Updated July 2, 2026
What are the standard percentage formulas?
There are sixteen standard percentage formulas in everyday use, covering four core operations: finding a part of a whole, finding what percent one number is of another, measuring percentage change or difference, and reversing any of those to find a missing value. The table below lists all sixteen with the formula and a worked numeric example for each, computed from this site's own calculator model.
Summary table
| Formula | Expression | Worked example | Result |
|---|---|---|---|
| Percentage of a number | Y x X / 100 | 20% of 80 | 16 |
| What percent X is of Y | X / Y x 100 | 16 is what % of 80 | 20% |
| Percentage increase | (New - Old) / Old x 100 | 80 to 100 | +25% |
| Percentage decrease | (Old - New) / Old x 100 | 100 to 80 | -20% |
| Percentage change (signed) | (New - Old) / Old x 100 | 500 to 400 | -20% |
| Percentage difference | |A - B| / ((A + B) / 2) x 100 | 80 vs 100 | 22.2% |
| Find the whole from a part | Whole = Part / (Percent / 100) | 45 is 30% of what | 150 |
| Add a percentage (multiplier) | Original x (1 + Percent / 100) | 160 plus 25% | 200 |
| Subtract a percentage (multiplier) | Original x (1 - Percent / 100) | 250 minus 30% | 175 |
| Reverse a discount (find original) | Sale Price / (1 - Percent / 100) | 84 after 30% off | 120 |
| Remove tax already included | Total / (1 + Rate / 100) | 120 incl. 20% VAT | 100 |
| Two changes compounded (not additive) | (1 + P1/100) x (1 + P2/100) | +10% then +10% | +21% total |
| Rise then equal fall (net loss) | (1 + P/100) x (1 - P/100) | +20% then -20% | -4% net |
| 25% as decimal / fraction | Percent / 100 | 25% | 0.25 = 1/4 |
| 33.3% as decimal / fraction | Percent / 100 | 33.3% | 0.333 = 1/3 |
| 10% mental-math shortcut | Shift decimal one place left | 10% of 350 | 35 |
Download the full table as a CSV: percentage-formulas-2026.csv.
Methodology
Every figure in this table is computed directly from the same arithmetic used by the percentage calculator on the homepage and explained in the formula guides linked from this site: ordinary percentage arithmetic (multiplication and division by 100), not a third-party statistic or survey. There is nothing to source externally because a percentage formula is a mathematical definition, not a measured quantity. We recompute and re-check every row by hand when the page is updated; this version was last checked 2026-07-02. If you find an arithmetic error, the contact page goes directly to us and we correct it promptly.
Worked example: compounding two changes
A price that rises 10% and then rises another 10% does not end 20% higher. Start at 100: after the first 10% rise it is 100 x 1.10 = 110; after the second 10% rise it is 110 x 1.10 = 121. The total increase is 21%, not 20%, because the second rise is applied to the already-larger base. The same logic explains why a 20% rise followed by a 20% fall lands at 96, a net 4% loss, not back at the start.
Cite this page
PercentageCalcTool, "2026 Percentage Formulas Reference", percentagecalctool.com/percentage-formulas-reference-2026, 2026-07-02. The underlying table is available as a CSV download for reuse with attribution.
Related guides
- The Percentage Formula Explained
- Percentage of a Number
- Percentage Increase
- Percentage Decrease
- Percentage Change
- What Percent Is X of Y
- Add a Percentage
- Subtract a Percentage
- Difference vs. Change
- Common Mistakes