A ratio calculator simplifies a ratio to lowest terms or solves a proportion for a missing value. 12 : 18 simplifies to 2 : 3, and 2 : 4 = C : 10 gives C = 5.
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How to use the ratio calculator
- Choose simplify or proportion mode.
- Enter A and B, then D (to solve for C) or C (to solve for D).
- Read the simplified ratio or the missing value.
How the ratio calculator works
The ratio calculator has two modes. In simplify mode, you enter A and B, and the tool reduces A : B by the greatest common factor. It first scales both terms by the power of ten that clears their decimals (up to six places), so 1.5 : 2.5 becomes 15 : 25 and then 3 : 5. The simplified ratio is the main result; the detail rows repeat the ratio as entered and give A ÷ B.
In proportion mode, the tool solves A : B = C : D for whichever term is missing. Leave C at 0 to solve for C, or enter C and leave D blank to solve for D:
- C = A × D ÷ B
- D = B × C ÷ A
A and B must not be 0.
Ratio calculator worked example
A recipe uses 2 cups of rice to 4 cups of water. In simplify mode, the ratio calculator shows 1 : 2. To make a bigger batch with 10 cups of water, switch to proportion mode with A = 2, B = 4 and D = 10. The tool gives C = 2 × 10 ÷ 4 = 5 cups of rice. Check by cross-multiplying: 2 × 10 = 4 × 5 = 20.
| Mode | A : B | Input | Result |
|---|---|---|---|
| Simplify | 2 : 4 | — | 1 : 2 |
| Simplify | 12 : 18 | — | 2 : 3 |
| Simplify | 1.5 : 2.5 | — | 3 : 5 |
| Proportion | 2 : 4 | D = 10 | C = 5 |
| Proportion | 3 : 5 | D = 40 | C = 24 |
What a ratio means
A ratio compares two quantities of the same kind. A class with 12 girls and 18 boys has a girls-to-boys ratio of 12 : 18, which simplifies to 2 : 3. Order matters: boys to girls is 3 : 2. A ratio is not the same as a fraction of the whole; girls make up 12 of 30 students, or 2/5, even though the ratio is 2 : 3. A rate compares different units, such as 60 miles per 2 hours, which simplifies to a unit rate of 30 miles per hour.
Solving proportions
A proportion states that two ratios are equal. Cross products of a true proportion are equal, which is where C = A × D ÷ B comes from. Proportions scale recipes, convert map distances, mix paint or concrete, and resize images while keeping the aspect ratio. A photo 3 units wide by 5 tall, resized to 40 tall, should be 3 × 40 ÷ 5 = 24 wide.
Aspect ratios
Screens and photos are described by ratios. A 1920 × 1080 screen simplifies to 16 : 9. A 1200 × 630 social image is 40 : 21. Enter the width and height in simplify mode and the ratio calculator finds the reduced form. To find a matching height for a new width, use proportion mode.
Ratios with three or more parts
The tool handles two-part ratios. For a three-part mix such as concrete at 1 : 2 : 3 cement, sand and gravel, add the parts (6) and divide the total amount by it. For 12 buckets in total, each part is 2 buckets, so you need 2, 4 and 6 buckets. You can also simplify pairs one at a time with the ratio calculator.
Common mistakes
Mixing units is the most common error: 1 foot to 6 inches is 12 : 6, or 2 : 1, not 1 : 6. Another is swapping the order of the terms. A third is placing D in the wrong position in a proportion; keep the same quantity on the same side of each ratio.
Tips
- Convert both terms to the same unit first.
- Leave C at 0 to solve for C, or fill in C to solve for D.
- Use the ratio calculator in proportion mode to scale recipes.
- Cross-multiply to check any proportion.
Related converters and calculators
Related calculators:
- Fraction calculator: fractions
- Percentage calculator: percent
- GCF calculator: common factors
- Unit converter: units
Sources
OpenStax Prealgebra 2e, 5.6: Ratios and rate; OpenStax Prealgebra 2e, 6.5: Solve proportions.
Formula and method
Simplify: scale A and B by 10^k (k <= 6) to integers, divide by GCD; headline is the simplified ratio. Proportion: C = A*D/B when C is 0, else D = B*C/A.
Default mode reprints A:B and shows an approximate integer simplification. Proportion mode solves for C given A, B, D (B != 0).
Questions about this calculator
How do I simplify a ratio?
Divide both terms by their greatest common factor.
How do I solve a proportion?
C = A × D ÷ B.
Can I use decimals?
Yes, up to six decimal places simplify exactly.
What is 1920:1080 simplified?
16:9.
Can it solve for D?
Yes. Enter A, B and C and leave D blank.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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