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How to Calculate Relative Change — Explained Step by Step

Q: How does it differ from percentage change?

Not in substance. Percentage change is relative change times 100: the factor 0.25 becomes 25%. It is the same quantity, shown once as a factor and once in percent.

Q: How does it differ from absolute change?

Absolute change is the plain difference new − old, here 20, measured in the unit of the quantity. Relative change relates that difference to the starting value (20 ÷ 80 = 0.25), which makes it comparable across values of different sizes.

Q: Can relative change be negative?

Yes. When the value falls, the difference is negative and so is the factor. From 100 to 80 you get (80 − 100) ÷ 100 = −0.2, or −20%. The sign is part of the result.

Q: Why divide by the old value and not the new one?

Relative change measures how much a value has changed compared with its starting point, so the reference is the old value, which goes in the denominator. Dividing by the new value gives a different, non-standard quantity.

Q: Is relative change a unit?

No, it is dimensionless. The units cancel when you divide, leaving a pure number. That is what makes it easy to compare.

Relative change relates the difference between two values to the starting value: (new − old) ÷ old. This makes growth comparable regardless of size. We work through the rise from 80 to 100 — the result is 0.25, or +25%. It fits Grade 7 work on percentages.

By Valerij Hofmann · Fullstack Developer

Updated May 29, 2026Beginner

Quick answer

Relative change is the difference between the new and old value, divided by the old value: (new − old) ÷ old. From 80 to 100 that is (100 − 80) ÷ 80 = 0.25, or +25%. It is dimensionless and can be given as a factor or as a percent.

At a glance

Summary of this tutorial
Example	80 → 100
Method	(new − old) ÷ old
Steps	4
Result	0.25 (+25%)
Check	80 · 1.25 = 100 ✓
Grade level	Grade 7 (ages 12–13)

Worked example: 80 → 100

EXAMPLE

(100 − 80) ÷ 80

The value rises from 80 to 100. We measure how large this change is relative to the starting value of 80.

The steps to relative change

These four steps work for any pair of old and new values, as long as the old value is not zero.

Step 1 · Start
80 → 100
Old value 80, new value 100.
Step 2 · Formula
(100 − 80) ÷ 80
Difference divided by the old value.
Step 3 · Difference
20 ÷ 80
Numerator worked out: new − old = 20.
Step 4 · Result
= 0.25 (+25%)
Factor 0.25, which is a 25% increase.

Why you divide by the old value

A difference on its own tells you little: +20 is a lot when you start from 80, but almost nothing when you start from 8,000. Dividing by the old value measures the change in multiples of the starting amount — the result is dimensionless and therefore comparable across quantities of very different sizes. That is exactly why relative change is used for growth rates, returns and scientific comparisons.

Practice it yourself

Open the relative change calculator

Enter your own values. See the factor, the percent and the full working.

Start the practice set

Several problems with solutions

Frequently asked questions

How do you calculate relative change?

Use the formula (new − old) ÷ old: subtract the old value from the new one and divide by the old value. From 80 to 100 that is (100 − 80) ÷ 80 = 20 ÷ 80 = 0.25, or +25%. The result is a dimensionless factor that you multiply by 100 to get a percent.

How does it differ from percentage change?

How does it differ from absolute change?

Can relative change be negative?

Why divide by the old value and not the new one?

Is relative change a unit?

Quick answer

At a glance

Worked example: 80 → 100

The steps to relative change

Step 1 · Start

Step 2 · Formula

Step 3 · Difference

Step 4 · Result

Why you divide by the old value

Practice it yourself

Frequently asked questions