Percentage, Ratio and Rounding Formulas
Formulas for percentage, percentage change, ratios, proportions, decimal places and significant figures, with worked electrical examples.
The formulas
| To find | Formula |
|---|---|
| A% of B | A × B / 100 |
| A as a percentage of B | A / B × 100 |
| Percentage change from A to B | (B − A) / |A| × 100 |
| B increased or decreased by A% | B × (1 ± A / 100) |
| Simplified ratio | divide both parts of A : B by their greatest common divisor |
| Share of A in A : B | A / (A + B) × 100 |
| Solving a proportion A : B = C : X | X = B × C / A |
| Rounding to d decimal places | keep d places; if the next digit is 5 or more, round away from zero |
| Significant figures | count from the first non-zero digit |
Percentage change is taken against the starting value, so a rise from 80 to 100 is +25% while the fall from 100 back to 80 is only −20%. The percentage change from zero is not defined. A ratio can be simplified only when both parts are whole numbers; multiply both by a power of ten first if they are decimals. Round only the final answer: rounding in the middle of a calculation adds up the errors.
Worked example: percentage change
A load rises from 80 A to 100 A and later falls back.
- Rise = (100 − 80) / 80 × 100 = 25%
- Fall = (80 − 100) / 100 × 100 = -20%
- The two are different because each uses its own starting value as the base
Worked example: a turns ratio
A transformer is rated 11,000 V / 415 V.
- Greatest common divisor of 11,000 and 415 = 5
- Simplified: 11,000 : 415 = 2,200 : 83
- Ratio = 11,000 / 415 = 26.51 : 1
- For a primary of 2,200 turns the secondary has 2,200 × 415 / 11,000 = 83 turns
Worked example: rounding
- 1,234.5678 to 2 decimal places = 1,234.57 (the next digit is 7)
- 1,234.5678 to 3 significant figures = 1,230 (the first three digits are 1, 2 and 3; the next digit is 4)
- A reading of 230 V quoted to 2 significant figures is 230 V
Frequently asked questions
Why is a 25% rise not undone by a 25% fall?
Each percentage is taken of a different base. After a 25% rise the new value is larger, so 25% of it is a bigger amount than the original rise. To undo a 25% rise you need a 20% fall.
What is the difference between percentages and percentage points?
A move from 10% to 12% is 2 percentage points but a 20% increase. Use percentage points for the difference between two percentages.
Why does 2.5 round to 3 and not 2?
The common rule rounds a half away from zero. Some software rounds a half to the nearest even number, which gives 2, so check which rule a tool uses.
How many significant figures should I quote?
No more than the least precise input supports. A voltage read to the nearest volt is not known to four figures just because a calculator shows them.
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