Percentage formulas
| To find | Formula | Example |
|---|---|---|
| P% of A | A × P ÷ 100 | 15% of 80 = 12 |
| A as a % of B | A ÷ B × 100 | 30 is 25% of 120 |
| Percent change | (new − old) ÷ old × 100 | 80 to 100 = +25% |
| Price after P% off | A × (1 − P ÷ 100) | $50 with 20% off = $40 |
| Original before P% was added | final ÷ (1 + P ÷ 100) | $120 including 20% = $100 before |
Why you can't just subtract the percentage
If a price including 20% tax is $120, the price before tax is not $96 (120 minus 20%). The 20% was added to the original price, so you divide: 120 ÷ 1.2 = $100. The "Reverse %" tab does this for you.
Percent vs. percentage points
When an interest rate goes from 2% to 3%, it rose by 1 percentage point but by 50 percent. Percentage points are the plain difference between two percentages; percent describes the change relative to where you started.
Frequently asked questions
If something goes up 30% and then down 30%, is it back where it started?
No. 100 up 30% is 130, and 130 down 30% is 91. The decrease is taken from the larger number.
Why is there no result when the old value is 0?
A change from zero can't be expressed as a percentage, because you would be dividing by zero. Compare the absolute amounts instead.
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