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Percentage change formula

The standard increase and decrease formula, sign behavior, and when the expression is undefined, with plain-language explanation.

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Quick answer

One expression covers both increases and decreases. The sign of (new − original) tells you the direction once you divide by the absolute original and scale to one hundred.

((N − O) ÷ |O|) × 100% where O is original and N is new

Introduction

The Percentage Change Calculator on the home page evaluates this expression in your browser. This article is for anyone auditing homework, a pricing memo, or a spreadsheet template who wants the algebra written out clearly.

If terminology still feels fuzzy, skim what is percentage change first. When you need narrative numbers, pair this page with worked examples.

Main content

What is it?

The formula belongs to a family of relative comparisons. You always measure change versus a baseline you are willing to defend. That baseline might be last quarter revenue, yesterday's closing balance, or a list price before a coupon.

Because the denominator uses |O|, negative originals still produce interpretable results: the numerator carries the direction of the move, while the denominator stays positive for stable scaling.

Formula

Core expression. Percentage change = ((N − O) ÷ |O|) × 100%.

Increases. When N > O, the numerator is positive, so the result is a positive percent.

Decreases. When N < O, the numerator is negative, so the result is a negative percent.

Undefined case. When O = 0, do not divide. Report absolute change or choose another baseline. The UI mirrors this guardrail.

Step-by-step guide

  1. Copy the original value into your sheet or notes.
  2. Copy the new value after the event you care about.
  3. Subtract: new minus original.
  4. Divide by the absolute original.
  5. Multiply by one hundred and label the outcome with units if needed.

Spreadsheet users often write =(B1-A1)/ABS(A1) when A1 holds the original and B1 the new value. Format the cell as percent only after you decide whether the raw cell stores decimals or whole percents.

Example

Original 250, new 300. Difference 50. Fifty divided by 250 is 0.20, so the change is +20%. If you swap the labels, you would compute −16.67% instead, which is why documentation should name the baseline month or price type.

For discount stories, read percentage decrease calculator. For growth headlines, read percentage increase calculator.

FAQ

Do I need a different formula for discounts?

No. Treat the pre-discount price as original and the paid price as new. The negative percent tells you how far price fell relative to the sticker baseline.

Why absolute value in the denominator?

It keeps the scale positive while letting the numerator communicate direction. Some organizations document their convention; match theirs when auditing.

How do I compare with percentage difference?

Difference formulas sometimes average denominators. That yields a different number than classic change. See the dedicated article for side-by-side wording.

What if rounding makes a small move look like zero?

Carry extra digits internally, round only for display, and state the precision when stakes are high.

Conclusion

Summary

The formula is short, but the baseline choice carries the narrative weight. Write down which value is O before you publish any percent.

Next steps: validate with the calculator, then explore change versus difference when your inputs are already percents.

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