Ratio Calculator – Simplify & Compare Ratios Online
Ratio Calculator
Simplify ratios, compare two ratios, and see the calculation steps.
Calculation Result
What Is a Ratio?
A ratio is a way to compare two quantities. It shows how much of one quantity there is in relation to another quantity. Ratios are commonly written using a colon, such as 2:3.
For example, if a classroom has 10 students wearing blue shirts and 15 students wearing white shirts, the ratio of blue shirts to white shirts is 10:15. This ratio can be simplified to 2:3.
How to Use the Ratio Calculator
This free Ratio Calculator has two main modes: Simplify Ratio and Compare Ratios.
Simplify Ratio
- Select Simplify Ratio.
- Enter the first number.
- Enter the second number.
- Select Simplify Ratio.
- The calculator finds the greatest common factor and shows the simplified ratio with steps.
Compare Ratios
- Select Compare Ratios.
- Enter the two numbers for Ratio 1.
- Enter the two numbers for Ratio 2.
- Select Compare Ratios.
- The calculator uses cross multiplication to determine whether the ratios are equivalent.
How to Simplify a Ratio
To simplify a ratio, divide both parts of the ratio by their greatest common factor, also called the GCF.
The GCF of 12 and 18 is 6.
12 ÷ 6 = 2
18 ÷ 6 = 3
Therefore: 12:18 = 2:3
How to Compare Two Ratios
One common way to compare two ratios is cross multiplication. Suppose you want to compare:
Multiply the first number of the first ratio by the second number of the second ratio. Then multiply the second number of the first ratio by the first number of the second ratio.
First cross product: 2 × 6 = 12
Second cross product: 3 × 4 = 12
Because both products are equal, the ratios are equivalent.
2:3 = 4:6
Ratio Formula
A ratio can be written as:
It can also be represented as a fraction:
For example, the ratio 3:5 can be represented as the fraction 3/5. The two forms describe the same relationship.
Ratio Examples
| Original Ratio | GCF | Simplified Ratio |
|---|---|---|
| 4:8 | 4 | 1:2 |
| 6:9 | 3 | 2:3 |
| 10:15 | 5 | 2:3 |
| 12:18 | 6 | 2:3 |
| 20:30 | 10 | 2:3 |
Common Ratio Mistakes
1. Dividing Only One Number
When simplifying a ratio, both numbers must be divided by the same factor. Dividing only one side changes the relationship.
2. Reversing the Order
The order of a ratio matters. For example, 2:3 is not the same relationship as 3:2.
3. Comparing Numbers Directly
When comparing ratios, simply comparing the individual numbers can be misleading. Cross multiplication or another equivalent comparison method should be used.
4. Using Different Scale Factors
Equivalent ratios must maintain the same relationship between their corresponding parts.
Frequently Asked Questions
What does a ratio mean?
A ratio compares two quantities and describes their relative relationship. For example, 2:3 means 2 parts compared with 3 parts.
How do I simplify a ratio?
Divide both parts of the ratio by their greatest common factor. For example, 12:18 becomes 2:3 after dividing both numbers by 6.
How do I compare two ratios?
You can compare A:B and C:D using cross multiplication. Compare A × D with B × C.
Are 2:3 and 4:6 equivalent ratios?
Yes. Both ratios simplify to 2:3, so they represent the same relationship.
Can a ratio contain decimals?
Yes. This calculator accepts decimal values. For best results, use values that can be represented accurately by your device.
Can a ratio contain zero?
A ratio can contain zero in some mathematical contexts, but a comparison involving division by zero is undefined. This calculator therefore requires both ratio denominators used in a comparison to be nonzero.