Simplify a ratio, or solve for a missing value in a proportion
💡 Why This Matters Ratios and proportions come up in recipes, scale models, mixing solutions, and map reading. This tool simplifies a ratio to its cleanest form, or solves for a missing number when you know three of the four values in a proportion.
The "golden ratio" (about 1.618:1) shows up in nautilus shells, sunflower seed spirals, and pinecones — mathematicians and artists have been fascinated by it for over 2,000 years.
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A ratio compares two quantities, written A:B. Simplifying works the same way as a fraction — divide both numbers by their greatest common factor until nothing further divides evenly. Solving a proportion (A:B = C:D, with one value unknown) uses cross-multiplication: the product of the outer terms equals the product of the inner terms, so the missing value can be isolated algebraically.
A simplified ratio shows the same relationship in its smallest whole-number form — 10:15 and 2:3 describe the exact same proportion, just with smaller, easier-to-work-with numbers. A solved proportion gives you the missing quantity that keeps both sides of the equation equivalent, which is exactly what you need when scaling a recipe or converting a map distance to real distance.
This calculator works with whole-number ratios and standard two-term proportions. A ratio term of zero on the side you're simplifying, or a zero in the position needed to solve for the missing value, is mathematically undefined and will be flagged rather than silently miscalculated.
Use the Simplify mode to reduce awkward numbers (like a survey result of "45 out of 60 people") into a cleaner comparison. Use the Solve mode whenever you know a relationship should hold in the same proportion — scaling ingredients, converting model dimensions to real ones, or figuring out how much of something you need at a different scale.
Simplify example: A survey of 45 people found 30 prefer coffee to tea. As a ratio, that's 30:45. The greatest common factor of 30 and 45 is 15, so 30÷15 : 45÷15 = 2:3.
Solve example: A recipe uses a 4:6 ratio of flour to sugar. If you're scaling up and using 10 cups of flour, how much sugar? Set up 4:6 = 10:? — cross-multiply: 4 × ? = 6 × 10, so ? = 60 ÷ 4 = 15 cups of sugar.
Simplifying a ratio means dividing both numbers by their greatest common factor until no common factor remains — turning something like 10:15 into its simplest equivalent, 2:3.
Cross-multiply: if A:B = C:D and D is unknown, then A × D = B × C, so D = (B × C) ÷ A. This keeps the two ratios equivalent.
A ratio compares two separate quantities (like 3 cats to 5 dogs), while a fraction represents a part of a whole (like 3/8 of a pizza). They use the same math, but a ratio doesn't imply the two numbers add up to a total.
Yes — ratios like 2:3:5 (comparing three quantities at once) are common in recipes and mixing formulas. This calculator handles two-term ratios; for three or more terms, simplify by dividing all numbers by their shared greatest common factor.