Ratio Calculator
Three ratio jobs in one card: find the missing value in a proportion A:B = C:D (leave the unknown blank), simplify any ratio to lowest terms with its fraction and percentage readings, or scale a ratio up and down for recipes, models, and screens.
Reading a ratio three ways
A ratio like 2:3 says “for every 2 of the first thing there are 3 of the second.” The same relationship can be read as the fraction 2/3 (the first is two-thirds of the second) or as shares of a whole (the first is 40% of the total, the second 60%). Equivalent ratios come from multiplying or dividing both sides by the same number, which is why 16:9, 1280:720, and 1920:1080 are all the same shape of screen.
How it’s calculated
Proportions solve by cross-multiplication (A×D = B×C). Simplification multiplies decimal entries up to whole numbers, then divides both sides by their GCF from Euclid’s algorithm. Scaling multiplies or divides both terms by your factor. Fraction reading = A/B; share reading = A/(A+B) and B/(A+B).
Both ratio terms must be positive numbers; results display to 6 significant digits where they are not exact.
Worked example
3 : 4 = x : 20 — cross-multiply: x = 3 × 20 ÷ 4 = 15. Simplifying 12:18: the GCF is 6, giving 2 : 3, which reads as the fraction 2/3 ≈ 0.667 and as shares 40% / 60%. Scaling 16:9 by 120 gives 1920 : 1080 — full HD.
Common mistakes
- Adding the same number to both sides — ratios scale by multiplication, never by addition (2:3 is not 3:4).
- Reading A:B as “A percent of the total” — A’s share of the whole is A÷(A+B), not A÷B.
- Cross-multiplying the wrong diagonal when solving proportions.
- Flipping the order: a 4:3 photo and a 3:4 photo are different orientations.
Where it is used
- Cooking and baking: scaling ingredient ratios up or down.
- Screens, photos, and video: aspect ratios like 16:9 and 4:3.
- Maps, models, and blueprints: scale factors.
- Mixing: paint, mortar, fuel, and fertilizer ratios.
Frequently asked questions
How do I solve a proportion like 3:4 = x:20?
Cross-multiply: in A:B = C:D the products A×D and B×C are equal. So x = 3×20 ÷ 4 = 15. Leave the unknown box empty and the calculator applies exactly that cross-multiplication for whichever position is missing.
How do I simplify a ratio?
Divide both sides by their greatest common factor: 12:18 has a GCF of 6, so it simplifies to 2:3. Ratios with decimals are first multiplied up to whole numbers (2.5:1.5 → 25:15 → 5:3) before reducing.
How does a ratio become a fraction or percentage?
A:B corresponds to the fraction A/B (12:18 = 2/3 ≈ 0.667). As shares of the whole, A takes A÷(A+B) — for 12:18 that is 40% versus 60%. Both readings are shown so you can pick the one your problem means.
How do I scale a ratio up or down?
Multiply (or divide) both sides by the same factor — the ratio stays equivalent. A 16:9 frame scaled by 120 becomes 1920:1080, which is exactly how screen resolutions preserve their aspect ratio.
Can a ratio have more than two parts?
Yes — mix ratios like 1:2:3 work the same way: scale all parts by the same factor and reduce by the GCF of all parts. This tool focuses on two-part ratios; for three-part mixes, simplify pairs against their common GCF by hand or scale each part equally.