Find the missing term in a : b = c : d, or reduce a ratio to its simplest form.
Enter the values to see the result here.
Formula
A proportion states ba=dc. Cross-multiplying gives ad=bc, so any one missing term follows from the other three:
a=dbc,b=cad,c=bad,d=abc
To simplify a:b, divide both terms by their greatest common divisor, after scaling decimals to integers.
Worked example
A concrete mix uses 2 parts cement to 5 parts sand. How much sand is needed for 18 kg of cement?
Set 2:5=18:d.
d=25×18=45 kg of sand.
Simplifying: 45:60 has gcd=15, so it reduces to 3:4.
Common mistakes
Mixing up the order. 2:5=18:d is not the same as 5:2=18:d.
Mixing units inside a ratio: 1 m : 50 cm is 100 : 50, or 2 : 1, not 1 : 50.
Adding the same amount to both terms and expecting the ratio to stay. 3:4 plus 2 each is 5:6, a different ratio.
Leaving two terms blank. The tool needs exactly one blank to solve.
Frequently asked questions
What does it mean for two ratios to be proportional?
Two ratios are proportional when they describe the same relationship, such as 3 : 4 and 9 : 12. Cross-multiplying gives equal products, 3 × 12 = 4 × 9.
How do I use this to scale a recipe?
Put the original amount in a, the original servings in b, and the new servings in c, then leave d blank. The result is the new amount. For 200 g for 4 servings scaled to 6 servings, enter 200, 4, 6.
What if my ratio has decimals?
The simplifier scales decimals up to whole numbers first, so 1.5 : 2.5 becomes 3 : 5. It handles up to six decimal places.
How do I split a total in a given ratio?
Add the ratio parts, divide the total by that sum, and multiply by each part. To split 90 as 2 : 3 : 4, the parts sum to 9, one part is 10, and the shares are 20, 30 and 40.