X% of Y
Finds a portion of a value. Useful for tips, discounts, VAT, and interest.
(percent ÷ 100) × value
Find X% of Y, what percent X is of Y, and percentage change between two values — with the formula and a clear step-by-step breakdown.
Finds a portion of a value. Useful for tips, discounts, VAT, and interest.
(percent ÷ 100) × value
Finds what portion of the whole a given value represents. Useful for grades and comparisons.
(part ÷ whole) × 100
Finds the relative change between two values. Useful for prices, salaries, and statistics.
((B − A) ÷ |A|) × 100
Frequently used percentages of common amounts.
| % | 50 | 100 | 200 | 500 | 1000 |
|---|---|---|---|---|---|
| 1% | 0.5 | 1 | 2 | 5 | 10 |
| 5% | 2.5 | 5 | 10 | 25 | 50 |
| 10% | 5 | 10 | 20 | 50 | 100 |
| 15% | 7.5 | 15 | 30 | 75 | 150 |
| 20% | 10 | 20 | 40 | 100 | 200 |
| 25% | 12.5 | 25 | 50 | 125 | 250 |
| 50% | 25 | 50 | 100 | 250 | 500 |
| 75% | 37.5 | 75 | 150 | 375 | 750 |
Convert the percentage to a decimal by dividing by 100, then multiply by the value. For example, 25% of 200 = (25 ÷ 100) × 200 = 0.25 × 200 = 50.
Divide the part by the whole and multiply by 100. For example, "18 out of 25" = (18 ÷ 25) × 100 = 72%. Useful for test scores and part-to-whole comparisons.
Subtract the old value from the new value, divide by the absolute value of the old, and multiply by 100. From 80 to 100: ((100 − 80) ÷ 80) × 100 = +25% increase. From 50 to 35: ((35 − 50) ÷ 50) × 100 = −30% decrease.
Percent is a relative change; percentage points are the absolute difference between two percentage values. If interest rises from 4% to 5%, that is a 1-percentage-point increase but a 25% relative increase.
To add 20% (e.g. VAT): multiply by 1.20 — 100 × 1.20 = 120. To subtract 20% (e.g. a discount): multiply by 0.80 — 100 × 0.80 = 80. Faster than computing the percentage separately.
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