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Simplify a ratio and solve proportions like a:b = c:x for the missing value.
Simplify a ratio and solve proportions like a:b = c:x for the missing value.
Enter values above and click Calculate — results will appear here with the formula explained.
A ratio compares two quantities. Simplifying divides both terms by their greatest common divisor, producing the smallest whole-number pair with the same relationship — 16:10 simplifies to 8:5.
Ratios are also used to scale quantities. If you know a:b, scaling a up to some new value c requires scaling b by the same factor: x = c × b ÷ a. This cross-multiplication trick is the basis for recipes, map scales, aspect ratios and mixing instructions.
Part-to-part versus part-to-whole trips beginners: 3:2 describes the mix, while 3/5 and 2/5 describe each share of the total. Paint mixing, concrete (1:2:3 cement:sand:gravel) and financial splits all need the conversion step — divide each term by the sum to move between the two views.
Ratios scale unit prices instantly: $24 for 16 oz is $1.50/oz, so 10 oz costs $15 at the same ratio. Grocery 'which size is cheaper' decisions are ratio problems in disguise — compute per-unit on both sizes rather than trusting package claims.
Map and model scales are ratios with units attached: 1:50,000 means 1 cm represents 500 m, and scale-model 1:18 divides every real dimension by 18. Aspect ratios (16:9, 4:3, 3:2) govern screens and photos the same way — scaling one side requires the proportional other, which this calculator's third field solves directly.
Three-term ratios extend the pattern (a:b:c) for recipes and allocations: divide each by their GCD jointly, and scale by matching any single term. Gear ratios, dilution series and cocktail specs all live here — cross-multiplication generalizes to x = c × b ÷ a per paired term.
Simplify a ratio and solve proportions like a:b = c:x for the missing value. Formula: a : b = c : x ⟹ x = (c × b) ÷ a. Example: A recipe uses sugar and flour in a 16:10 ratio, simplifying to 8:5.
A ratio compares two quantities. Simplifying divides both terms by their greatest common divisor, producing the smallest whole-number pair with the same relationship — 16:10 simplifies to 8:5.
Ratios are also used to scale quantities. If you know a:b, scaling a up to some new value c requires scaling b by the same factor: x = c × b ÷ a. This cross-multiplication trick is the basis for recipes, map scales, aspect ratios and mixing instructions.
Part-to-part versus part-to-whole trips beginners: 3:2 describes the mix, while 3/5 and 2/5 describe each share of the total. Paint mixing, concrete (1:2:3 cement:sand:gravel) and financial splits all need the conversion step — divide each term by the sum to move between the two views.
Ratios scale unit prices instantly: $24 for 16 oz is $1.50/oz, so 10 oz costs $15 at the same ratio. Grocery 'which size is cheaper' decisions are ratio problems in disguise — compute per-unit on both sizes rather than trusting package claims.
Map and model scales are ratios with units attached: 1:50,000 means 1 cm represents 500 m, and scale-model 1:18 divides every real dimension by 18. Aspect ratios (16:9, 4:3, 3:2) govern screens and photos the same way — scaling one side requires the proportional other, which this calculator's third field solves directly.
Three-term ratios extend the pattern (a:b:c) for recipes and allocations: divide each by their GCD jointly, and scale by matching any single term. Gear ratios, dilution series and cocktail specs all live here — cross-multiplication generalizes to x = c × b ÷ a per paired term.
A recipe uses sugar and flour in a 16:10 ratio, simplifying to 8:5. If you use 24 cups of sugar, the flour needed is 24 × 10 ÷ 16 = 15 cups. As shares: 8/13 ≈ 62% sugar-side to 5/13 ≈ 38% — the same ratio wearing part-to-whole clothes.
Formulas are standard public references (see our methodology). External standards are cited in the text where they apply.
Last reviewed: September 2026 · Report an error