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A percentage expresses a quantity as a fraction of 100, making it easy to compare proportions across different scales (e.g. comparing a 90/100 score to a 45/50 score by converting both to percentages). A ratio compares two quantities directly to each other, and is most useful in its simplest form — found by dividing both numbers by their greatest common divisor (GCD).
| Question | Formula |
|---|---|
| X% of Y | (X/100)×Y |
| X is what % of Y | (X/Y)×100 |
| Percentage change (old→new) | (New−Old)/Old×100 |
| Simplified ratio a:b | (a/gcd(a,b)) : (b/gcd(a,b)) |
Multiply Y by X/100. For example, 18% of 250 = (18/100)×250 = 45.
Divide the first number by the second, then multiply by 100. For example, 45 is (45/180)×100 = 25% of 180.
Use (New Value - Old Value)/Old Value × 100. A positive result is a percentage increase; a negative result is a percentage decrease.
Because percentage change is always calculated relative to the starting value, and the starting value changes between the two steps. Increasing 200 by 25% gives 250, but decreasing 250 by 25% gives 187.5, not back to 200 — you would need a 20% decrease from 250 to return to 200.
Find the greatest common divisor (GCD) of both numbers, then divide both by it. For example, 24:36 has GCD 12, simplifying to 2:3.
A ratio compares two quantities directly to each other (like 2:3), while a percentage expresses one quantity as a fraction of 100, often relative to a whole or total — both describe proportions, but percentages are standardized to a base of 100 for easy comparison across contexts.
For a ratio a:b representing parts of a whole (a+b), the percentage each part represents is a/(a+b)×100 and b/(a+b)×100 respectively — for example, a 2:3 ratio splits as 40% and 60%.
A component's percentage tolerance (e.g. a resistor rated ±5%) tells you the real range of possible actual values around its nominal rating, which matters for circuit designs sensitive to precise component values.
Yes — a percentage above 100% simply means the value being described is larger than the reference value it is being compared to (for example, 150% of 200 = 300, or a percentage increase can easily exceed 100% for values that more than double).
Using the wrong value as the "old" (base) value in the denominator — always divide by the original/starting value, not the new value, or the calculated percentage change will be incorrect.
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