Relative Change Calculator

Calculate the percentage change between two values or find an initial or final value based on a percentage change.

Formula source: Investopedia — investopedia.com

Relative Change Calculator

The Relative Change Calculator helps you find the relative change between an initial value and a final value. It also gives you the relative change as a percentage, so you can read the result at a glance.

Below, you’ll learn what relative change means, how the formula works, and how to run the numbers with a few clear examples.

If you only need an increase or a decrease, you may prefer a percentage increase calculator or a percentage decrease calculator.

What relative change means

Relative change tells you how much something changed compared to where it started (the reference value). This makes it easier to compare changes across different scales, because the change is measured in relation to the starting point.

Here’s the formula:

Relative change = (xf - xi) / |xi|

Where:

  • xi is the initial value
  • xf is the final value
  • |xi| means the absolute value of the initial value

That absolute value matters for two reasons:

  • The result has no units, so it works the same with miles, meters, dollars, or anything else.
  • The sign stays meaningful, positive for an increase and negative for a decrease, without flipping just because the starting value was negative.

Quick unit example

If a distance goes from 4 km to 6 km:

(6 - 4) / |4| = 0.5

If you convert to meters, it goes from 4000 m to 6000 m:

(6000 - 4000) / |4000| = 0.5

Same answer, because the units cancel out.

Important limitation

The initial value can’t be zero. Since the formula divides by |xi|, relative change is not defined when xi = 0.

Relative change percentage

To express relative change as a percent, multiply by 100:

Relative change % = ((xf - xi) / |xi|) * 100

How to calculate relative change step by step

To compute relative change from an initial value xi to a final value xf:

  1. Find the difference: Δx = xf - xi
  2. Divide by the absolute initial value: Relative change = Δx / |xi|
  3. Multiply by 100 for percent form: Relative change % = (Δx / |xi|) * 100

You can check your work any time with the Relative Change Calculator.

Example problems

1) Minimum wage change

A wage rises from $7/hr to $15/hr.

  • xi = 7
  • xf = 15

Relative change:

(15 - 7) / |7| = 8/7 = 1.1429

So the relative change is 1.1429, which is 114.29%.

2) Relative error (a common special case)

A vibrating object has a theoretical frequency of 75 Hz. An experiment measures 80 Hz. Find the relative error.

Relative error uses the same structure as relative change, just with different labels:

Relative error % = 100 * (xe - xt) / |xt|

Where:

  • xt is the theoretical value
  • xe is the experimental value

Now plug in the values:

100 * (80 - 75) / |75| = 100 * 5/75 = 6.667%

The relative error is 6.667%.

If you want a tool built for that case, you can use the relative error calculator.

How to use the Relative Change Calculator

Using the tool is straightforward:

  1. Enter the initial (reference) value.
  2. Enter the final (measured) value.
  3. The calculator returns the relative change and the relative change percentage automatically.

If you’re tracking a value across multiple points in time, the percentage change calculator may be a better fit.

Formula source: Investopedia — investopedia.com

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People also ask

A relative change calculator shows how much a value changed compared to where it started, written as a percentage. It’s commonly called a percent change calculator.

It answers, “How big was the change, relative to the original value?”

A common formula is:

% change = 100 × (new - old) / |old|

  • new - old gives the raw difference
  • dividing by |old| compares that difference to the starting value (the baseline)
  • multiplying by 100 converts it to a percent

Many calculators use the absolute value |old| so the denominator isn’t negative.

Check the sign of the result:

  • Positive percent change means an increase (the new value is higher).
  • Negative percent change means a decrease (the new value is lower).

Because the old value is the baseline. Relative change is about how big the shift is compared to where you began.

Example: going from 50 to 60 is a change of 10, and 10/50 = 0.2, so that’s 20%. The same 10-point increase from 200 to 210 is only 5%, because the baseline is larger.

Percent change isn’t defined when the old value is 0, because you can’t divide by zero.

In that case, a calculator may show an error, “undefined,” or ask you to use a different measure (like the absolute change, which is just new - old).

Yes, many can, and they often use |old| in the denominator to avoid sign confusion.

That result says the value changed by 200% relative to the magnitude of the starting value.

  • Percent change can be positive or negative, it covers both increases and decreases.
  • Percent increase only describes increases, so it’s usually written as a positive number.

If you’re tracking anything that can go down (prices, weight, revenue, speed), percent change is the clearer choice.

No, because the second percent is applied to a different base.

Example:

  • Start at 100, +25% gives 125
  • Then -25% of 125 is 31.25, so you land at 93.75

So you don’t return to 100, because percentages compound based on the current value.

Treat the percents as numbers and use the same formula:

% change = 100 × (new% - old%) / |old%|

Usually, no. Percent changes depend on the base each time, so averaging can mislead.

A better approach is:

  • compute the percent change for each step, or
  • compare the first value to the final value and compute one overall percent change