Percentage Calculator
Five common percentage questions from two numbers: A% of B, A as a percentage of B, the percentage change from A to B, and B increased or decreased by A%.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates A% of B, A as a percentage of B, percentage change from A to B and 2 more results from number A and number B. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
For the error of a reading against a true value use the percentage error calculator, which divides by the reference value and tells you whether the reading is high or low. Percentage points are a different thing: a rise from 10% to 12% is 2 percentage points but a 20% increase. For a share between parts, see the ratio calculator.
Cross-check: 23 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Pure mathematics or statistics; no electrical standard governs the method |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 23 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Number A | 15 |
| Number B | 200 |
- 15% of 200 = 15 × 200 / 100 = 30
- 15 as a percentage of 200 = 15 / 200 × 100 = 7.5%
- Change from 15 to 200 = (200 − 15) / |15| × 100 = 1,233.33333333%
- 200 increased by 15% = 200 × (1 + 15 / 100) = 230
- 200 decreased by 15% = 200 × (1 − 15 / 100) = 170
Assumptions
- All five results are shown at once; read the one that answers your question
- Percentage change is relative to the starting value A, so going from 80 to 100 is +25% but going from 100 to 80 is −20%
- A percentage change from zero is not defined, and A as a percentage of zero is not defined; each is shown as a dash
- Values are plain numbers, so use the same unit for A and B
For the error of a reading against a true value use the percentage error calculator, which divides by the reference value and tells you whether the reading is high or low. Percentage points are a different thing: a rise from 10% to 12% is 2 percentage points but a 20% increase. For a share between parts, see the ratio calculator.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Number A | (number) | any number | The percentage for "A% of B" and for the increase or decrease, and the starting value for "percentage change from A to B". |
| Number B | (number) | any number | The number the percentage is taken of, and the end value for "percentage change from A to B". |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| A% of B | (number) | Shown to 8 decimal places | |
| A as a percentage of B (A / B × 100) | (number) | Shown to 8 decimal places | |
| Percentage change from A to B | (number) | Shown to 8 decimal places | |
| B increased by A% | (number) | Shown to 8 decimal places | |
| B decreased by A% | (number) | Shown to 8 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with number a
| Number A | A% of B | A as a percentage of B | Percentage change from A to B |
|---|---|---|---|
| 1.5 | 3 | 0.75 | 13,233.33333333 |
| 3.75 | 7.5 | 1.875 | 5,233.33333333 |
| 7.5 | 15 | 3.75 | 2,566.66666667 |
| 15 | 30 | 7.5 | 1,233.33333333 |
| 30 | 60 | 15 | 566.66666667 |
| 60 | 120 | 30 | 233.33333333 |
| 150 | 300 | 75 | 33.33333333 |
Other inputs are the same as in the worked example above.
Standards and further reading
Complex numbers, rectangular and polar form and angle conversion are standard mathematics, not the subject of a standard. Standards apply when the result feeds an electrical design, and they set the method there.
Frequently asked questions
What do I need to enter?
Enter number A and number B. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
All five results are shown at once; read the one that answers your question. Percentage change is relative to the starting value A, so going from 80 to 100 is +25% but going from 100 to 80 is −20%. A percentage change from zero is not defined, and A as a percentage of zero is not defined; each is shown as a dash. Values are plain numbers, so use the same unit for A and B.
Which calculators should I use next?
Common next steps are Percentage Error, Ratio Calculator, Mean, Median and Mode and Rounding and Significant Figures. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 23 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Percentage, Ratio and Rounding Formulas: Formulas for percentage, percentage change, ratios, proportions, decimal places and significant figures
- Percentage Error Formulas for Measurements: Percentage error formulas for engineers: absolute, relative and percentage error of a meter reading
- Measurement Uncertainty Formulas: Measurement uncertainty formulas: the standard uncertainty of a rectangular limit
More Engineering Mathematics calculatorsAll engineering calculatorsPercentage Calculator in Elecmetric