Quick answer
A fraction n/d corresponds to the ratio n : d. 3/4 is the ratio 3:4.
Enter a numerator and denominator. The calculator returns the ratio.
Related tools: Ratio to Fraction Calculator: Convert a ratio a:b to a fraction a/b. Fraction Calculator: Add, subtract, multiply and divide fractions with simplified and mixed-number results. Ratio Calculator: Simplify a ratio of two whole numbers.
How to use the Fraction to Ratio Calculator
- Enter numerator (a whole number, 0 or more).
- Enter denominator (a whole number, 1 or more).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Numerator | A whole number | ≥ 0 |
| Denominator | A whole number | ≥ 1 |
Formula and method
Formula
n/d = n : d
IEEE-754 double precision; shown to at most 6 decimal places.
Direct conversion using the GCD to simplify.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Numerator = 3; Denominator = 4.
| Result | Value |
|---|---|
| Ratio | 3:4 |
The first line is the headline result (ratio). IEEE-754 double precision; shown to at most 6 decimal places.
Part to part and part to whole
The ratio 3:4 compares two parts, while the fraction 3/4 compares a part to the whole of 4. If boys and girls are in the ratio 3:4, boys are 3/7 of the group, not 3/4.
Simplify
Ratios use whole numbers, and the second value must be positive. 6/8 becomes 6:8, which simplifies to 3:4. Scaling a ratio keeps the same relationship.
Part-to-whole versus part-to-part
The calculator writes 3/4 as 3:4, which compares the numerator with the denominator. If 12 of 16 students passed, 12/16 reduces to 3/4 and the passed-to-total ratio is 3:4.
Do not confuse that with a part-to-part ratio. When 3 of every 4 pass, the passed-to-failed ratio is 3:1, because the failed share is 1 of the 4.
How the result changes with numerator
Holding every other input at the first worked example, this table changes only numerator. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Numerator | Ratio |
|---|---|
| 2 | 1:2 |
| 3 | 3:4 |
| 6 | 3:2 |
| 12 | 3:1 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Denominator: entering "0" shows "Denominator must be at least 1." beside that field and no result.
Choosing between the Fraction to Ratio Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Ratio to Fraction Calculator](/math/ratio-to-fraction-calculator/) | a and b | Fraction |
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
| [Ratio Calculator](/math/ratio-calculator/) | first number and second number | Simplified ratio |
| [Inch Fraction Calculator](/math/inch-fraction-calculator/) | decimal inches and nearest | Nearest fraction |
| [Fraction to Decimal Calculator](/math/fraction-to-decimal-calculator/) | numerator and denominator | Decimal |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Whole numbers
- Second value must be positive
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for denominator to confirm this.
Frequently asked questions
What ratio is 2/5?
The fraction 2/5 is the ratio 2:5 between the numbers, though 2 of 7 total parts if it describes a part of a whole.
How do I turn a ratio into a fraction?
Use the part over the total.
What is the difference?
Fractions describe part of a whole.
Does 3/4 mean 3 to 4 or 3 to 1?
Written as numerator : denominator it is 3:4 (part to whole). Compared with the remaining part it is 3:1 (part to part).
Can I enter an improper fraction such as 9/4?
Yes. 9/4 becomes 9:4, because only whole numbers and a positive second value are required.
What does the Fraction to Ratio Calculator calculate?
Convert a fraction to a ratio. It returns Ratio.
What formula does the Fraction to Ratio Calculator use?
n/d = n : d. Direct conversion using the GCD to simplify.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Whole numbers.
What are the limits of this calculator?
Whole numbers. Second value must be positive.
What is an example of a fraction to Ratio result?
With numerator 3 and denominator 4, the ratio is 3:4.
Related calculators
- Ratio to Fraction Calculator — Convert a ratio a:b to a fraction a/b.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Ratio Calculator — Simplify a ratio of two whole numbers.
- Inch Fraction Calculator — Convert decimal inches to the nearest fractional inch.
- Fraction to Decimal Calculator — Convert a fraction to a decimal, showing repeating digits.
- Ratio Percentage Calculator — Percentage share of each part of a ratio.
- Modulo Calculator — Remainder of a division, with floored and truncated conventions.
- Multiplication Calculator — Product of a list of numbers.
- Greater Than Less Than Calculator — Compare two numbers.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.