Percentage Decrease Calculator

Our percentage decrease calculator (also known as a percent decrease calculator) quickly and accurately determines the reduction from a starting value to a final value, expressing the change as a percentage. Whether you are tracking a price drop, analyzing data trends, or calculating a discount, this tool simplifies the process.

Directions for use

To use this percentage reduction calculator, simply enter your starting and final values into the corresponding input fields and click “Calculate.” The tool will instantly return the exact percentage decrease.

If your final value is larger than your starting value, the calculated percentage decrease will naturally be negative. In this scenario, the calculator automatically adapts to display both the negative percentage decrease and the corresponding (positive) percentage increase.

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

Percentage decrease calculation

To manually calculate the percentage decrease from a starting value (Vₛ) to a final value (V𝒻), follow these 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 convert the fraction into a percentage.

The following formula summarizes these exact 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 and V𝒻 = 10. Following the steps of the calculation algorithm above, we can determine the drop:

1. Subtracting the final value from the starting value, we get Vₛ – V𝒻 = 80 – 10 = 70.
2. Since Vₛ is positive (Vₛ > 0), its absolute value is |Vₛ| = Vₛ. Dividing the result of step 1 by |Vₛ|, we get: 70/|80| = 70/80 = 7/8 = 0.875.
3. Multiplying the result of step 2 by 100 gives us our percentage: 0.875 × 100 = 87.5.

Alternatively, you can simply apply the summarized formula:

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

Answer

The percentage decrease from 80 to 10 is 87.5%.

Negative percentage decrease

Logically, when the final value is greater than the starting value (V𝒻 > Vₛ), the value has increased rather than decreased. Let’s examine how this scenario plays out within the algorithm and formula described above.

Notice how in step 1, we subtract V𝒻 from Vₛ: Vₛ – V𝒻. When V𝒻 is larger than Vₛ, the result of this subtraction becomes negative. This is the only step that dictates the mathematical sign of the final result. In step 2, we divide by the absolute value of Vₛ (which is always positive), and in step 3, we multiply by 100—neither of which alters the sign.

Consequently, if V𝒻 > Vₛ, the initial subtraction yields a negative number, ultimately resulting in a negative percentage decrease. In simpler terms, a negative percentage decrease is mathematically equivalent to a percentage increase.

Example 2

Find the percentage decrease from -25 to 25.

Solution

We are given Vₛ = -25 and V𝒻 = 25. Applying the steps of our calculation algorithm:

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 1 by |Vₛ|, we get: (-50)/|(-25)| = (-50)/25 = -(50/25) = -2.
3. Multiplying the result of step 2 by 100, we get: (-2) × 100 = -200.

Or, using the summarized formula:

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

Because the calculated percentage decrease is negative, this scenario actually represents a percentage increase.

Answer

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

This means the percentage increase from -25 to 25 is 200%.

Percentage change formula

The core mathematical principles for both increases and decreases can be unified into a single percentage change formula:

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

In this context, if the calculated value is positive, we are looking at a percentage decrease. If the calculated value is negative, we are looking at a percentage increase.

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 and V𝒻 = 0.01. Because the starting value is larger than the final value, we can immediately conclude that this represents a percentage decrease. Let’s apply the percentage change formula to confirm this conclusion and determine the exact value of the drop:

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

The calculated percentage change is negative, confirming our initial assumption that we are dealing with a percentage decrease. The absolute value of this percentage decrease is 90%.

Answer

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

Real-life applications

Calculating percentage reductions is incredibly useful in everyday scenarios, such as tracking retail discounts, evaluating budget changes, or measuring depreciation.

Example 4

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

Solution

We are given Vₛ = 80 and V𝒻 = 60. First, let’s use the step-by-step algorithm to find the exact percentage decrease:

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

Alternatively, using the summarized formula:

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

Answer

The percentage decrease from $80 to $60 is 25%.

Example 5

The percent decrease formula can also be used in reverse to determine a final value if the starting value and the percentage decrease are already known.

For example, imagine you received an email informing you that your salary will decrease by 5% next month. Your current salary is $800 per week. What will be your new weekly salary?

Solution

We are given Vₛ = 800 and a percentage decrease = 5%. Let’s substitute the known values into the formula to solve for V𝒻, which represents your future salary:

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

$$5=\frac{800-V_f}{|800|}×100$$

After canceling out 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 per week.