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Relative Change Calculator

Calculate relative change online — free, step by step. The change as a factor and as a percent from an old and new value, with full working.

Quick answer
How do you calculate relative change?
Relative change is the difference between new and old, divided by the old value: (new − old) ÷ old. It is dimensionless and can be given as a factor (e.g. 0.25) or as a percent (25%). Unlike absolute change, it accounts for the starting magnitude.
The tool

Enter values — get full working

Comma or dot as decimal separator, negative values allowed.
Step-by-step
Press Calculate to see every step.
HowTo

Relative Change Calculator — step-by-step

How do you calculate relative change?
  1. 1
    Step 1 of 4

    Identify the old and new value

    Set the starting (old) value and end (new) value. Example: old = 80, new = 100.

  2. 2
    Step 2 of 4

    Compute the difference

    new − old = 100 − 80 = 20.

  3. 3
    Step 3 of 4

    Divide by the old value

    20 ÷ 80 = 0.25 — the relative change as a factor.

  4. 4
    Step 4 of 4

    Convert to percent (optional)

    0.25 · 100 = 25%. Factor and percent describe the same relative change.

Examples

Relative Change Calculator — examples

Worked examples with full working
80 → 100
(100 − 80) ÷ 80
0.25 (25%)
100 → 80
(80 − 100) ÷ 100
−0.2 (−20%)
50 → 75
(75 − 50) ÷ 50
0.5 (50%)
200 → 200
(200 − 200) ÷ 200
0 (0%)
10 → 13
(13 − 10) ÷ 10
0.3 (30%)
1,000 → 950
(950 − 1000) ÷ 1000
−0.05 (−5%)
Theory

What is relative change?

Relative change relates the absolute change to the starting value: (new value − old value) ÷ old value. It is a dimensionless number and converts directly to percent (times 100). While absolute change is measured in the unit of the quantity (e.g. 20 items), relative change is comparable across different starting sizes — which is why it is used for growth rates, returns and scientific comparisons. Relative change and percentage change are the same thing, shown once as a factor and once in percent.

Pitfalls

Common mistakes

Confusing factor and percent

The factor 0.25 equals 25%, not 0.25%. Multiply by 100 for the percent.

Referencing the new value

Relative change uses the old value in the denominator.

Ignoring the sign

A negative factor means a decrease — the sign is part of the result.
FAQ

Frequently asked questions

Glossary

Glossary — key terms explained simply

Whole (base)
The reference value that equals 100%.
Part (value)
The amount that belongs to a percentage.
Rate
The percentage (per hundred).
Difference
The result of a subtraction (new − old).
Relative
Expressed against a reference, dimensionless.
Absolute
In the unit of the quantity, without reference.
Factor
Number you multiply by (e.g. 1.25 for +25%).
Percentage point
Absolute difference between two percentages.