Formula
Simplified ratio = first value ÷ common factor : second value ÷ common factor. Part share = part ÷ (first value + second value) × 100. Scaled part = target total × part share.
Math
Ratio Calculator
Simplify two-number ratios, scale them to a new total, and show the part-to-part and part-to-whole percentages.
Calculator
Working calculator
Live result2:340.00% / 60.00% of total; scaled to 100.00 = 40.00 and 60.00
Formula used
Simplified ratio = first value ÷ common factor : second value ÷ common factor. Part share = part ÷ (first value + second value) × 100. Scaled part = target total × part share.
This is the method behind the answer, so the result can be checked rather than simply trusted.What-if check
Scale the same ratio
The relationship stays the same while the total changes. This helps turn a simplified ratio into a recipe, mix, worksheet or quote quantity without losing the original proportion.
| Target total | First part | Second part |
|---|---|---|
| 50.00 | 20.00 | 30.00 |
| 100.00 | 40.00 | 60.00 |
| 200.00 | 80.00 | 120.00 |
Visual proof
Parts of the whole
Blue and gold show the two parts inside the combined whole, making the difference between a part-to-part ratio and part-to-whole percentages visible.
Printable calculation report
Result: 2:3. Assumption: Both ratio parts are treated as non-negative quantities.
- First value
- 12
- Second value
- 18
- Scale to total
- 100
- Page/date context
- 2026-05-16 UTC page version
- Page URL
- https://calculationtime.com/calculators/ratio-calculator
Worked example
For 12 and 18, the greatest common divisor is 6. Divide both parts by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so the simplified ratio is 2:3. The total parts are 5, so the first share is 40% and the second share is 60%. Scaled to 100, the parts are 40 and 60.
Professional note
Master’s Tip: keep the original units beside the ratio. A 2:3 mix, classroom score split or map scale can share the same arithmetic while meaning very different things in practice.
Regional and unit assumptions
Standard or basis: transparent proportional arithmetic. The page simplifies part-to-part ratios and shows part-to-whole percentages without claiming a trade, recipe, finance or statistical standard.
Assumptions and limitations
- Both ratio parts are treated as non-negative quantities.
- Whole-number values are simplified by their greatest common divisor; decimal values are reduced by decimal-place scaling before the same idea is applied.
- If both parts are zero, the ratio is undefined because there is no total relationship to compare.
- The optional target total scales the same relationship; it does not change the ratio itself.
Methodology & Accuracy
How this calculator is checked
CalculationTime pages are built around visible arithmetic: the formula, assumptions, worked example and practical limitations are shown so the result can be checked rather than simply trusted.
Formula used
Simplified ratio = first value ÷ common factor : second value ÷ common factor. Part share = part ÷ (first value + second value) × 100. Scaled part = target total × part share.
Standard or basis
Standard or basis: transparent proportional arithmetic. The page simplifies part-to-part ratios and shows part-to-whole percentages without claiming a trade, recipe, finance or statistical standard.
Where a calculator follows a named legal, trade or industry standard, that standard is cited visibly. Otherwise the page uses transparent general arithmetic and states its limits.Master's Tip
Master’s Tip: keep the original units beside the ratio. A 2:3 mix, classroom score split or map scale can share the same arithmetic while meaning very different things in practice.
Related calculators
Questions
How do you simplify a ratio?
Find a common factor shared by both values, then divide both sides of the ratio by that factor.
What is the ratio 12 to 18 simplified?
The greatest common divisor of 12 and 18 is 6, so 12:18 simplifies to 2:3.
Is a ratio the same as a percentage?
No. A ratio compares quantities to each other. A percentage usually compares one quantity with the combined whole out of 100.
How do I scale a ratio to a total?
Add the ratio parts, divide each part by that total to get its share, then multiply each share by the target total.
Can a ratio include zero?
One side can be zero when the other side is positive, such as 0:5. A 0:0 ratio is undefined because there is no relationship to compare.
Calculation note
Ratios are a compact way to compare quantities. They are useful in recipes, maps, classrooms, mixtures, trade estimates and reports because the relationship can stay the same even when the total size changes.
Ratios preserve relationships
A ratio such as 2:3 says that for every two units of the first quantity there are three units of the second. Scaling to 20:30, 40:60 or 200:300 keeps the same relationship even though the total quantity changes.
Part-to-part and part-to-whole are different views
The ratio 2:3 compares the first part directly with the second part. The same relationship can also be expressed against the whole: the first part is 2 out of 5 total parts, or 40%, and the second part is 3 out of 5, or 60%.
Simplifying helps communication
Simplifying a ratio removes unnecessary scale from the comparison. A teacher, estimator or homeowner can understand 2:3 faster than 12:18, while still keeping the original numbers in the printable report for traceability.
Sources and further readingBritannica: Ratio