Ratio Calculator
Proportion: A : B = C : D Leave exactly ONE field empty to solve for it.
This free ratio calculator simplifies ratios like 12:18 to 2:3, solves proportions with one missing value such as 4:5 = x:20, and splits any total into a given ratio with exact shares. Every answer shows step-by-step working, and the three modes cover the most common ratio problems in school math, cooking, and map scales.
What Is a Ratio Calculator?
A ratio calculator is a tool that works with ratios, which compare numbers to show how much of one thing there is for each unit of another. Writing 3:2 means that for every 3 units of the first quantity there are 2 units of the second. Recipes, paint mixes, map scales, and sports statistics all use ratios to keep relationships consistent when amounts change.
This ratio calculator handles the three most common ratio tasks: it reduces a ratio to lowest terms (18:24 becomes 3:4), it solves proportions with one unknown (4:5 = x:20), and it divides a total into ratio parts (splitting 25 in the ratio 3:2 gives shares of 15 and 10).
How to Use the Ratio Calculator
Switch between the three modes using the buttons at the top of the widget:
- Simplify a ratio. Type 2 or 3 whole-number parts separated by a colon or comma, for example 12:18 or 6,9,12, then press “Simplify Ratio”.
- Solve a proportion. Fill in three of the four fields for A:B = C:D and leave exactly one field empty, then press “Solve for Missing Value”.
- Split a total. Type the total amount and the ratio parts, for example total 25 with parts 3:2, then press “Calculate Shares”.
- Read the steps. Every answer includes numbered working.
Simplify Ratios with the Greatest Common Divisor
A ratio is in simplest form when its parts share no common factor other than 1. Find the greatest common divisor (GCD) of all the parts and divide each part by it. For 18:24, the GCD is 6, so dividing both parts by 6 gives 3:4. The same method works for three-part ratios: the GCD of 6, 9, and 12 is 3, so 6:9:12 simplifies to 2:3:4.
Simplified ratios are far easier to compare: reduce both ratios first, then compare part by part. The LCM calculator is the natural companion tool, since least common multiples and greatest common divisors are the two workhorses of fraction and ratio arithmetic. A fraction to decimal calculator handles decimal values whenever you need them.
Solve Proportions by Cross-Multiplication
A proportion states that two ratios are equal, written A:B = C:D. When one value is unknown, cross-multiply: set A times D equal to B times C and solve. For 4:5 = x:20, cross-multiplying gives 5 times x equals 4 times 20, so x equals 80 divided by 5, which is 16.
Proportions show up in everyday math. If a recipe serving 4 people uses 5 cups of flour, the flour for 20 people comes from 4:5 = x:20, giving x = 16 cups. One value must be unknown, and all known values must be positive.
Split a Total in a Given Ratio
Dividing a total by a ratio takes three quick steps. Add the ratio parts to get the total number of parts, divide the total by that count to get the value of one part, then multiply each ratio part by the value of one part. To split 25 in the ratio 3:2, there are 5 parts, each worth 25 / 5 = 5, and the shares are 3 x 5 = 15 and 2 x 5 = 10.
The method works for any number of parts. Splitting 100 in the ratio 1:2:3 means 6 parts in total, each worth 100 / 6 = 16.67, giving shares of 16.67, 33.33, and 50. Budgets, inheritances, ingredient batches, and team workloads are classic examples: settle the ratio first, then let the math assign the fair shares.
Worked Examples
Each example below matches the widget’s output exactly:
| Example | Calculation | Result |
|---|---|---|
| Simplify 18:24 | GCD of 18 and 24 is 6; divide each part by 6 | 3 : 4 |
| Simplify 12:18 | GCD of 12 and 18 is 6; divide each part by 6 | 2 : 3 |
| Simplify 6:9:12 | GCD of 6, 9, and 12 is 3; divide each part by 3 | 2 : 3 : 4 |
| Solve 4:5 = x:20 | x = 4 x 20 / 5 | x = 16 |
| Solve 4:7 = x:21 | x = 4 x 21 / 7 | x = 12 |
| Split 25 by 3:2 | 5 parts; each part = 25 / 5 = 5; shares = 15 and 10 | 15 and 10 |
| Split 100 by 1:2:3 | 6 parts; each part = 100 / 6 = 16.67; shares = 16.67, 33.33, 50 | 16.67, 33.33, and 50 |
Ratio Calculator FAQs
How do I simplify a ratio?
Divide every part by their greatest common divisor. For 18:24, the GCD is 6, so the simplified ratio is 3:4. The Simplify tab above shows the steps.
What is a proportion in math?
A proportion is an equation stating that two ratios are equal, written A:B = C:D. For example, 2:3 = 4:6 is true because both sides describe the same relationship.
How do you solve a missing value in a proportion?
Cross-multiply and divide. In 4:5 = x:20, multiply 4 by 20 to get 80, then divide by 5 to get x = 16. The Solve Proportion tab finds the answer when you leave one field empty.
How do you divide a number in a given ratio?
Add the ratio parts, divide the total by that sum to find the value of one part, then multiply. Splitting 25 in the ratio 3:2 gives 5 parts, each worth 5, for shares of 15 and 10.
Can a ratio have three numbers?
Yes, such as 6:9:12 for flour, sugar, and butter in a recipe. Divide every part by the GCD of all parts, giving 2:3:4 here.
What is the difference between a ratio and a fraction?
A ratio compares parts to each other (3:2 compares two parts directly), while a fraction compares a part to the whole (3/5 is one part out of five).