Enter values and press Calculate.
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)) |
These three are mixed up constantly, and in engineering the confusion has consequences.
The efficiency case shows why it matters. Going from 90% to 95% sounds like a modest five-point gain, but look at the losses instead: they fall from 10% to 5%, which is a halving of the heat to be dissipated. For a 1 kW converter that is 100 W of waste heat becoming 50 W — often the difference between needing a fan and not. In power electronics, loss is usually the more informative way to state efficiency.
Regulation is quoted as a percentage with a specific definition:
Regulation (%) = (Vno-load − Vfull-load) / Vfull-load × 100
Note the denominator is the full-load voltage, not the no-load one. Using the wrong denominator gives a slightly different answer, and the difference grows as regulation worsens.
Stacking three ±5% components does not give ±15% in practice. That figure is the absolute worst case, requiring all three to sit at their extremes in the same direction simultaneously. Because real tolerances are distributed rather than clustered at the limits, the statistical combination is the root-sum-square — √(5²+5²+5²) ≈ ±8.7%.
Which to use depends on consequence. Design to worst case where failure is unacceptable; design to root-sum-square where a small fraction of out-of-spec units can be screened or adjusted in production.
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.
A percentage point is an arithmetic difference between two percentages; a percent change is relative to the starting value. Going from 90% to 95% is 5 percentage points but a 5.6% relative increase.
Because loss shows the engineering consequence more clearly. Efficiency rising from 90% to 95% halves the losses, which halves the heat to dissipate — a far more meaningful statement than a five-point gain.
(Vno-load − Vfull-load)/Vfull-load × 100. The denominator is the full-load voltage, which is a common source of small discrepancies between calculations.
Only in the absolute worst case. Statistically they combine as a root-sum-square, so three ±5% parts give about ±8.7% rather than ±15%. Use worst case where failure is unacceptable, and root-sum-square where production screening is possible.
Subtract the original value from the new one, divide by the original, and multiply by 100. A negative result indicates a decrease.
A ratio compares two quantities directly, such as a 10:1 transformer turns ratio, and is not expressed out of a hundred. A percentage is always a proportion of a whole.
Scientific Calculator • Energy Cost Calculator • All Calculators