Ratio Calculator | Convert Between Ratios, Fractions & Percentages

While ratios and fractions can both be written using similar notation (e.g., 3/4), they represent different concepts. A fraction represents a part of a whole—3/4 means 3 parts out of a total of 4 parts, or 75% of something. A ratio compares quantities that may be unrelated—3:4 means there are 3 units of one thing for every 4 units of another thing. Fractions must always sum to a whole (numerator is part of the denominator), while ratio terms are independent quantities being compared. For example, a room with 15 men and 20 women has a men-to-women ratio of 3:4 (simplified from 15:20), but men aren't a fraction of women—they're separate counts being compared.

To find a missing value in a proportion such as a:b = c:x, use cross multiplication: a × x = b × c, then solve for x by dividing both sides by a: x = (b × c) ÷ a. For example, if 2:5 = x:20, then 2 × 20 = 5 × x, so 40 = 5x, and x = 8. This works because in equal ratios, the product of the means equals the product of the extremes. This method applies to any proportion problem, including scale conversions, recipe adjustments, or finding unknown quantities that must maintain a specific relationship with known quantities.

To simplify a ratio, find the greatest common divisor (GCD) of all terms and divide each term by this value. For example, to simplify 24:36:60, first find the GCD (12) and divide each term: 24÷12 : 36÷12 : 60÷12 = 2:3:5. For non-integer ratios like 2.5:3.75, multiply all terms by a power of 10 to get integers (25:37.5, then 250:375), find the GCD (125), and simplify (2:3). For mixed units, convert to the same unit first—e.g., 1 foot : 9 inches becomes 12 inches : 9 inches, which simplifies to 4:3. Always verify your simplified ratio by checking whether multiplying by the same factor recovers the original values.