⚖️ Ratio Calculator
If 3 : 4 = 9 : x, then x = 12 — solved exactly by cross-multiplication, with fractions kept as fractions. Plus one-click ratio simplification (48 : 36 = 4 : 3).
Working (cross-multiplication)
x = (4 × 9) ÷ 3 = 12
Exact rational arithmetic — 2 : 3 = 5 : x gives x = 15/2, not 7.4999…. Recipes, map scales, aspect ratios, mixing. Runs locally.
How the ratio calculator works
The solver treats a : b = c : x as the equation a/b = c/x and cross-multiplies: x = b×c ÷ a, computed in exact rational arithmetic so the answer comes back as a fraction when it is one (2 : 3 = 5 : x gives x = 15/2, displayed with its decimal). The simplifier divides both sides of a ratio by their greatest common divisor to reach lowest terms. Inputs accept integers, decimals and fractions, so "1.5 : 2.25" and "3/4 : 9/8" both work.
Ratios are the arithmetic of scaling: recipes (3 cups flour to 4 of water, how much for 9 cups flour?), map scales, screen aspect ratios (1920 : 1080 simplifies to 16 : 9 — try it), paint mixing, gear ratios. The classic error is scaling one side and eyeballing the other; cross-multiplication is the two-line method that never misses, and the tool shows it for your numbers.
Frequently asked questions
How do I solve a proportion like 3 : 4 = 9 : x?
Cross-multiply: 3x = 4 × 9, so x = 36/3 = 12. The tool does exactly this and shows the line of working — with exact fractions when the answer isn't whole.
How do I simplify a ratio?
Divide both parts by their greatest common divisor. 48 : 36 → both divide by 12 → 4 : 3. Switch to the "Simplify" tab and it happens instantly.
Why is 1920 : 1080 the same as 16 : 9?
Because both parts share the factor 120: 1920÷120 = 16 and 1080÷120 = 9. That's what "same aspect ratio" means — the simplified ratios match.
Can ratios contain decimals or fractions?
Yes — every input is converted to an exact rational first, so 1.5 : 2.25 solves precisely (it's 2 : 3), with no floating-point residue.
Is anything uploaded?
No — the math runs locally and offline.