How the Ratio Calculator works
Choose Simplify a ratio, Solve a missing term, or Divide a total by a ratio. The result shows the formula, substitutions, assumptions, and exact fraction values. Decimal values can repeat or be truncated with an ellipsis. Add an optional unit label for display; the calculator does not convert units.
Choose a calculation mode
- Simplify a ratio: reduce two or more terms by their greatest common divisor. Terms can be entered with colons, commas, or whitespace, such as
8:12:20. - Solve a missing term: enter two ratios with the same number of terms and mark one value with
?, such as3:4and?:20. The calculator uses a fully known, nonzero matching pair to find the scale factor. - Divide a total by a ratio: enter a zero or positive total and a ratio. Each part is calculated with
part(i) = total × term(i) / (sum of all terms).
How to use the Ratio Calculator
- Select Simplify a ratio, Solve a missing term, or Divide a total by a ratio.
- Enter the required values. Use whole numbers, decimals, or fractions such as
3/4. Separate ratio terms with a colon, comma, or whitespace. - Enter an optional unit label. It is carried into the result text and does not trigger conversion.
- Select Calculate to show the result, formula, steps, and assumptions.
- After a result appears, select Copy result or Download result (.txt).
- Select Reset to clear the inputs and return to the default Simplify a ratio mode.
Validation and limitations
- Each ratio needs at least two valid numeric terms. Ratio terms must be zero or positive, and they cannot all be zero.
- Solve a missing term allows exactly one
?. The two ratios must have the same length and include a fully known, nonzero matching pair to determine the scale factor. - Divide a total by a ratio rejects a negative total.
- Fractions remain exact. A decimal equivalent may be repeating or truncated with an ellipsis; it is not a replacement for the exact fraction.
- Unit labels are display text only. Enter values in the same unit because no conversion is performed.
- Parsing and calculation run in the browser on the values you enter. The tool does not fetch outside data or provide professional advice.
Frequently asked questions
How do I simplify a ratio?
Enter at least two terms, separated by a colon, comma, or whitespace, then select Calculate. The calculator finds the greatest common divisor and divides each term by it.
How do I solve a missing term in a ratio?
Select Solve a missing term, enter two same-length ratios, and mark exactly one term with ?. A fully known, nonzero matching pair must be available to derive the scale factor.
How do I divide a total by a ratio?
Select Divide a total by a ratio, enter a zero or positive total and a ratio, and the calculator returns each part as total × term / (sum of terms). It also checks that the parts add back to the total.
Does the calculator convert between units?
No. The optional unit field is a label carried into the result text. Enter all values in the same unit.
Is this certified or professional advice?
No. This is a general-purpose arithmetic tool. It calculates from the exact values entered and does not infer professional, engineering, financial, or medical assumptions.