Percentage Calculator
Ratios and increase/decrease rates with ease.
① What is P% of X?
P% of X
10
② What percent of Y is X?
X as % of Y
20%
③ Change rate from A to B
Rate of change
+50%
What is the Percentage Calculator?
A percentage expresses a ratio out of 100. This tool handles the three most common percentage calculations on one page: ① what P% of a number X is, ② what percent one number is of another, and ③ the increase or decrease rate when a value changes from A to B.
How to use it
Pick the tab you need and enter your values — results update instantly as you type. Use ① for discounts, ② for score ratios, and ③ for growth or decline rates.
Formulas
| Type | Formula | Example |
|---|---|---|
| P% of X | X × P ÷ 100 | 20% of 50 = 10 |
| X as % of Y | X ÷ Y × 100 | 40 is 20% of 200 |
| Change A→B | (B − A) ÷ A × 100 | 100→150 is +50% |
Everyday examples
- Sale price: a ₩45,000 item at 30% off → 45,000 × (100−30) ÷ 100 = ₩31,500.
- Score ratio: 200 out of 250 → 200 ÷ 250 × 100 = 80%.
- Revenue growth: ₩3.2M last month → ₩4.0M this month → (400−320) ÷ 320 × 100 = 25% up.
- Tip / fee: 10% of a ₩60,000 bill → 60,000 × 10 ÷ 100 = ₩6,000.
Percent (%) vs. percentage point (%p)
When a news headline says "the base rate rose from 3% to 4%," it looks like the number only went up by 1 — but that's a 1 percentage point (%p) rise, not a 1% rise. The actual relative change is (4−3) ÷ 3 × 100 = 33.3%. If a deposit rate moves from 3% to 4%, the interest you actually receive increases by 33.3%, so dismissing it as "only 1%p" badly understates the real change in interest cost or income.
In short, %p is the arithmetic gap between two percentages (4%−3%=1%p), while % is the relative change against the base value ((4−3)÷3×100=33.3%). Entering 3 and 4 as the before/after values in mode ③ of this calculator gives 33.333333% — that figure is the %, not the %p.
A common mistake when reversing a discount to find the original price
For "a 20%-off price is ₩8,000 — what was the original price?", it's tempting to add 20% of 8,000 (₩1,600) and guess ₩9,600. But applying a real 20% discount to 9,600 gives 9,600 × 0.8 = ₩7,680, which doesn't match the ₩8,000 you started with. A discount is always a percentage of the original price, so if the original price is X, then X × 0.8 = 8,000, giving X = 8,000 ÷ 0.8 = ₩10,000 (check: 10,000 × 0.8 = ₩8,000, matches).
In other words, you must divide by (1 − discount rate), not add the discount rate back. Here are the reversal multipliers for common discount rates.
| Discount | Multiplier | Calculation |
|---|---|---|
| 10% | × 1.111 | 1 ÷ 0.9 = 1.1111… |
| 20% | × 1.25 | 1 ÷ 0.8 = 1.25 |
| 30% | × 1.429 | 1 ÷ 0.7 = 1.4286… |
| 50% | × 2 | 1 ÷ 0.5 = 2 |
Change rates aren't symmetric — down 50% then up 50%?
A 50% drop from 100 gives 100 × 0.5 = 50. A 50% rise from that 50 gives 50 × 1.5 = 75. Even though the drop and the rise were both 50%, the value doesn't return to 100 — it lands at 75% of the original, because the 50% rise is applied to a base (50) that's already been cut in half.
By the same logic, if an investment falls 50%, recovering to the original amount requires not a 50% rise but a 100% rise (50 × 2 = 100). The bigger the drop, the more the required recovery rate outpaces it — that's the core of this asymmetry.