How do I scale a recipe with ratios?

Set up the proportion original : new = ingredient : unknown and cross-multiply. Scaling every ingredient by the same factor keeps the ratios intact.

Can a ratio have decimals?

Yes, though ratios are usually converted to whole numbers by multiplying both terms by the same power of ten before simplifying.

What is the difference between a ratio and a rate?

A rate is a ratio between quantities with different units, such as kilometres per hour. The arithmetic is identical.

Ratio Calculator

Simplify a ratio to its lowest terms, or solve a proportion A : B = C : D when one of the four values is unknown.

Fill in the fields above and select Calculate to see your result and the full working.

Formula used

Simplify by dividing both terms by their greatest common divisor. Solve proportions by cross-multiplying: D = B × C ÷ A

How to use this calculator

Choose simplify or solve.
Enter A and B; in solve mode add C as well.
In simplify mode you also get the decimal form and the percentage split.

Example calculation

Simplify 24 : 36 —

GCD of 24 and 36 is 12

24 ÷ 12 : 36 ÷ 12 = 2 : 3

Solve 24 : 36 = 8 : D → D = 36 × 8 ÷ 24 = 12.

What does this result mean?

Ratios compare parts to each other, while fractions compare a part to the whole. In a 3 : 2 ratio the first quantity is three-fifths of the total, not three-halves. Scaling recipes, mixing paint or converting map distances are all proportion problems, solved by cross-multiplication.

Frequently asked questions

How do I scale a recipe with ratios?: Set up the proportion original : new = ingredient : unknown and cross-multiply. Scaling every ingredient by the same factor keeps the ratios intact.
Can a ratio have decimals?: Yes, though ratios are usually converted to whole numbers by multiplying both terms by the same power of ten before simplifying.
What is the difference between a ratio and a rate?: A rate is a ratio between quantities with different units, such as kilometres per hour. The arithmetic is identical.

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