How to Calculate Percentages: Of a Number, Percent Change, and Reverse %
Turn “what is 18% of this?” and “prices rose from X to Y—what’s the % change?” into one repeatable recipe you can sanity-check in seconds.
How to Calculate Percentages: Of a Number, Percent Change, and Reverse %
Updated May 2026 · ~8 min read
Percentage formulas depend on the selected denominator. Percent change is undefined when the starting value is zero, percentage points differ from percent change, and sequential changes compound rather than add.
When these formulas show up
- Portfolio and positions: what fraction of your net worth is one holding? That is a percent of a whole.
- Price moves: reporting “the stock is up 12%” is percent change relative to an old price.
- Retail and invoices: reverse percentages answer “what was the list price before 25% off?” once you know the final price.
The formula
Percent change = (new−old)/|old| × 100 when old is nonzero
State the base and sign convention. Zero denominators require an undefined result rather than a silent zero.
A denominator-aware percentage example
A rise of 10% followed by a fall of 10% does not return to the starting value.
Common mistakes
- Using the wrong denominator.
- Returning 0% when the base is zero.
- Confusing percent with percentage points.
- Adding sequential percentage changes.
Try the calculator
Use the interactive calculator to plug in your numbers and see results instantly—without redoing the math by hand.
Open percentage calculator →FAQ
What if the starting value is zero?
Percent change is undefined.
Can percentages exceed 100%?
Yes, depending on the ratio.
Are percentage points the same as percent?
No.
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Educational Disclaimer
This article is for educational and informational purposes only and should not be considered investment, financial, tax, or legal advice. Market information may change over time, and readers should verify important details independently before making financial decisions.