Ratio Calculator
Simplify a ratio A : B, find each part as a share of the whole, and solve the proportion A : B = C : X for the missing value. Works for turns ratios
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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.
Open in the calculator with these values
About this calculator
This page calculates simplified ratio, first part, simplified ratio, second part, A / B and 3 more results from A, B and C. 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
Use this for a transformer turns ratio, a gear or pulley ratio, a voltage divider split, a scale drawing or a mix. For a transformer the voltage ratio equals the turns ratio. To turn the share into a percentage change or a percentage of a total, use the percentage calculator.
Cross-check: 24 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 | 24 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 |
|---|---|
| A | 12 |
| B | 18 |
| C (optional) | 5 |
- Greatest common divisor of 12 and 18 = 6, so 12 : 18 = 2 : 3
- A / B = 12 / 18 = 0.66666667
- Shares: A = 40%, B = 60%
- X = B × C / A = 18 × 5 / 12 = 7.5
Assumptions
- The simplified ratio is found only when A and B are whole numbers; for decimals multiply both by a power of ten first, such as 1.5 : 2.5 becomes 15 : 25
- A and B must be greater than zero
- The proportion assumes a direct (linear) relation; for an inverse proportion, where one quantity falls as the other rises, use X = A × B / C
- Whole numbers above 9,007,199,254,740,991 are not held exactly and are not simplified
Use this for a transformer turns ratio, a gear or pulley ratio, a voltage divider split, a scale drawing or a mix. For a transformer the voltage ratio equals the turns ratio. To turn the share into a percentage change or a percentage of a total, use the percentage calculator.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| A | (number) | greater than 0 | The first part of the ratio A : B. Must be greater than zero. |
| B | (number) | greater than 0 | The second part of the ratio A : B. Must be greater than zero. |
| C (optional) | (number) | greater than 0; may be left blank | To solve A : B = C : X for X, enter C. Leave blank to only simplify A : B. |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Simplified ratio, first part | (number) | Shown to 0 decimal places | |
| Simplified ratio, second part | (number) | Shown to 0 decimal places | |
| A / B (ratio as a decimal) | (number) | Shown to 8 decimal places | |
| A as a share of A + B (%) | (number) | Shown to 6 decimal places | |
| B as a share of A + B (%) | (number) | Shown to 6 decimal places | |
| X in A : B = C : X (X = B × C / 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 a
| A | Simplified ratio, first part | Simplified ratio, second part | A / B |
|---|---|---|---|
| 1.2 | — | — | 0.06666667 |
| 3 | 1 | 6 | 0.16666667 |
| 6 | 1 | 3 | 0.33333333 |
| 12 | 2 | 3 | 0.66666667 |
| 24 | 4 | 3 | 1.33333333 |
| 48 | 8 | 3 | 2.66666667 |
| 120 | 20 | 3 | 6.66666667 |
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 a, b and c (optional). Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
The simplified ratio is found only when A and B are whole numbers; for decimals multiply both by a power of ten first, such as 1.5 : 2.5 becomes 15 : 25. A and B must be greater than zero. The proportion assumes a direct (linear) relation; for an inverse proportion, where one quantity falls as the other rises, use X = A × B / C. Whole numbers above 9,007,199,254,740,991 are not held exactly and are not simplified.
Which calculators should I use next?
Common next steps are Percentage Calculator, Quadratic Equation Solver, Exponent and Root Calculator 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. 24 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
- Transformer Formulas: Current and Fault Level: Transformer formulas for turns ratio, full-load current, impedance and fault current
- Percentage Error Formulas for Measurements: Percentage error formulas for engineers: absolute, relative and percentage error of a meter reading
More Engineering Mathematics calculatorsAll engineering calculatorsRatio Calculator in Elecmetric