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Our Relative Change Calculator is designed to assist you in determining the relative change between the initial and final values of a variable, along with calculating the percentage of relative change. This article aims to elucidate the concept of relative change and apply the relative change formula through illustrative examples.

Understanding Relative Change:

Relative change is a quantitative measure that assesses the difference or variation in a variable relative to a reference or initial value. It facilitates the comparison of two quantities, taking into account their respective magnitudes.

Relative Change Formula:

The formula for relative change is expressed as:

Relative Change Relative Change(xi​,xf​)=∣xi​∣xf​−xi​​

Here, xi​ represents the initial value of a variable, and xf​ is the final value. The division by the absolute value of the initial number ensures that the relative change is unitless and remains constant irrespective of the measurement units used.

For instance, if the initial value is 4 km and the final value is 6 km, the relative change is 6−44=0.546−4​=0.5. This result remains the same even if the units are changed to meters.

Calculating Relative Change:

To calculate relative change between initial value xi​ and final value xf​, follow these steps:

  1. Subtract the initial value from the final value to find their difference: Δx=xf​−xi​.
  2. Divide this difference by the absolute value of the initial value to obtain the relative change: Relative change=∣xi​∣Δx​.
  3. Multiply the relative change by 100 to get the relative change percentage: Relative change %=100×∣xi​∣Δx​.

Example Problems:

  1. If the minimum wage increases from $7/hr to $15/hr, the relative change is calculated as 15−7∣7∣=1.1429∣7∣15−7​=1.1429 or 114.29%.
  2. For a vibrating object with a theoretical frequency of 75 Hz and a measured frequency of 80 Hz, the relative error is 100×80−75∣75∣=6.667%100×∣75∣80−75​=6.667%.

Using the Relative Change Calculator:

The tool is user-friendly:

  1. Enter the initial or reference value.
  2. Input the final or measured value.
  3. The calculator will automatically provide the relative change and the relative change percentage.

FAQ:

  1. Why use the absolute value of a reference value for relative change?
    • Using the absolute value ensures that relative change is positive for an increase and negative for a decrease. Avoiding the absolute value could yield confusing negative values for a relative increase.
  2. Relative change from 75 to 25?
    • The relative change from 75 to 25 is -0.6667 or -66.67%.
  3. Percent change from 35 to 21?
    • The percentage relative change from 35 to 21 is -40%.