Ratio Calculator
Solve unknowns, simplify ratios, and split amounts by ratio
How to calculate ratios: solve, simplify, and distribute
A ratio describes an equal relationship between two quantities and is commonly used for recipes, proportions, and allocation problems. Terms are separated by colons, and knowing any three terms of a proportion is enough to find the fourth.
This tool provides three modes: solve a ratio, simplify a ratio, and split a total by ratio. After entering the values, click Calculate to see the complete ratio and simplified result. Everything is calculated locally in your browser, and your input is never uploaded.
What is the basic principle for solving a ratio?
The proportion A : B = C : D is equivalent to A × D = B × C, known as the cross-product property. Therefore, any three known terms can be used to find the fourth. For example, 2 : 5 = 8 : ? gives 20 because 5 × 8 ÷ 2 = 20. The calculator applies the correct formula according to the selected unknown, clears and disables the unknown field automatically.
How do you simplify a ratio?
Divide every term by the greatest common divisor. For example, 10 : 25 becomes 2 : 5, while 2 : 4 : 6 becomes 1 : 2 : 3. Simplification does not change the ratio itself; it only reduces the size of its terms. This is useful for recipes, bills of materials, and image dimensions.
How do you split an amount by ratio?
First add all ratio terms to get the total number of parts. Divide the total amount by that number to find the value of one part, then multiply by each ratio term. For example, splitting 1000 by 2 : 3 : 5 gives 10 total parts, so the results are 200, 300, and 500. The result is displayed as a table with each share and its corresponding amount.
Can ratio terms contain decimals?
Yes. For example, 0.5 : 1.5 is scaled to 5 : 15 and then simplified to 1 : 3. No ratio term can be zero because a ratio represents a multiplicative relationship. The calculator shows a clear error instead of returning a meaningless result.
How are three-term and four-term ratios used?
Three-term ratios are often used to divide a total into three shares, while four-term ratios are common in recipes and proportional tables. The simplify mode supports two to four terms separated by colons. For more terms, you can calculate in stages or first determine the total number of parts.
Can the results be used directly?
The ratio equation and allocation details can be copied directly. To convert a ratio into percentages, divide each term by the sum of all terms and multiply by 100, or use the percentage calculator. For fractional values, you can use the fraction calculator.
How do you use a ratio calculator? Three modes for solving and distributing ratios
- Solve for an unknown term in A : B = C : D by entering any three values, for example 2 : 5 = 8 : ? gives 20
- Solve proportions using the cross-product property A × D = B × C, with the selected unknown field cleared and disabled automatically
- Simplify ratios by dividing all terms by their greatest common divisor, such as 10:25 to 2:5 and 2:4:6 to 1:2:3
- Split a total according to a ratio, such as 1000 divided by 2:3:5 into 200, 300, and 500
- Support two to four ratio terms and decimal values, with 0.5:1.5 simplified to 1:3
- All calculations run locally in the browser, input is never uploaded, and results can be copied with one click