Ratio Calculator
Solve for a missing ratio value, simplify ratios, or compare two ratios for equivalence. Works with integers and decimals.
Enter 3 values. Leave one blank to solve for it. A and B cannot both be blank.
Ratio Reference Table
The ratio reference table shows common ratio pairs, their simplified form, and their decimal equivalents for quick lookup.
| Ratio | Simplified | Decimal (A/B) | Percentage |
|---|---|---|---|
| 1:1 | 1:1 | 1.0000 | 100% |
| 1:2 | 1:2 | 0.5000 | 50% |
| 2:3 | 2:3 | 0.6667 | 66.67% |
| 3:4 | 3:4 | 0.7500 | 75% |
| 4:5 | 4:5 | 0.8000 | 80% |
| 16:9 | 16:9 | 1.7778 | 177.78% |
| 4:3 | 4:3 | 1.3333 | 133.33% |
| 12:8 | 3:2 | 1.5000 | 150% |
| 25:100 | 1:4 | 0.2500 | 25% |
| 1:3 | 1:3 | 0.3333 | 33.33% |
How to Solve a Ratio
Ratio problems follow the structure A:B = C:D, which reads “A is to B as C is to D.” To solve for a missing value, the calculator uses cross multiplication.
Solve for D (given A, B, C)
The formula is: D = C × (B ÷ A). For example, if A=2, B=3, C=8, then D = 8 × (3/2) = 12. So 2:3 = 8:12.
Solve for C (given A, B, D)
The formula is: C = D × (A ÷ B). For example, if A=1, B=4, D=20, then C = 20 × (1/4) = 5. So 1:4 = 5:20.
How to Simplify a Ratio
To simplify a ratio, find the greatest common divisor (GCD) of both values and divide each by it. For 18:12, the GCD is 6, so 18:12 simplifies to 3:2. The calculator performs this automatically and shows each step.
Converting a Ratio to a Fraction
A part-to-part ratio can be converted to fractions representing each part’s share of the whole:
- Add the two ratio terms: 1 + 2 = 3 (this is the whole)
- Write each part over the whole: 1/3 and 2/3
- So in the ratio 1:2, the first part is 1/3 of the whole and the second is 2/3
Ratio vs Proportion vs Fraction
A ratio compares two quantities side by side, such as 3:4. A proportion states that two ratios are equal: 3:4 = 6:8. A fraction expresses one quantity as a part of a total, such as 3/4. While related, each form serves a different purpose in mathematics.
Frequently Asked Questions
To solve for a missing value in A:B = C:D, use cross multiplication. If D is unknown, the formula is D = C times (B divided by A). If C is unknown, use C = D times (A divided by B). Enter the three known values above and the calculator solves for the fourth automatically.
To simplify a ratio, divide both terms by their greatest common divisor (GCD). For example, 12:8 has a GCD of 4, so 12 divided by 4 and 8 divided by 4 gives the simplified form 3:2. The Simplify tab above handles this automatically.
To convert a part-to-part ratio to fractions, add both terms to find the whole. Then write each term over the whole as a fraction. The ratio 1:3 has a whole of 4, giving fractions 1/4 and 3/4.
Two ratios A:B and C:D are equivalent if A divided by B equals C divided by D, or equivalently if A times D equals B times C (cross multiplication). Use the Compare tab above to test any two ratios for equivalence instantly.
A ratio is a comparison of two quantities, such as 3:4. A proportion is a statement that two ratios are equal, written as 3:4 = 6:8. Solving a proportion means finding the unknown value that makes both sides equal.
Yes. The ratio calculator accepts integers and decimal values in all fields. For example, you can enter 2.5:5 = C:20 and the tool will solve for C correctly. Scientific notation inputs are also supported.