Percentage Change Calculator

The calculator determines the percentage change from one value to another. The input values can be positive or negative. This calculator can also be used as a rate of change calculator or price change calculator.

Directions for Use

To calculate percentage change using the calculator, enter Value 1 (V₁) and Value 2 (V₂) into their respective fields and press “Calculate.” Here V₁ represents the starting value, or the old value, and V₂ – the final value, or the new value. You can press “Enter” on your keyboard to start the calculation.

The calculator accepts whole and decimal numbers as inputs. If you have to calculate percentage change for fractions, you will first need to perform fraction-to-decimal conversion. Note, that if you do enter a fraction in one of the fields, the calculator will automatically disregard everything that comes after the fraction bar. For example, if you enter “4/5,” the calculator will see it as “4.”

Percentage Change Calculation

Percentage Change Formula

Percentage change describes the change from the old number value to the new number value in terms of percentages. To calculate the percentage change from the old value V₁ to the new value V₂, you need to perform the following steps:

1. Find the absolute change between the values:

Absolute Change = V₂ - V₁

2. Find the relative change through dividing the absolute change by the modulus of the old value:

Relative Change = Absolute Change/ |V₁|

3. Find the percentage change by multiplying the Relative change by 100:

Percentage Change = Relative change × 100

We can combine the steps above into one formula:

Percentage Change = [(V₂ - V₁) / |V₁|] × 100

Percentage increase or decrease

The numerator of the above formula can be either positive or negative since V₂ can be smaller or larger than V₁. However, the denominator is always positive since a modulus represents it. This means that the final value of the percentage change can be either positive or negative.

When V₂ > V₁, meaning that the final value is larger than the initial value, the percentage change will be positive, and we are talking about a percentage increase.

When V₂ < V₁, meaning that the final value is smaller than the initial value, the percentage change will be negative, and we are talking about a percentage decrease.

Using the Percentage Change Formula

For example, let’s calculate the percentage change from 25 to 10 using the algorithm described above. In this case

V₁ = 25, V₂ = 10, |V₁| = |25| = 25

Absolute Change = V₂ - V₁ = 10 – 25 = -15

Note that this value is negative.

Relative Change = Absolute Change/ |V₁| = -15/25 = -0.6

Percentage Change = Relative change × 100 = (-0.6) × 100 = -60%

The value of the percentage change is negative. Therefore, here we have a percentage decrease.

Answer

60% decrease.

Calculation Examples

Example 1

Imagine you want to invest in gold and buy several ounces in June 2022, when the price was $1836.57 per ounce. In July 2022, the price per ounce dropped to $1732.74. What was the price change in percent?

Solution

To find the price change in percent, we need to calculate percentage change between the two prices. In this example, the starting value V1 = 1836.57, the final value V₂ = 1732.74, |V₁| = |1836.57| = 1836.57.

Let’s calculate percentage change based on the algorithm described above.

Absolute Change = V₂ - V₁ = 1732.74 - 1836.57 = −103.83

Relative Change = Absolute Change/ |V₁| = (−103.83)/ 1836.57 = −0.0565347

Percentage Change = Relative change × 100 = (−0.0565347) × 100 = −5.65347%

The percentage change in the gold price per ounce between June and July 2022 amounted to −5.65347%, which means there was a 5.65347% decrease.

Answer

The price change of gold per ounce decreased by 5.65347% in July 2022 compared to June 2022.

Example 2

In August 2022, the price increased to $1764.56. What is the price change in percent between July and August?

Solution

In this case, the starting value V₁ = 1732.74, the final value V₂ = 1764.56, |V₁| = |1732.74| = 1732.74.

Absolute Change = V₂ - V₁ = 1764.56 - 1732.74 = 31.82

Relative Change = Absolute Change/ |V₁| = 31.82/ 1732.74 = 0.018364

Percentage Change = Relative change × 100 = 0.018364 × 100 = 1.8364%

The percentage change in price per gold ounce between June and August 2022 was 1.8364%. Which means there was a 1.8364% increase.

Answer

The price of a gold ounce has increased by 1.8364% between July and August 2022.

Note, that if in August the price would go back to its June value, the absolute value of percentage change between June and July would still be different from the percentage change between July and August.

Remember that for the change between June and July, we had the following values: the starting value V₁ = 1836.57, the final value V₂ = 1732.74, |V₁| = |1836.57| = 1836.57. This amounted to a decrease of 5.65347%.

Example 3

Now imagine that in August, the price would go back up to the exact value of June. In this case, the values would be: V₁ = 1732.74, the final value

V₂ = 1836.57, |V₁| = |1732.74| = 1732.74

Solution

Let’s calculate the relevant percentage change using the percentage change formula:

Percentage Change = [(V₂ - V₁) / |V₁|] × 100 = ((1836.57-1732.74))/|1732.74| × 100 = 103.83 / 1732.74 × 100 = 0.0599224 × 100 = 5.99224%

Answer

Percentage change in this case amounts to 5.99224% which means there was a 5.99224% increase.

Finally, we see, that even though the prices in June and August were the same, the values of price change in percent were different. From June to July the price has decreased by 5.65347%, while from July to August it increased by 5.99224%.

This is because percentage change is a relative value calculated based on the starting value. Even though the change in price in dollars was the same, the relative change, based on the starting value, was different.