Fraction Calculator
Add, subtract, multiply or divide two fractions. The answer is given as a simplified fraction, a mixed number, a decimal and a percentage, with the working.
Try your own numbers
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 result, numerator, result, denominator, mixed number, whole part and 3 more results from first fraction, numerator, first fraction, denominator, operation, second fraction, numerator and 1 more input. 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 fractions for ratios of standard sizes and for exact relations, such as the reciprocal sum behind parallel resistors. For a decimal you want to turn into a fraction, multiply both parts by a power of ten and simplify with the ratio calculator. Convert to a percentage with the figure shown here or with the percentage calculator.
Cross-check: 39 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 | 39 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 |
|---|---|
| First fraction, numerator | 1 |
| First fraction, denominator | 2 |
| Operation | Add (+) |
| Second fraction, numerator | 1 |
| Second fraction, denominator | 3 |
- 1/2 + 1/3 = (1 × 3 + 1 × 2) / (2 × 3) = 5 / 6
- Greatest common divisor of 5 and 6 = 1, so the simplest form is 5/6
- Mixed number: 5/6 needs no whole part
- Decimal = 5 / 6 = 0.8333333333
Assumptions
- All four numbers are whole numbers no larger than 1,000,000 in size, so the arithmetic is exact
- No denominator may be zero, and when dividing the second fraction may not be zero
- The result is reduced to lowest terms with the minus sign on the numerator and a positive denominator
- The mixed number is the whole part (toward zero) and a remainder numerator over the same denominator, so −7/2 is −3 and 1/2
- The decimal value is rounded for display; the fraction is the exact answer
Use fractions for ratios of standard sizes and for exact relations, such as the reciprocal sum behind parallel resistors. For a decimal you want to turn into a fraction, multiply both parts by a power of ten and simplify with the ratio calculator. Convert to a percentage with the figure shown here or with the percentage calculator.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| First fraction, numerator | (number) | -1,000,000 or more, up to 1,000,000 | Whole numbers only, up to 1,000,000 in size. A negative fraction takes the minus sign on the numerator. |
| First fraction, denominator | (number) | -1,000,000 or more, up to 1,000,000 | A whole number that is not zero. |
| Operation | (choice) | Add (+); Subtract (−); Multiply (×); Divide (÷) | |
| Second fraction, numerator | (number) | -1,000,000 or more, up to 1,000,000 | |
| Second fraction, denominator | (number) | -1,000,000 or more, up to 1,000,000 | A whole number that is not zero. |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Result, numerator (simplified) | (number) | Shown to 0 decimal places | |
| Result, denominator (simplified) | (number) | Shown to 0 decimal places | |
| Mixed number, whole part | (number) | Shown to 0 decimal places | |
| Mixed number, remainder numerator | (number) | Shown to 0 decimal places | |
| Decimal value | (number) | Shown to 10 decimal places | |
| As a percentage (%) | (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 first fraction, numerator
| First fraction, numerator | Result, numerator | Result, denominator | Mixed number, whole part |
|---|---|---|---|
| 1 | 5 | 6 | 0 |
| 2 | 4 | 3 | 1 |
| 4 | 7 | 3 | 2 |
| 10 | 16 | 3 | 5 |
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 first fraction, numerator, first fraction, denominator, operation, second fraction, numerator, second fraction and denominator. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
All four numbers are whole numbers no larger than 1,000,000 in size, so the arithmetic is exact. No denominator may be zero, and when dividing the second fraction may not be zero. The result is reduced to lowest terms with the minus sign on the numerator and a positive denominator. The mixed number is the whole part (toward zero) and a remainder numerator over the same denominator, so −7/2 is −3 and 1/2. The decimal value is rounded for display; the fraction is the exact answer.
Which calculators should I use next?
Common next steps are Ratio Calculator, Percentage Calculator, Rounding and Significant Figures and Resistors in Parallel. 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. 39 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
- Resistor Formulas: Series, Parallel, Divider: Resistor formulas for series and parallel resistance, the voltage divider and power in a resistor
- Measurement Uncertainty Formulas: Measurement uncertainty formulas: the standard uncertainty of a rectangular limit
More Engineering Mathematics calculatorsAll engineering calculatorsFraction Calculator in Elecmetric