Math Calculators
Percentage Decrease Calculator

# Percentage Decrease Calculator

The percentage decrease calculator finds a percentage decrease from the starting value to the final value and identifies whether the change is an increase or a decrease.

Percentage Decrease

50% decrease

There was an error with your calculation. The percentage decrease calculator, or percent decrease calculator, finds the decrease from one value (the starting value) to another (the final value) in percentages.

## Directions for use

To use this percentage reduction calculator, enter the starting and final values into the corresponding input fields, and press “Calculate.” The calculator will return the percentage decrease value. Suppose the final value is larger than the starting value. In that case, the calculated percentage decrease will be negative, and the calculator will display both the negative percentage decrease and the corresponding (positive) percentage increase.

You can input integers, decimals, and numbers in e-notation. Both input values can be either positive or negative.

## Percentage decrease calculation

To calculate the percentage decrease from the starting value Vₛ to the final value V𝒻, take the following steps:

1. Subtract the final value from the starting value: Vₛ – V𝒻.
2. Divide the result of step 1 by the absolute value of Vₛ: (Vₛ – V𝒻) / |Vₛ|.
3. Multiply the result of step 2 by 100 to get the result in percentages.

The following formula can summarize the above steps:

$$Percentage\ decrease=\frac{V_s-V_f}{|V_s|}×100$$

### Example 1

Find the percentage decrease from 80 to 10.

Solution

We are given Vₛ = 80, V𝒻 = 10. Following the steps of the above algorithm, we can calculate:

1. Subtracting the final value from the starting value, we get Vₛ – V𝒻 = 80 – 10 = 70.
2. Vₛ is positive, Vₛ > 0, therefore, |Vₛ| = Vₛ. Dividing the result of step one by |Vₛ|, we get: 70/|80| = 70/80 = 7/8 = 0.875.
3. Multiplying the result of step 2 with 100, we get: 0.875 × 100 = 87.5

Or, following the summarized formula:

$$Percentage\ decrease=\frac{V_s-V_f}{|V_s|}×100=\frac{80-10}{|80|}×100=70/80×100=0.875×100=87.5$$

The percentage decrease from 80 to 10 is 87.5%.

## Negative percentage decrease

It’s obvious that when the final value is larger than the starting value, V𝒻 > Vₛ, there is an increase, not a decrease, in the value. Let’s examine how this fact is reflected in the algorithm and the formula described above.

Notice how in step 1 of the algorithm, we subtract V𝒻 from Vₛ: Vₛ – V𝒻. When Vₛ > V𝒻, the result of this subtraction is positive. This is the only step that influences the sign of the final value since in step 2 we divide it by the absolute value of Vₛ, and absolute values are always positive. In step 3 we multiply the result by 100, which doesn’t change the final sign.

This means that if V𝒻 > Vₛ, the result of the subtraction from step 1 will be negative, and after we complete the calculation, we will get the negative percentage decrease. Or, in other words, a percentage increase.

### Example 2

Find the percentage decrease from -25 to 25.

Solution

We are given Vₛ = -25, V𝒻 = 25. Following the steps of the above algorithm, we can calculate the following:

1. Subtracting the final value from the starting value, we get Vₛ – V𝒻 = -25 – 25 = -50.
2. Vₛ is negative, Vₛ < 0, therefore, |Vₛ| = -Vₛ. Dividing the result of step one by |Vₛ|, we get: (-50)/|(-25)| = (-50)/25 = -(50/25) = -2.
3. Multiplying the result of step 2 with 100, we get: (-2) × 100 = -200

Or, following the summarized formula:

$$Percentage\ decrease=\frac{V_s-V_f}{|V_s|}×100=\frac{(-25)-25}{|(-25)|}×100=(-50)/25×100=(-2)×100=-200$$

The percentage decrease is negative. Therefore, in this case, there is a percentage increase.

The percentage decrease from -25 to 25 is -200%. The percentage increase from -25 to 25 is 200%.

## Percentage change formula

The formulas for percentage increase and percentage decrease can be summarized in a common percentage change formula:

$$Percentage\ decrease=\frac{V_s-V_f}{|V_s|}×100$$

In this case, if the percentage change is positive, we are talking about a percentage increase. If the percentage change value is negative, we are talking about a percentage decrease.

### Example 3

Find the percentage change from 0.1 to 0.01. Is the change represented by a percentage increase or a percentage decrease?

Solution

We are given Vₛ = 0.1, V𝒻 = 0.01. Since the starting value is larger than the final value, we can immediately conclude that we will be talking about a percentage decrease in this case. Let’s use the percentage change formula to confirm the above conclusion, as well as to find the value of the percentage decrease:

$$Percentage\ decrease=\frac{V_s-V_f}{|V_s|}×100=\frac{0.01-0.1}{|0.1|}×100=((-0.09))/0.1×100=(-0.9)×100= -90$$

The calculated percentage change is negative, which confirms our conclusion that, in this case, we are talking about a percentage decrease. The value of the percentage decrease equals 90%.

The change from 0.1 to 0.01 can be described as a 90% decrease.

## Real-life applications

### Example 4

The price of a video game in March was $80, and in April, it was$60. What is the percentage decrease in price?

Solution

We are given Vₛ = 80, V𝒻 = 60. Let’s first use the calculation algorithm with steps to find the percentage decrease value:

1. Subtracting the final value from the starting value, we get Vₛ – V𝒻 = 80 – 60 = 20.
2. Vₛ is positive, Vₛ > 0, therefore, |Vₛ| = Vₛ. Dividing the result of step one by |Vₛ|, we get: 20/|80| = 20/80 = 2/8 = 1/4 = 0.25.
3. Multiplying the result of step 2 with 100, we get 0.25 × 100 = 25.

Or, following the summarized formula:

$$Percentage\ decrease=\frac{V_s-V_f}{|V_s|}×100=\frac{80-60}{|80|}×100=20/80×100=2/8×100=0.25×100=25$$

The percentage decrease formula can also be used inversely to find the final value if the starting value and percentage decrease are known. For example, imagine you received an e-mail informing you that your salary will decrease by 5% next month. Your current salary is $800 per week. What will be your new salary? Solution We are given Vₛ = 800, percentage decrease = 5%. Let’s substitute the known values in the percentage decrease formula to identify the necessary value of V𝒻, which will represent your future salary: $$Percentage\ decrease=\frac{V_s-V_f}{|V_s|}×100$$ $$5=\frac{800-V_f}{|800|}×100$$ After removing the zeros from 800 and 100, we get: $$5=\frac{800-V_f}{8}$$ 5 × 8 = 800 - V𝒻 40 = 800 - V𝒻 V𝒻 = 800 – 40 = 760 Answer Your new salary will be$760.