Ratio Calculator

A proportion is two ratios set equal to each other, and the useful thing about it is that knowing three of the four terms pins down the fourth. Recipes scaled for a different number of people, map distances, mixing ratios, model scales and currency at a fixed rate are all the same arithmetic wearing different clothes.

How it is calculated

a : b = c : d ⟹ d = b × c ÷ a

The step people skip is checking which way round the pairs go. In a : b = c : d the first term of each ratio has to describe the same kind of thing — parts of flour to parts of water, not flour in one ratio and water in the other. Get that backwards and the arithmetic is flawless and the answer is wrong.

Source: A proportion states that two ratios are equal: a : b = c : d, which holds exactly when a × d = b × c, so any one of the four terms follows from the other three

Questions people ask

What is the rule of three?

The same thing under an older name. Three known terms, one unknown, solved by multiplying the two that sit diagonally and dividing by the third. It was taught as a recipe long before it was taught as algebra, which is why it has its own name at all.

How do I scale a recipe?

Put the original quantity and the original number of servings in the first ratio, then the number of servings you want. The missing term is the new quantity. Baking is the one place to be careful: tin size and cooking time do not scale in proportion, only the ingredients do.

Why does the ratio in lowest terms only appear sometimes?

Because reducing needs whole numbers. 12 : 18 shares a divisor of 6 and becomes 2 : 3, but 2.5 : 4 has no such divisor and stays as it is. If you want it reduced, scale both terms up to integers first.

What does the scale factor tell me?

How many times bigger the second ratio is than the first. A factor of 3 means everything triples, which is the number you want when resizing a drawing or a model rather than solving for a single term.

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