Ratio Calculator
Simplify ratios and solve for missing values.
How to Use Ratio Calculator
- 1Choose "Simplify" to reduce a ratio or "Solve" to find a missing value
- 2Enter the known values
- 3Click Calculate to get the result
About Ratio Calculator
The Ratio Calculator helps you work with ratios in two ways: simplify a given ratio to its lowest terms by dividing both parts by their greatest common divisor, or find a missing value in a proportion using cross multiplication.
For simplification, enter any two integers and get the reduced form instantly — for example, 6:4 becomes 3:2. For solving proportions, enter three known values and the calculator applies the formula D = (B x C) / A to find the fourth value.
All calculations run in your browser with no server calls, delivering instant results for cooking, recipe scaling, map reading, engineering ratios, and algebra homework.
Key Features of Ratio Calculator
- Simplify any ratio A:B to its lowest terms using the GCD
- Solve for a missing value in a proportion A:B = C:D
- Works with integers and decimal ratio values
- Shows the GCD used in simplification
- Clear step-by-step explanation of the calculation
- Supports large ratio values without precision loss
- Instant result display without page reload
- Copy result to clipboard with one click
Examples
Simplify a ratio
Reduce 12:8 to its simplest form by dividing by the GCD.
Input
12:8 (Simplify mode)
Output
3:2 (GCD = 4)
Solve a proportion
Find the missing value in the proportion 3:4 = 9:?
Input
A=3, B=4, C=9 (Solve mode)
Output
D = 12
Common Use Cases
- Scaling up or down cooking recipes to a different number of servings
- Solving proportion problems in school math and algebra homework
- Mixing paint colors or solutions in the correct proportions
- Calculating aspect ratios for screen or image resizing
- Determining map scale distances from real-world measurements
- Checking if two business metrics are proportionally related
Troubleshooting
Entering zero as one of the ratio values
Solution
A ratio value of zero is invalid because you cannot simplify or solve a proportion that contains zero in the denominator position. Use a small positive value instead.
Confusing simplify mode with solve mode
Solution
Simplify mode takes a single A:B ratio and reduces it to lowest terms. Solve mode takes three known values (A, B, C) and finds the fourth (D) using cross multiplication.
Expecting a whole-number result when values do not divide evenly
Solution
The missing value D = (B x C) / A may be a decimal if the numbers do not divide evenly. This is correct and expected behavior.
Frequently Asked Questions
How are ratios simplified?
Ratios are simplified by dividing both values by their greatest common divisor (GCD). For example, 12:8 is simplified to 3:2 because the GCD of 12 and 8 is 4.
What is cross multiplication?
Cross multiplication is used to find a missing value in a proportion. If A:B = C:D, then D = (B x C) / A. It works because a true proportion means A x D = B x C.
Can I use decimal values in a ratio?
Yes. The calculator accepts decimal values like 1.5:2.5. However, the simplified result may also be a decimal if the values do not reduce to whole numbers.
What is the difference between simplifying and solving a ratio?
Simplifying reduces a two-part ratio A:B to its lowest terms. Solving finds a missing fourth value when three values of a proportion A:B = C:D are known.
Is this the same as the Rule of Three?
Yes, the solve mode is mathematically equivalent to the Rule of Three (cross multiplication). Both find the missing value in a four-part proportion.
Can the ratio have three or more parts?
The calculator currently handles two-part ratios (A:B). For three-part ratios like 1:2:3, you can simplify each pair independently using the simplify mode.
What if my ratio is already in simplest form?
The calculator will still process it and confirm that the GCD is 1. The result will show the same ratio, confirming it cannot be simplified further.
Is my data private?
Yes. All calculations run entirely in your browser. No data is sent to or stored on any server.