Ratio Calculator

Simplify a ratio, split a total, or solve for a missing term.

What a ratio is

A ratio compares two quantities of the same kind. Writing 12 : 18 says that for every 12 of the first there are 18 of the second. Because it is a comparison rather than a count, multiplying or dividing both terms by the same non-zero number leaves the ratio unchanged — which is what simplifying does.

Simplifying

Divide both terms by their greatest common factor. For 12 : 18 the GCF is 6, so the ratio reduces to 2 : 3. That is the lowest-terms form and the one to give unless the question asks otherwise.

Ratio, fraction and percent

A ratio of 2 : 3 can be read three ways, and mixing them up is the usual error. As a fraction of the other part it is 2/3. As a share of the whole it is 2/5, because the total is 2 + 3 = 5 parts. So 2 : 3 is 40% of the total, not 66.7%.

Splitting a total

To share 200 in the ratio 2 : 3, add the parts to get 5, divide the total by that to get 40 per part, then multiply out: 80 and 120. Check by adding — the parts must return the original total.

Solving a proportion

A proportion states two ratios are equal. Given 2 : 3 = 10 : x, cross-multiply: 2x = 30, so x = 15. Enter a third term above and the calculator does this step and shows it.

Common mistakes

• Treating a part-to-part ratio as a part-to-whole fraction.
• Comparing ratios with different units — convert first.
• Reversing the order. 2 : 3 and 3 : 2 are different ratios.