Ratio Calculator

Ratio Calculator: solve ratio problems step-by-step. Clear formula, worked example, and FAQs included.

A ratio calculator simplifies ratios to their lowest terms, solves missing values in proportions (A:B = C:D), and divides a total quantity into parts according to a given ratio. Ratios describe the relative size of two or more quantities — they appear in recipes, scale drawings, map scales, financial analysis, mixture problems, probability, and geometry. A ratio of 6:9 simplifies to 2:3 by dividing both parts by their greatest common divisor (GCD = 3). Percentage Calculator and Average Calculator provide related mathematical tools.

Simplify: Enter A and B — the calculator divides both by their GCD to give the simplest form.
Solve proportion: Enter three values in A:B = C:D — the calculator solves for D using cross-multiplication: D = (B × C) ÷ A.
Scale and divide: Enter a ratio A:B and a total — the calculator splits the total proportionally.

Ratio formulas

Simplify: A:B → (A÷GCD):(B÷GCD)

Proportion: A:B = C:D → D = (B × C) ÷ A

Divide total T in ratio A:B → Part A = T × A÷(A+B), Part B = T × B÷(A+B)

Cross-multiplication check: if A:B = C:D then A×D = B×C (the cross-products are equal).

Example: Divide $240 in ratio 3:5. Total parts = 8. Each part = $30. Part A = 3×$30 = $90. Part B = 5×$30 = $150. Check: $90+$150 = $240 ✓

Reading ratio results

Ratio types

A simplified ratio uses the smallest whole numbers that maintain the same relationship — 6:9 simplifies to 2:3 (the same ratio, just using smaller numbers). A unit ratio expresses the relationship as 1:n — e.g. 2:3 becomes 1:1.5. A percentage expresses part A as a percentage of the total — in 2:3, part A is 40% of the total. Cross-multiplication verifies a proportion: in A:B = C:D, if A×D = B×C the proportion is valid.

Math tips and best practices

To simplify a ratio with decimals, multiply both parts by 10 (or 100) to get whole numbers first, then divide by the GCD.
A map scale of 1:50,000 means 1 cm on the map = 50,000 cm (500 m) in reality — the same ratio simplification rules apply.
For recipe scaling, ratio thinking avoids errors: if a recipe uses flour:sugar in ratio 3:1, tripling the recipe keeps the same ratio.
Three-part ratios (A:B:C) divide a total into three parts: each part = Total × (that part ÷ sum of all parts).

The golden ratio φ ≈ 1.618:1 appears in art, architecture, and nature — it is the ratio where the whole is to the larger part as the larger part is to the smaller part.
A standard HD screen has an aspect ratio of 16:9 — this cannot be simplified further as GCD(16,9) = 1.
A 1:100 scale architectural drawing means every 1 cm represents 1 metre of the real structure.

Common mistakes to avoid

Confusing ratio with fraction — a ratio of 2:3 means 2 parts to 3 parts (5 parts total), not 2/3 of a whole. Part A is 2/5 (40%), not 2/3 (67%).
Not finding the GCD first when simplifying — trying to simplify 36:48 to 9:12 misses that the GCD is 12, giving the fully simplified form 3:4.
Cross-multiplying incorrectly in proportions — in A:B = C:D, the correct cross-products are A×D and B×C, not A×C and B×D.
Using different units on each side of a ratio — a ratio of 500 g : 1 kg must first be converted to the same unit (500 g : 1000 g = 1:2).

Ratio calculations are exact mathematical operations for the inputs provided. In regulated contexts — pharmaceutical compounding, construction specifications, food labelling, financial ratio disclosures — always verify ratio calculations against authoritative specifications and applicable standards. Map scale ratios and engineering scale drawings are subject to professional standards and should be verified by a licensed surveyor or engineer before use in construction or navigation.