Purpose and steps
Ratio Calculator validates first integer, second integer, scale factor before applying the displayed equation. The ratio 0:0 is undefined; other zero or negative terms are preserved.
- Reduce an integer ratio and scale both original terms by the same factor. The reduced ratio expresses relative size; scaled terms retain the chosen numerical scale.
- Enter First integer, Second integer, Scale factor in the stated format. Baseline values are for reproduction.
- Check the output unit and convention: Read simplified ratio with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input and compare the result. The ratio 0:0 is undefined; other zero or negative terms are preserved. Decimal ratios must first be converted to equivalent integers.
Input reference and units
These values reproduce the model’s demonstration. Replace them with your own records or measurements; they are not recommended targets.
On a small screen, swipe the table horizontally to see all columns.
| Parameter | Demonstration value | How to enter it |
|---|---|---|
| First integer | 12 | Enter first integer without adding a unit suffix. Scope: The ratio 0:0 is undefined; other zero or negative terms are preserved. |
| Second integer | 18 | Enter second integer without adding a unit suffix. Scope: The ratio 0:0 is undefined; other zero or negative terms are preserved. |
| Scale factor | 1 | Multiply both original ratio terms by this factor; the reduced ratio stays unchanged. |
Model-specific method
How this calculator produces its result
Ratio Calculator: reduced ratio = (a/gcd(a,b)) : (b/gcd(a,b)); scaled = original × scale. Input definitions: a = First integer; b = Second integer; scale = Scale factor. Use the selected convention throughout the calculation.
Ratio Calculator: calculation relationships
Reduce an integer ratio and scale both original terms by the same factor. The reduced ratio expresses relative size; scaled terms retain the chosen numerical scale. The ratio 0:0 is undefined; other zero or negative terms are preserved. Decimal ratios must first be converted to equivalent integers.
A ratio describes relative size rather than a total. Divide 14 and 21 by their GCD 7 to obtain 2:3. Scaling the original terms by 2 gives 28:42, still the same ratio; it does not give the reduced terms 4:6. To allocate a total in a 2:3 ratio, first divide the total by 2+3, then multiply by each part.
reduced ratio = (a/gcd(a,b)) : (b/gcd(a,b)); scaled = original × scale
- a: First integer. Enter first integer without adding a unit suffix. Scope: The ratio 0:0 is undefined; other zero or negative terms are preserved.
- b: Second integer. Enter second integer without adding a unit suffix. Scope: The ratio 0:0 is undefined; other zero or negative terms are preserved.
- scale: Scale factor. Multiply both original ratio terms by this factor; the reduced ratio stays unchanged.
- Result units: stated beside each output
- Calculation relationship: reduced ratio = (a/gcd(a,b)) : (b/gcd(a,b)); scaled = original × scale
- Supported domain: see the limits below
Worked example
Ratio Calculator baseline input: First integer: 12; Second integer: 18; Scale factor: 1. Output: Simplified ratio = 2:3; Scaled first term = 12; Scaled second term = 18. Substitute these values into the displayed equation to reproduce the result.
Reproduce the default scenario
This reproduces the default inputs in the reference table above; it is not an additional independent example. Displayed rounding may differ from intermediate precision.
- Simplified ratio
- 2:3
- Scaled first term
- 12
- Scaled second term
- 18
Reading results without overstating them
- Read simplified ratio with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.
Assumptions and exclusions
- The ratio 0:0 is undefined; other zero or negative terms are preserved.
- Decimal ratios must first be converted to equivalent integers.
Sources and content notes
Toolify describes the implemented algorithm and its assumptions. Sources below support the topic or applicable rules; they do not endorse this calculator. Examples are illustrative, and published rules take precedence over simplified estimates.
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