your income increased by 21.6%.
- In the second example, to get the final percentage, you can multiply the answer in decimal (-0.40) by 100: 0.40 × 100 = -40%. This means that the new price of the pants, $ 30, represents 40% less than the previous price of $ 50. In other words, the pants were 40% off. Another way to look at it is to consider that $ 20 price difference as 40% of the initial price, which was $ 50. As this price variation implies a lower final value, the sign to use is the negative one.

### Method 2 of 2: Calculate a Percent Decrease Using an Alternative Method

#### Step 1. Subtract the new value from the original value

To calculate a price decrease using this formula, subtract the smallest number (the new or final value) from the largest number (the old or original value). Keep in mind that this method is the opposite of the one used to find a percentage change with the standard formula.

### For example, suppose you want to find out by how much the enrollment of a school has varied from year to year. If this year's enrollment is 12 125 and last year it was 13,500, subtract 12 125 from 13,500. This results in 1,375

#### Step 2. Divide the answer by the original value

Remember that if you want to determine a percentage decrease, the original value is the largest number.

### In this case you will have to divide 1375 (the difference between the numbers) by 12 125 (the original value). This is equal to 0.1134

#### Step 3. Multiply the answer by 100

Converting the answer from decimal to percent is easy. You just have to multiply the value by 100.

### Multiply 0.1134 by 100. This equals 11.34. Therefore, enrollment decreased by 11.34%

#### Tip:

If you use this equation and end up with a negative number, it means there was a percentage decrease.