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How to use
This ratio and proportion calculator simplifies A:B, splits a total in that ratio, and solves any missing term in A:B = C:D. Select A, B, C or D as the unknown and enter the three known quantities; the tool cross-multiplies and checks the two ratios. A ratio compares quantities while a proportion states that two ratios are equal.
- Choose ordinary ratio simplification and optional split, or the missing-term proportion mode.
- Select the unknown term A, B, C or D in A:B = C:D.
- Enter the other three known positive quantities in their named fields.
- Calculate and verify the recovered term using A÷B and C÷D.
How it is calculated
Example
For 2:3 = 8:12, missing A gives 3×8÷12=2; missing B gives 2×12÷8=3; missing C gives 2×12÷3=8; and missing D gives 3×8÷2=12. Separately, 12:18 simplifies to 2:3, and splitting 500 in that ratio gives 200 and 300.
Important notes
A ratio is not automatically a percentage. A:B describes a relationship between two values, while A's share of the combined total is A ÷ (A+B). Decimal inputs are scaled to integers before simplification, with a practical precision limit to avoid floating-point artifacts.
Worked examples and interpreting results
The ratio 2:3 divides a total of 100 into shares of 40 and 60. There are five ratio parts altogether, so the first share is two fifths of the total, rather than two thirds.
| Case | Calculation | Result |
|---|---|---|
| First share | 100 × 2 ÷ (2 + 3) | 40 |
| Second share | 100 × 3 ÷ (2 + 3) | 60 |
| Solve 2:3 = 8:D | D = 3 × 8 ÷ 2 | 12 |
How to check the result
Check that the shares add up to the total and retain the ratio 2:3. Reducing 8:12 to 2:3 preserves the ratio; solving a proportion must never divide by zero.
Frequently asked questions
How do I simplify a ratio?
Scale decimal terms to integers when needed, then divide both terms by their greatest common divisor.
What is the difference between a ratio and a proportion?
A ratio compares two quantities, such as 2:3. A proportion states that two ratios are equal, such as 2:3 = 8:12.
How do I split a total in a 3:2 ratio?
Add the ratio parts first: 3+2=5. The first share is total × 3/5 and the second is total × 2/5.