ConvertOnlineRelative Change Calculator
(Initial Value)
(Final Value)
How to use this Relative Change Calculator 🤔
- Enter ✎ value for Initial Value (initial).
- Enter ✎ value for Final Value (final).
- As soon as you enter the required input value(s), the Relative Change is calculated immediately, and displaed in the output section (present under input section).
Calculating Relative Change
Relative change is a measure used to compare the difference between an initial value and a final value relative to the initial value, expressed as a percentage. It is often used in finance, economics, and various scientific fields to assess growth, decline, or changes over time.
The formula to calculate the relative change is expressed as:
\( \text{Relative Change} = 100 \times \dfrac{ \text{final value} - \text{initial value} }{ |\text{initial value}| } \)
where:
- Initial Value represents the starting value.
- Final Value represents the value after the change.
By subtracting the initial value from the final value, dividing by the absolute value of the initial value, and then multiplying by 100, you obtain the relative change as a percentage.
Examples
The following examples demonstrate how to calculate the relative change between an initial value and a final value using the given formula.
1. A stock price increased from $50 to $75 over a month. What is the relative change in the stock price?
Answer
Given:
- Initial Value = $50 (Stock price at the beginning of the month)
- Final Value = $75 (Stock price at the end of the month)
The formula to calculate the relative change is:
\( \text{Relative Change} = 100 \times \dfrac{ \text{Final Value} - \text{Initial Value} }{ |\text{Initial Value}| } \)
Substituting the given values into the formula:
\( \text{Relative Change} = 100 \times \dfrac{75 - 50}{50} \)
Calculate the difference between the final and initial values:
\( \text{Relative Change} = 100 \times \dfrac{25}{50} \)
Simplifying further:
\( \text{Relative Change} = 100 \times 0.5 = 50\% \)
Therefore, the stock price increased by 50% over the month.
2. A company’s revenue decreased from $200,000 last year to $150,000 this year. What is the relative change in revenue?
Answer
Given:
- Initial Value = $200,000 (Revenue last year)
- Final Value = $150,000 (Revenue this year)
The formula to calculate the relative change is:
\( \text{Relative Change} = 100 \times \dfrac{ \text{Final Value} - \text{Initial Value} }{ |\text{Initial Value}| } \)
Substituting the given values into the formula:
\( \text{Relative Change} = 100 \times \dfrac{150000 - 200000}{200000} \)
Calculate the difference between the final and initial values:
\( \text{Relative Change} = 100 \times \dfrac{-50000}{200000} \)
Simplifying further:
\( \text{Relative Change} = 100 \times -0.25 = -25\% \)
Therefore, the company’s revenue decreased by 25% from last year to this year.
3. The population of a small town grew from 10,000 to 12,500 over five years. What is the relative change in the town's population?
Answer
Given:
- Initial Value = 10,000 (Population five years ago)
- Final Value = 12,500 (Current population)
The formula to calculate the relative change is:
\( \text{Relative Change} = 100 \times \dfrac{ \text{Final Value} - \text{Initial Value} }{ |\text{Initial Value}| } \)
Substituting the given values into the formula:
\( \text{Relative Change} = 100 \times \dfrac{12500 - 10000}{10000} \)
Calculate the difference between the final and initial values:
\( \text{Relative Change} = 100 \times \dfrac{2500}{10000} \)
Simplifying further:
\( \text{Relative Change} = 100 \times 0.25 = 25\% \)
Therefore, the town’s population increased by 25% over the five years.
4. The value of a car depreciated from $30,000 to $24,000 over two years. What is the relative change in the car’s value?
Answer
Given:
- Initial Value = $30,000 (Car value two years ago)
- Final Value = $24,000 (Current car value)
The formula to calculate the relative change is:
\( \text{Relative Change} = 100 \times \dfrac{ \text{Final Value} - \text{Initial Value} }{ |\text{Initial Value}| } \)
Substituting the given values into the formula:
\( \text{Relative Change} = 100 \times \dfrac{24000 - 30000}{30000} \)
Calculate the difference between the final and initial values:
\( \text{Relative Change} = 100 \times \dfrac{-6000}{30000} \)
Simplifying further:
\( \text{Relative Change} = 100 \times -0.2 = -20\% \)
Therefore, the car’s value decreased by 20% over the two years.
Formula
To calculate the relative change, you can use the following formula.
where
Calculation
Once you enter the input values in the calculator, the output parameters are calculated.