Ratio Calculator
Simplify ratios, solve equivalent proportions, or scale both terms by the same factor.
Runs in this browser. No upload by this tool. Values are not saved by this calculator.
One term may be zero, but 0 : 0 is not a defined ratio. Negative values are supported.
The last target field you edit is treated as the known value. The other target value is solved from the base proportion.
A non-zero factor applied to both terms keeps the pair proportional to the base ratio.
Simplified ratio
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Copy the current ratio result or download a local report.
Creates an editable Word report locally in this browser.
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How Ratio Calculator works
Use the calculator first. The sections below explain simplifying ratios, solving equivalent proportions, scaling both terms, decimal and zero handling, worked examples, and the exact arithmetic boundaries behind the result.
How to use the calculator
- Choose Simplify, Equivalent, or Scale.
- Enter ordinary decimal values for the fields required by that mode. Examples stay in the help text until you choose Use Example.
- Review the primary ratio plus the proportional, precision, or method check shown with the result.
- When solving an equivalent ratio, edit one target field; the other target term is calculated from the base proportion.
- Copy the current result or save it locally as Word, Markdown, text, JSON, or through the browser Print / Save PDF workflow.
Worked examples
Simplify 1920 : 1080
The exact common divisor reduces 1920 : 1080 to 16 : 9. The quotient A ÷ B is approximately 1.77777778.
Simplify a decimal ratio
1.5 : 0.5 is converted to exact integer fractions and reduces to 3 : 1; repeated floating-point multiplication is not used to guess when the values become integers.
Solve an equivalent proportion
For a base ratio of 16 : 9, setting Target A to 1920 solves Target B as 1080. The target pair satisfies the same cross-product relationship as the base pair.
Scale 4 : 3 by 2.5
Multiplying both terms by 2.5 produces 10 : 7.5. The displayed numbers change, while the pair remains proportional to 4 : 3.
Choose the ratio job you need
The three modes answer different questions. Pick the one that matches the information you already have.
| Mode | You enter | The calculator returns | Typical use |
|---|---|---|---|
| Simplify | Two ratio terms | A reduced equivalent integer pair plus A ÷ B when defined | Reduce 1920 : 1080 to 16 : 9 or simplify decimal ratios. |
| Equivalent | A base ratio and one target term | The missing target term and an exact proportional check | Solve 16 : 9 = 1920 : x. |
| Scale | Two terms, a non-zero factor, and multiply/divide | Both terms after applying the same factor | Resize a proportional pair without changing its ratio relationship. |
Frequently asked questions
What is a ratio?
A ratio compares two quantities in an ordered pair such as 4 : 3. The calculator works with the numerical relationship between the two terms; it does not infer units or what the quantities represent.
How do I simplify a ratio?
Enter both terms in Simplify mode. The calculator converts decimal text to exact rational form, moves both terms to a common integer scale, and divides by the greatest common divisor.
Can this calculator simplify decimal ratios?
Yes. Ordinary decimal notation is converted to exact rational integers before reduction, so values such as 1.5 : 0.5 simplify exactly to 3 : 1.
How does Equivalent mode solve a missing ratio value?
Equivalent ratios satisfy the cross-product relationship A × D = B × C. Enter the known base pair, then edit one target field and the calculator solves the other target term when the solution is unique.
What does Scale mode do?
Scale mode multiplies or divides both terms by the same non-zero factor. That changes the displayed terms while preserving proportional equivalence to the starting ratio.
Can a ratio contain zero?
Yes. 0 : n and n : 0 are supported when n is non-zero and the requested operation is defined. The pair 0 : 0 is rejected because it does not define a usable ratio.
Can ratio values be negative?
Yes. Negative ordinary-decimal inputs are supported. In simplified output, a negative sign is normalized to the left term when the right term is non-zero.
Does the calculator accept scientific notation?
No. This candidate accepts ordinary decimal notation with up to 12 whole-number digits and up to 8 decimal places. Scientific notation such as 1e6 is not accepted.
Which file formats can I save?
A valid result can be copied or saved locally as a Word DOCX, Markdown, plain text, JSON, or through the browser Print / Save PDF workflow.
Is an account required?
No account is required to calculate, copy, or download a result with this version of the tool.
Method and limitations
This candidate uses exact decimal-string normalization to rational integers with BigInt for the calculation core. Derived non-integer display values are rounded only for presentation.
Ordinary signed decimal notation is accepted with up to 12 whole-number digits and 8 decimal places. Scientific notation is rejected.
Decimal inputs are represented exactly, moved to a common integer scale, then reduced by the greatest common divisor.
The missing target term is solved from the proportional cross-product relationship using exact rational arithmetic when the requested direction has a unique solution.
Multiply or divide both terms by the same non-zero rational factor. A zero factor is rejected because it would collapse the pair to 0 : 0.
One term may be zero. 0 : 0 is invalid. Simplified negative ratios normalize the sign to the left term when the right term is non-zero.
Simplification is exact. Derived non-integer values are displayed to at most 8 decimals using half-away-from-zero rounding.
This Tool calculates two-term numerical ratios. It does not infer dimensions, units, image-cropping decisions, recipe meaning, financial meaning, or other domain-specific interpretation from the numbers alone.
Runs in this browser. No upload by this tool. Values are not saved by this calculator. Copy and download locally, then review before sharing.