A ratio calculator helps simplify ratios, solve equivalent ratios, compare proportional relationships, and convert ratios into other useful forms.
✔ Simplify two- or three-number ratios
✔ Solve missing values and equivalent ratios
✔ Convert ratios to fraction, decimal, percentage, and 1:n / n:1 forms
How to Use the Ratio Calculator
- Choose the ratio calculation that matches your problem.
- Enter the known values in the labeled fields.
- Select Calculate to see the result and step-by-step working.
Press Enter while typing to calculate quickly. Use Copy Result to copy the complete calculation.
What Is a Ratio?
A ratio compares the relative size of two or more quantities. For example, 6:9 compares 6 parts with 9 parts and simplifies to 2:3.
Ratios can be written as 2:3, 2/3, or 2 to 3. The order matters: 2:3 and 3:2 describe different relationships.
How to Simplify a Ratio
To simplify a whole-number ratio, find the greatest common divisor (GCD), also called the greatest common factor (GCF), of all terms and divide every term by it.
Example: 24:36 → GCD = 12 → 24 ÷ 12 : 36 ÷ 12 = 2:3
Simplifying Decimal Ratios
Decimal ratios should first be converted to whole-number form by multiplying every term by the same power of 10. For example:
0.5:1.5
Multiply both terms by 10 → 5:15
GCD of 5 and 15 = 5
5 ÷ 5 : 15 ÷ 5 = 1:3
Simplifying Three-Number Ratios
The same method works for three values. Find a common divisor shared by all three terms.
2:6:4
GCD = 2
2 ÷ 2 : 6 ÷ 2 : 4 ÷ 2 = 1:3:2
Equivalent Ratios and Scaling
Equivalent ratios describe the same proportional relationship. You can create an equivalent ratio by multiplying or dividing every term by the same non-zero value.
3:5 scaled by 4
3 × 4 : 5 × 4 = 12:20
How to Find a Missing Ratio Value
When two ratios are equal, they form a proportion. You can solve for a missing term with cross multiplication.
A:B = C:D → A × D = B × C
2:3 = x:9
2 × 9 = 3x
18 = 3x
x = 6
Ratio vs Proportion
A ratio compares quantities, such as 2:3. A proportion states that two ratios are equal, such as 2:3 = 4:6. Proportions are commonly used to solve missing values and scale relationships.
For a dedicated equality-of-ratios tool, use the Proportion Calculator.
Convert a Ratio to Fraction, Decimal or Percentage
For a two-term ratio A:B, the first term compared with the second can be written as:
- Fraction: A/B
- Decimal: A ÷ B
- Percentage: (A ÷ B) × 100%
A ratio can also be normalized to 1:n or n:1. For example, 2:3 is approximately 1:1.5 and 0.6667:1.
For additional conversions, use the Percentage Calculator or Fraction to Decimal Converter.
Common Ratio Mistakes
Reversing the order: 2:3 and 3:2 describe different relationships.
Stopping before the ratio is fully simplified: 12:8 → 6:4 is reduced, but the simplest form is 3:2.
Using different units: Convert quantities to the same unit before comparing them as a ratio.
Confusing part-to-part with part-to-whole: If a group contains 3 girls and 5 boys, girls-to-boys is 3:5, while girls as a fraction of the full group is 3/8.
Worked Ratio Examples
Example 1: Simplify 18:24
GCD = 6
18 ÷ 6 = 3
24 ÷ 6 = 4
Result: 3:4
Example 2: Compare 2:3 and 4:6
2 × 6 = 12
3 × 4 = 12
The ratios are equivalent.
Example 3: Recipe Ratio
A recipe uses flour and water in a 3:1 ratio. Scaling both terms by 2 gives 6:2, which keeps the same relationship.
Example 4: Three-Term Mix
Concrete mix 2:4:6 simplifies by GCD 2.
Result: 1:2:3
How to Verify a Ratio Result
You can verify equivalent ratios with cross multiplication. For example, 24:36 = 2:3 because:
24 × 3 = 72 and 36 × 2 = 72
Frequently Asked Questions
Yes. Decimal terms are first converted to whole-number form by multiplying every term by the same power of 10, then simplified using the GCD.
Yes. Ratios such as 2:6:4 compare three values. This calculator can simplify a three-term ratio by finding the common divisor of all three terms.
Use the Solve Missing Value mode. Enter three known terms in A:B = C:D and leave exactly one field blank. The calculator solves the missing value with cross multiplication.
Compare their cross products. If A × D equals B × C for A:B and C:D, the ratios are equivalent.
A ratio compares quantities. A proportion states that two ratios are equal.
Yes in some contexts, such as 0:5. However, 0:0 does not define a meaningful ratio, and a second term of 0 cannot be converted into a finite decimal or percentage.
They are closely related, but context matters. A ratio often compares one quantity with another, while a fraction commonly represents a part of a whole.
Calculation Method
How we calculate: Decimal ratio terms are normalized to whole-number form when required, then simplified using their greatest common divisor. Equivalent ratios and missing values use standard proportional relationships and cross multiplication.
Need a related calculation? Try the Proportion Calculator, Percentage Calculator, or Fraction to Decimal Converter.
