Three Modes
Simplify: divide A and B by GCD(A,B). Solve Missing: cross-multiply — if a:b = c:d and c is unknown, c = a×d/b. Scale to Total: factor = total / (A+B); Part A = A × factor, Part B = B × factor.
Frequently Asked Questions
Divide both numbers by their greatest common divisor (GCD). For example, 12:8 — GCD(12,8) = 4 — simplified to 3:2. This gives the ratio in its lowest terms.
Cross-multiply: if a/b = c/d, then a×d = b×c. Solve for the missing variable. For example, if 3:4 = x:20, then 3×20 = 4×x → x = 15.
Divide the total by the sum of the ratio parts, then multiply each part by that factor. For ratio 3:2 and total 100: sum = 5, factor = 20, parts = 60:40.
A ratio compares two quantities (A:B), while a fraction represents A out of a total (A/(A+B)). A 3:1 ratio means for every 3 parts of A there is 1 part of B. As a fraction of the total, A = 3/4. This calculator can convert between both forms.
Ratios appear everywhere: gear ratios (speed vs torque), compression ratios (engine performance), aspect ratios (structural and aerodynamic design), mixing ratios (concrete, fuels, chemicals), signal-to-noise ratios (electronics), and stress ratios (fatigue analysis).
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