Simplify a ratio to its lowest terms, or leave any one box empty and get the missing term of the proportion — with the cross-multiplication shown.
A : B = C : D
Fill any three boxes and leave one blank to solve for it. Fill just A and B to simplify a ratio.
:=:
Example: a recipe uses 3 parts flour to 4 parts water. Scaling to 12 parts flour, how much water? Leave D blank.
Missing value
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A : B simplified—
C : D simplified—
A ÷ B as a decimal—
A as % of B—
A's share of A + B—
Proportion holds?—
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How a ratio works
A ratio compares two quantities by division. Writing 3 : 4 says that for every 3 of the first thing there are 4 of the second — it says nothing about the absolute amounts, only the relationship. That is why 3 : 4, 6 : 8 and 30 : 40 are the same ratio.
Simplifying
Divide both sides by their greatest common divisor. For 30 : 40 the GCD is 10, giving 3 : 4. Decimal ratios are scaled up to whole numbers first: 1.5 : 2 becomes 15 : 20, which reduces to 3 : 4.
Solving a proportion
Two equal ratios form a proportion: A : B = C : D. Cross multiply and the products match — A × D = B × C. Rearranging that identity gives you any missing term:
Missing
Formula
A
B × C ÷ D
B
A × D ÷ C
C
A × D ÷ B
D
B × C ÷ A
So 3 : 4 = 12 : D gives D = 4 × 12 ÷ 3 = 16. Twelve parts flour needs sixteen parts water.
They are three ways of saying the same thing, and which one you use is mostly convention. A 3 : 4 ratio is the fraction 3/4 when you compare A to B, but only 3/7 of the total once you add both parts together — that distinction trips people up constantly. Mixing instructions ("1 : 4 concentrate to water") mean one part in five, not one part in four.
Where ratios show up
Recipes and dilutions scale by ratio. Screen and photo aspect ratios (16 : 9, 4 : 3, 3 : 2) are ratios. Gear ratios, map scales, mixing fuel for a two-stroke engine, drink recipes, concrete mixes, and financial measures like the current ratio or debt-to-equity all work the same way: keep the relationship constant while the absolute numbers change.
Divide both numbers by their greatest common divisor. For 18 : 24 the GCD is 6, so the simplified ratio is 3 : 4. If the ratio contains decimals, multiply both sides by 10, 100 or 1000 first until both are whole numbers, then reduce.
How do I solve A : B = C : D for a missing value?
Cross multiply. Because A × D always equals B × C in a true proportion, you can rearrange for whichever term is unknown. Leave that box blank here and the answer appears with the working shown underneath.
Is a 1:4 dilution one part in four or one in five?
One part in five. A 1 : 4 ratio means one part concentrate plus four parts water, so five parts in total, and the concentrate is 20% of the mixture. This is the single most common ratio mistake.
Can this calculator handle decimals and negative numbers?
Decimals work fine — they are scaled to whole numbers before simplifying. Negative numbers will solve the proportion arithmetically, but a negative ratio rarely means anything physically, so check your inputs if you see one.
What does the 'share of total' figure mean?
It converts the ratio into a percentage of the whole. In a 3 : 4 ratio, A is 3 ÷ 7 = 42.9% of the combined total, not 75%. Use this when you need to split an amount rather than compare two amounts.