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Simplify ratios to lowest terms using GCD and solve proportions like a:b = c:x for any missing value — useful for recipes, map scales, aspect ratios, and mixing ingredients.
Math
Generated on May 23, 2026
Enter three values and leave one blank to solve for the missing number. Or enter A and B to simplify the ratio.
Simplify ratios to lowest terms using GCD and solve proportions like a:b = c:x for any missing value — useful for recipes, map scales, aspect ratios, and mixing ingredients.
A ratio calculator simplifies ratios to their lowest terms (for example, 12:18 becomes 2:3) and solves proportions where one value is unknown (for example, 3:4 = x:12 gives x = 9). Ratios compare two quantities of the same kind — ingredients in a recipe, sides of a rectangle, parts of a mixture, or cost per unit — and are fundamental in cooking, map reading, finance, chemistry, construction, and design. Proportions extend ratios to equality between two ratios, a tool used for scaling drawings, converting recipes, and solving many everyday 'same rate' problems.
Formula
Simplify: divide both parts by GCD(a, b). Solve a:b = c:d via cross-multiplication: a × d = b × c, then isolate the unknown.You're tripling a biryani recipe for a wedding and the original called for 2 cups rice to 3 cups water — what's it now? Or you're a contractor pricing a mortar mix at 1:4 cement to sand and need 50 bags of sand worth of cement. Or maybe you're sizing a photo at 16:9 to fit a 1920-pixel-wide YouTube thumbnail and need the exact pixel height. These are all the same problem: ratios that need to simplify or proportions that need to solve for one missing piece. Cross-multiplication is the entire toolkit — a/b equals c/d means a times d equals b times c — and from that one identity flows recipe scaling, map reading, currency exchange, scale drawings, paint mixing, and aspect ratio math. Where people get tripped up: misreading what '1:4' means in a particular context. In a recipe it usually means '1 part to 4 parts plus the 1' for 5 total. In chemistry it might mean '1 part concentrate in 4 parts total solution' (so 3 parts solvent). The math doesn't change but the answer does. Read the notation before plugging numbers in. This tool simplifies any ratio to lowest terms using GCD and solves any a:b = c:x for the unknown — useful enough to keep open in a tab if you cook, build, or design.
A ratio calculator simplifies ratios to their lowest terms (for example, 12:18 becomes 2:3) and solves proportions where one value is unknown (for example, 3:4 = x:12 gives x = 9). Ratios compare two quantities of the same kind — ingredients in a recipe, sides of a rectangle, parts of a mixture, or cost per unit — and are fundamental in cooking, map reading, finance, chemistry, construction, and design. Proportions extend ratios to equality between two ratios, a tool used for scaling drawings, converting recipes, and solving many everyday 'same rate' problems.
Dividing both parts of a ratio by their greatest common divisor (GCD) reduces it to its simplest form without changing the underlying relationship — the simplified ratio describes the same proportion, just using smaller numbers. Cross-multiplication works because equal ratios have equal cross-products — it turns the proportion into a linear equation, which is easy to solve for any single unknown term.
Widely-used aspect ratios (width:height) for displays, photography, and video production.
| Ratio | Decimal | Example Use | Sample Resolution |
|---|---|---|---|
| 1:1 | 1.00 | Instagram post, square photo | 1080×1080 |
| 4:3 | 1.33 | Older TVs, iPad | 1024×768 |
| 3:2 | 1.50 | DSLR full-frame photos | 6000×4000 |
| 16:10 | 1.60 | MacBook, business laptops | 1920×1200 |
| 5:3 | 1.67 | Older widescreen | 1280×768 |
| 16:9 | 1.78 | HDTV, YouTube, modern laptops | 1920×1080 |
| 1.85:1 | 1.85 | Cinema standard | — |
| 9:16 | 0.56 | TikTok, Instagram Stories | 1080×1920 |
| 21:9 | 2.33 | Ultrawide monitors | 3440×1440 |
Concrete mortar mix 1:4 = 1 part cement to 4 parts sand — the standard for brick-laying.
Film stock 35mm cinema: 1.85:1 for standard projections, 2.39:1 for anamorphic widescreen.
Golden ratio (1:1.618) is frequently called the 'most aesthetic ratio' in art and design.
Screen resolution stays sharp only if the aspect ratio of the image matches the display's aspect ratio.
12:18 simplifies to 2:3 (GCD = 6) — useful when presenting mixing ratios or recipe proportions cleanly.
Recipe scaling: if 2 cups of flour are used per egg and you have 3 eggs, solving 2:1 = x:3 gives x = 6 cups.
Map scale 1:50,000 means 1 cm on the map equals 50,000 cm (500 m) in reality — the basis of all topographic navigation.
Dilution 1:10 usually means 1 part concentrate per 10 total parts (or sometimes 1 part concentrate plus 10 parts solvent — always confirm notation).
Mortar mix 1:4 for standard bricklaying means 1 part cement to 4 parts sand, the most common proportion in residential construction.
Paint tinting: achieving a specific color may require mixing 3 parts base with 1 part tint — a 3:1 ratio for consistent results.
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