Ratio and Proportion Calculator
Solve the missing fourth term in an equivalent proportion written as a:b = c:x.
Content updated July 31, 2026
Enter the known terms in a : b = c : x.
Ratios are unitless only when both terms use compatible units. Values are calculated at full precision and displayed with up to six decimals.
Equivalent ratios describe the same relationship at different scales. Enter the three known terms in a:b = c:x and the calculator solves the missing fourth term, shows the scale factor, and normalizes the first ratio.
This is useful for recipes, maps, models, mixtures, and any situation where two quantities must stay in the same proportion. Make sure paired terms use compatible units before comparing them.
The Ratio and Proportion formula
a : b = c : x ⇒ a/b = c/x ⇒ x = (b × c) ÷ aa is the non-zero first term · b and c are the other known terms · x is the missing fourth term.
Worked example
For 2:3 = 8:x, cross multiply to get 2x = 3×8 = 24, then divide by 2. The missing term is x = 12, and the scale factor is 8÷2 = 4.
Assumptions, rounding, and limitations
Assumptions
- The two ratios are intended to be equivalent.
- The first term is greater than zero; the other known terms are non-negative.
- Corresponding quantities already use compatible units.
Rounding: The calculation uses full floating-point precision; displayed results show up to six decimal places.
Limitations
- Solves only the fourth term in a:b = c:x.
- Does not automatically convert units or attach meaning to the ratio terms.
Solving a proportion by cross multiplication
For a:b = c:x, write the ratios as a/b = c/x. Cross multiplication gives a×x = b×c, so divide both sides by a to get x = b×c/a.
The first term cannot be zero because the formula divides by it. The calculator accepts zero for b or c, in which case the missing fourth term is zero.
Frequently asked questions
▶How do I solve a proportion?
Cross multiply, then divide by the coefficient beside the unknown. For a/b = c/x, calculate x = b×c/a.
▶What is a scale factor?
It is the multiplier that changes one equivalent ratio into the other. In a:b = c:x, the scale factor from the first ratio to the second is c/a.
▶Can a ratio contain decimals?
Yes. Equivalent ratios can contain any finite non-negative values as long as the first term is greater than zero.
▶Do the ratio terms need the same units?
Corresponding terms should use compatible units. Convert them first when necessary; for example, do not compare centimetres with metres without conversion.
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Open calculator →Disclaimer: Ratio and Proportion Calculator results are estimates for general information and education only, and are not financial, tax, legal or medical advice. Verify important decisions with a qualified professional.