Compound Ratio Calculator
Combine two or three ratios into their compound ratio by multiplying antecedents and consequents, then simplify to lowest terms.
How it works
Compound ratio = (a₁ : b₁) compounded with (a₂ : b₂) … = (a₁·a₂·…) : (b₁·b₂·…), then divide both by their GCD
The compound ratio of several ratios is formed by multiplying all the first terms (antecedents) together and all the second terms (consequents) together. It answers questions like "if A:B and B:C are known, what is A:C" when the middle terms line up. The result is then reduced to lowest terms by dividing both sides by their greatest common divisor. Leave a ratio as 1:1 to compound only two.
Worked example
Compounding 2 : 3 with 4 : 5 gives (2·4) : (3·5) = 8 : 15. Since 8 and 15 share no common factor other than 1, the compound ratio is already in lowest terms: 8 : 15 ≈ 0.5333 as a decimal.
Sources: Ratio — Wikipedia
Frequently asked questions
What is a compound ratio?
It is the single ratio obtained by multiplying two or more ratios term by term: the antecedents (first terms) multiply to form the new antecedent, and the consequents (second terms) multiply to form the new consequent. For example, 2:3 compounded with 4:5 is 8:15.
How is it different from adding ratios?
Ratios are not added — compounding multiplies them. Compounding is used when ratios chain together, like scaling one quantity by two successive factors. The duplicate ratio (a ratio compounded with itself) and the triplicate ratio are special cases of the same idea.
Why compound only two ratios sometimes?
If you only have two ratios, leave the third set to 1 : 1. Multiplying by 1:1 changes nothing, so the calculator returns the compound of just the first two ratios.
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This calculator is for educational purposes. Double-check important results before acting on them.