Ratio Calculator

These three ideas are closely related but not identical. A ratio compares quantities of the same kind — 3 cups of flour to 2 cups of sugar is 3 : 2. A fraction expresses one part relative to a whole — flour is 3/5 of the dry mix. A rate compares quantities measured in different units and keeps those units — 60 miles per hour, or $4 per pound. The Ratio Calculator moves fluidly between the ratio and fraction views: the ratio 16 : 9 is the same as the fraction 16/9, the decimal 1.778, and the percentage 177.8%. The part-of-whole breakdown converts each term into its share of the total, which is what you want when dividing something up rather than comparing two sides.

Order always matters. The ratio 2 : 3 is different from 3 : 2, just as the fraction 2/3 is different from 3/2. When you read a ratio aloud as “A to B,” keep the same order in your math.

A proportion says two ratios are equal: A : B = C : D. Whenever three of the four values are known, the fourth is fixed. The reliable way to find it is cross-multiplication: because A/B = C/D, multiplying diagonally gives A × D = B × C. Rearranging isolates whichever term is missing — for the last term, D = (B × C) / A. This single technique powers an enormous range of practical problems: scaling a recipe up from 4 servings to 10, converting between map distance and real distance, resizing an image while keeping its aspect ratio, and currency or unit conversions. In this calculator you simply leave one box blank and the missing value appears, with the full cross-multiplication shown under “Show working.”

The only thing that can go wrong is dividing by zero, which happens when the term you would divide by is zero. The calculator flags that case instead of returning a misleading number.

Simplifying reduces a ratio to its smallest whole-number form by dividing every term by their greatest common factor. 1920 : 1080 shares a GCF of 120, so it reduces to 16 : 9 — the same shape expressed in the smallest numbers. Decimal ratios such as 0.5 : 2 are first scaled up to whole numbers (5 : 20) and then reduced (1 : 4). Scaling keeps a ratio's proportions while changing its size: multiply every term by a factor, or fix one side to a new value and let the calculator find the other. Splitting goes the other way — you start with a total and a ratio, and the calculator divides the total into parts that add back up exactly. Splitting $3,000 in 50 : 30 : 20 yields $1,500, $900, and $600. Because the method is based on each part's fraction of the whole, the shares never drift or fail to sum to the original total, even with three or more parts or with awkward decimal ratios.