Ratio Calculator
Simplify a Ratio A : B
Scale a Ratio (A : B = ? : D)
Divide a Value in Ratio A : B
About this calculator
Simplify a ratio such as 12 : 18 to 2 : 3, scale a ratio to a new size, or split a total into parts in a given ratio. The three blocks cover the most common ratio tasks in one place.
Use it for recipes, maps and model scales, mixing paint or concrete, sharing profits between partners and aspect ratios.
How to use it
- To simplify, enter A and B.
- To scale, enter the ratio A : B and a new C. The tool gives D.
- To divide a total, enter the Total and the parts A and B.
Formulas
Simplify by dividing both terms by their GCD. Scale with D = C × B ÷ A. Divide a total T in the ratio a : b with part A = T × a ÷ (a + b) and part B = T × b ÷ (a + b).
Worked example
Examples
| Simplify 12 : 18 | 2 : 3 |
| Scale 3 : 4 to 9 : ? | 12 |
| Split 1,000 in 3 : 2 | 600 and 400 |
| Mix 1 : 4 cement to sand for 50 kg | 10 kg and 40 kg |
Tips and common mistakes
- A ratio has no units. Keep both terms in the same unit before simplifying.
- Check by adding the parts: 3 + 2 = 5 parts, and 600 + 400 = 1,000.
- Write the order carefully: A : B is not the same as B : A.
- For three-way splits, extend the same method with a + b + c.
- Convert decimals to whole numbers before simplifying, for example 1.5 : 2 becomes 3 : 4.
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common divisor.
How do I divide an amount in a ratio?
Add the parts, divide the total by that sum and multiply by each part.
What is a ratio of 2 : 3 as a fraction?
The first term is 2/5 of the total.
How do I scale a recipe with a ratio?
Multiply every ingredient by the same factor.
Can a ratio have more than two terms?
Yes, such as 2 : 3 : 5.
What is the difference between ratio and proportion?
A ratio compares two quantities. A proportion says two ratios are equal.