How to use it
- Find the calculation you need and type your numbers into it.
- The result and the formula with your numbers update instantly; copy the result.
- Change Decimals at the top for more precision.
Percentage formulas
| Calculation | Formula | Example |
|---|---|---|
| P% of Y | Y × P ÷ 100 | 15% of 200 = 30 |
| X as a percent of Y | X ÷ Y × 100% | 30 is 15% of 200 |
| Percentage change | (B − A) ÷ |A| × 100% | 80 → 100: +25% |
| Increase or decrease by P% | A × (1 ± P%) | 200 + 15% = 230 |
| Original before a change | F ÷ (1 ± P%) | 120 after +20% was 100 |
| Percentage difference | |A − B| ÷ ((A + B) ÷ 2) × 100% | 10 and 20 differ by 66.67% |
Rises and falls are not symmetric
Each percentage is taken on the previous base. 100 up 20% is 120; down 20% from there is 24 lower, leaving 96. State the base when you report price changes or sales recoveries.
| Change | Result | vs start |
|---|---|---|
| Up 10% then down 10% | 99.00 | -1.00% |
| Up 20% then down 20% | 96.00 | -4.00% |
| Up 25% then down 25% | 93.75 | -6.25% |
| Up 50% then down 50% | 75.00 | -25.00% |
Percent vs percentage points
A conversion rate rising from 2% to 3% is up 1 percentage point and also up 50%. Both are true but mean different things: points subtract two percentages, percent change is relative to the original.
Frequently asked questions
Why divide by |A| for percentage change?
So the direction reads naturally: −100 to −50 (a smaller loss) is a rise. Dividing by the absolute original makes rises positive and falls negative; with an original of 0 a percentage is meaningless, so use the absolute change.
Percentage change vs percentage difference?
Change has a direction and uses the old value as the base (A to B); difference has no direction and uses the average of both, suited to comparing peers such as two suppliers' quotes.
How accurate are the results?
Formulas are exact and compounding is simulated period by period, shown to the cent. Real returns fluctuate and banks differ on day counts, tax and fees, so use the results for planning and comparison.