Simplify and scale a ratio

Add a target total, and it also calculates the proportional amount assigned to every term. The result shows the original ratio, its lowest-term form, the number of simplified parts, the multiplier, and the scaled values. It works with whole numbers, zeros, and terminating decimals, making it useful for recipes, allocations, mixtures, plans, and classroom checks.

Reduce two or three terms without losing their relationship

A ratio describes relative shares, so multiplying or dividing every term by the same value leaves the relationship unchanged. The calculator first converts each supplied number into an exact integer representation. This matters when the input includes terminating decimals such as 1.5:2.25, because treating those values as approximate display text can produce an awkward answer. It then finds the greatest common divisor shared by all terms and divides each integer term by that divisor. For example, 18:24 becomes 3:4, while 6:9:15 becomes 2:3:5. Zero is allowed as an individual term because ratios such as 0:4:8 have a useful reduced form of 0:1:2. However, every term cannot be zero: 0:0 has no positive number of parts and therefore cannot be scaled. The output preserves the original numeric entries and provides both an array and a colon-separated version of the simplified ratio, so it is convenient for people and straightforward for software to consume.

Scale the simplified parts to an exact target total

After simplification, the calculator adds the reduced terms to find the total number of ratio parts. It divides the requested target total by that part count to obtain the scale factor, then multiplies each simplified term by the factor. Suppose a budget is divided in the ratio 2:3:5 and the available total is 1,000. There are ten parts, each part is worth 100, and the scaled result is 200, 300, and 500. The same method works when the result is fractional. A ratio of 1:2 scaled to a total of 10 produces 3.33333333333 and 6.66666666667 using stable output precision. The calculation is based on the simplified integers, which keeps the method transparent and avoids changing the intended proportions. A target total of zero is valid and produces zero for every scaled term. Negative totals are rejected because a share allocation with a negative target does not fit this calculator’s non-negative ratio model.

Choose valid inputs and interpret the returned fields

Provide exactly two or three finite numeric terms. Negative ratio terms always cause an input error, as do missing values, NaN, infinity, an all-zero ratio, or a list with the wrong number of entries. The target total must also be a finite, non-negative number. In the response, original_ratio repeats the accepted terms, while simplified_ratio contains the lowest whole-number form. The parts_total field is the sum of those simplified terms. The scale_factor tells you how much one simplified part is worth at the requested total, and scaled_ratio lists the final allocations in the same order as the input. Units are deliberately not attached: if the total represents grams, dollars, liters, seats, or hours, every scaled value uses that same unit. This makes the capability reusable without pretending to convert measurements. For production automation, keep the returned numeric array rather than parsing the colon-separated display string, and apply any domain-specific rounding only after deciding how remainders should be handled.