Ratio Calculator
Simplify multi-part ratios, solve unknown variables in proportions, and divide quantities using custom ratio splits.
Separate up to 10 positive numbers with colons, commas, or spaces.
2 : 3 : 5
12 : 18 : 30
Segment Percentage Weights
Proportions, Aspect Ratios, and Simplification
A ratio is a relationship between two or more quantities showing how many times one value contains another. Ratios can represent dimensional proportions, mixture recipe parts, or financial allocations.
1. Simplifying Ratios
Simplifying a ratio (such as 12:18:30) requires identifying the Greatest Common Divisor (GCD) of all numbers in the set. Dividing each term by the GCD (6 in this case) yields the simplest integers: 2:3:5.
2. Solving Proportions (A:B = C:D)
A proportionstatement equates two ratios: A / B = C / D. By cross-multiplying, we can isolate any single unknown variable (x). For example, solving for D gives: D = (B · C) / A.
3. Quantity Splitting (Distribution)
Splitting a total quantity W according to ratio parts [r1, r2, ... rn] requires finding the sum of all ratio weights S. The individual share of group i is: Wi = W × (ri / S).
Frequently Asked Questions About Ratios
How do you simplify a ratio?
To simplify a ratio, find the Greatest Common Divisor (GCD) of all numbers in the ratio, and then divide each number by that divisor. For example, the ratio 12:18:30 has a GCD of 6. Dividing each part by 6 gives the simplified ratio 2:3:5.
What is a proportion solver?
A proportion solver finds the value of a single missing variable when two ratios are equal (e.g., A/B = C/D). By using cross-multiplication, the solver solves for the missing parameter.
How is a sum divided by a specific ratio?
To split a sum by a ratio, sum the parts of the ratio to get the total parts. Divide the total sum by this number of parts to find the value of a single part, then multiply by each individual ratio factor.
Can this simplify ratios and solve proportions?
Yes. Simplify multi-part ratios, solve for missing values, and divide totals into shares.