Percentage Calculator — what percent of, increase or decrease by, percent change, reversing a discount
Four separate answers for the four questions people actually type: 87 out of 120 is what percent, 120 plus 15 percent, the percent change from 120 down to 102, and the original price when 240 is the 20%-off price. Live results, division by zero explained, float noise cleaned to 12 significant digits.
“X is what percent of Y?”
“A increased or decreased by B% — what do I get?”
“From A to B — by what percent did it change?”
“It is 240 after 20% off — what was the original price?”
Worked answers
| Question | You type | Answer | Also shown |
|---|---|---|---|
| What percent is 87 of 120 | X 87, Y 120 | 72.50% | 72.5% · 0.725 |
| 120 decreased by 15% | A 120, B -15 | 102 | -18 · 0.85 × |
| 120 down to 102 | A 120, B 102 | -15.00% | -18 · went down |
| 240 is the price after 20% off | now 240, off 20 | 300 | +60 · 80% |
Four formulas; points are not percents
Four questions, four formulas
| What you are asking | Formula | Worked example |
|---|---|---|
| 87 out of 120 is what percent | X ÷ Y × 100 | 87 ÷ 120 × 100 = 72.5% |
| 120 plus 15% | A × (1 + B ÷ 100) | 120 × 1.15 = 138 |
| 120 down to 102, percent change | (B − A) ÷ A × 100 | −15% |
| 240 is the price after 20% off | now ÷ (1 − rate) | 240 ÷ 0.8 = 300 |
The first two take a share of something, the third compares two numbers, and the last runs the second backwards — division instead of another multiplication. Most wrong answers come from dividing the percent change by B rather than A (the base is where you started), or from expecting a zero denominator to give zero. Zero is not a base, so those panels refuse to answer and say why.
Increase 10%, then decrease 10%, and you are 1% short
100 becomes 110, then 99. The two 10% cuts are different sizes: the first is 10, the second is 11, because it is taken from the already raised 110. In multiplier form it is obvious — 1.1 × 0.9 = 0.99 — and order does not matter. The reverse reading is just as useful: to undo a 10% rise you have to drop by 10 ÷ 110 ≈ 9.09%, not by 10%.
Percentage points are not percentages
When a rate moves from 5% to 8%, that is 3 percentage points but a 60% relative increase (3 ÷ 5). Saying “it rose 3%” gets heard as 5% × 1.03 = 5.15%, a different claim entirely. Interest rates, unemployment and test scores are already percentages, so quote their movement in points; the third panel above gives percent change, and you subtract for points yourself.
Stack discounts and growth by multiplying
“20% off, then another 20% off” is 0.8 × 0.8 = 0.64, a 36% total discount — not 40%. Compound growth is the same arithmetic over n periods, (1 + r)^n; adding the yearly rates only approximates it while r is small and n is short. Reversing a discount needs division: 240 after 20% off is 240 ÷ 0.8 = 300, while 240 × 1.2 gives 288 and quietly misses 12.
Questions that come up
Q: How do I back out a tax-inclusive price? Use the fourth panel with a negative rate: 113 including 13% tax means entering −13, which computes 113 ÷ 1.13 = 100. Entering 13 would give 113 ÷ 0.87 ≈ 130, the classic error.
Q: What about a negative starting value? The formula still runs, but the sign flips against intuition: −100 to −50 is a rise of 50 while (B − A) ÷ A reports −50%. Everyone reads that as “the loss halved”, so direction comes from the difference, magnitude from the ratio.
Q: Why does it show 72.5% instead of 72.500000001? JavaScript stores numbers as IEEE 754 doubles, so 0.1 + 0.2 really is 0.30000000000000004. Results are cleaned to 12 significant digits and shown at 2 decimals, with the unrounded value on the neighbouring card. Exact money totals belong in a spreadsheet or a decimal library. Everything runs in your browser: what you type never leaves this device.