Math Tools
Ratio Calculator
Simplify ratios or solve proportions with a clean algebraic engine.
A:B ratio
Enter two whole numbers or decimals. The tool will reduce the ratio to its simplest form.
Simplified Ratio
2:3
8:12 simplified via GCD of 4
Math Tools
Simplify ratios or solve proportions with a clean algebraic engine.
A:B ratio
Enter two whole numbers or decimals. The tool will reduce the ratio to its simplest form.
Simplified Ratio
2:3
8:12 simplified via GCD of 4
A ratio is a way of comparing two or more quantities to show their relative sizes. For example, a 2:1 ratio means for every 2 units of the first quantity, there is 1 unit of the second. A ratio calculator automates simplification (reducing to lowest terms), scaling (enlarging or shrinking proportionally), and equivalence checks—operations that would otherwise require manual arithmetic or finding the greatest common divisor.
The calculator accepts two or more numbers and finds their greatest common divisor (GCD) to reduce the ratio to its simplest form. For scaling, it multiplies all parts by a factor you specify. For comparison, it converts ratios to decimal form or finds a common denominator to check if they're equivalent. The tool handles whole numbers, decimals, and fractions, making it versatile for cooking, design, finance, and mathematics.
Simplified ratio = a:b ÷ GCD(a,b) | Scaled ratio = (a × k):(b × k) | Equivalent check: a/b = c/dGCD is the largest number dividing all parts evenly. k is the scaling factor (multiplier). Equivalent ratios have equal cross-products: a × d = b × c.
| Input | Result | Notes |
|---|---|---|
| Simplify 12:18 | 2:3 | GCD of 12 and 18 is 6; dividing both by 6 gives the simplest form |
| Scale 3:4 by a factor of 5 | 15:20 | Multiply each part by 5; useful for enlarging recipes or mixing ratios |
| Compare 4:6 and 2:3 | Equivalent | Both simplify to 2:3; cross-multiplication confirms: 4×3 = 6×2 |
A ratio compares two separate quantities (e.g. 3 boys to 5 girls = 3:5), while a fraction represents a part of a whole (e.g. 3/8 means 3 parts of 8 total). You can convert a ratio to a fraction by using one part as the numerator and the total as the denominator.
No. 7 and 11 are coprime (their GCD is 1), so 7:11 is already in simplest form. Not all ratios can be reduced further.
Enter the original ingredient amounts as a ratio, enter your scaling factor (e.g. 2 to double, 0.5 to halve), and the calculator multiplies all ingredients proportionally. This ensures your recipe tastes correct at any serving size.
Yes. Enter all three values and the calculator will simplify them together. For example, 6:9:12 simplifies to 2:3:4 by dividing each part by their GCD (3).
This happens when the original numbers don't share a common factor. For example, 5:8 stays 5:8 because 5 and 8 are coprime. Some ratios naturally include decimals or fractions when scaled.
A ratio is a comparison of two quantities (3:4); a proportion is an equation stating that two ratios are equal (3:4 = 6:8). Use the comparison feature to verify if two ratios form a valid proportion.