Ratio Calculators
All ratio math in one place. Solve, simplify, scale, compare, and convert ratios with step-by-step results.
Enter 3 of 4 values. Leave one blank.
What Each Ratio Calculator Does
The ratio calculators hub covers the five most common ratio operations. Choose the right tool from the tabs above based on your task.
Solve A:B = C:D
Find the fourth value when three are known. Uses cross multiplication. Works with decimals and integers.
Simplify a Ratio
Reduce a ratio to its lowest terms by dividing both values by their greatest common divisor.
Scale a Ratio
Multiply or divide a ratio by a constant factor to scale it up or down proportionally.
Compare Two Ratios
Test whether two ratios are equivalent using cross multiplication and decimal comparison.
Convert to Fraction
Convert a part-to-part ratio into part-to-whole fractions and show the percentage breakdown.
Ratio Formulas and Reference Table
The ratio formula table below lists the formulas used for each ratio operation with worked examples.
| Operation | Formula | Example | Result |
|---|---|---|---|
| Solve for D | D = C × (B / A) | A=2, B=3, C=8 | D = 12 |
| Solve for C | C = D × (A / B) | A=1, B=4, D=20 | C = 5 |
| Simplify A:B | Divide by GCD(A,B) | 18:12 | 3:2 |
| Scale by k | A×k : B×k | 2:3 × 4 | 8:12 |
| Compare A:B vs C:D | A×D = B×C? | 1:2 vs 3:6 | True (2=6… 1×6=6, 2×3=6) |
| Ratio to % | (A / (A+B)) × 100 | 1:3 | 25% and 75% |
| Ratio to fraction | A/(A+B), B/(A+B) | 2:3 | 2/5 and 3/5 |
Understanding Ratios
A ratio expresses how much of one quantity exists relative to another. Ratios appear in nearly every area of life and work: cooking (ingredient proportions), construction (material mixes), finance (debt-to-equity), maps (scale), photography (aspect ratios), and statistics (odds).
Part-to-Part vs Part-to-Whole
A part-to-part ratio, such as 3:2, compares two separate quantities directly. A part-to-whole ratio, such as 3:5, compares one part to the combined total. Understanding which type applies to your situation is the first step in solving any ratio problem correctly.
Equivalent Ratios
Equivalent ratios express the same relationship in different numbers. The ratios 1:2, 2:4, and 50:100 are all equivalent. You can verify equivalence by simplifying both ratios to their lowest terms or by confirming that the cross products are equal.
Scaling Ratios for Real Problems
Scaling a ratio is multiplying or dividing both terms by the same number. If a recipe uses flour and sugar in a 3:1 ratio and you want to triple the batch, the scaled ratio becomes 9:3 (or still 3:1 simplified). The Scale Ratio tab makes this instant for any inputs.
Common Real-World Uses for Ratio Calculators
- Scaling recipes up or down from an original serving size
- Calculating aspect ratios for images and video formats
- Mixing materials such as concrete, paint, or chemicals in correct proportions
- Working out map scales and real-world distances
- Solving proportion problems in algebra and test prep
- Finance ratios such as price-to-earnings or debt-to-equity
- Converting odds to probabilities in statistics and betting contexts
Frequently Asked Questions
A ratio in math is a comparison of two or more quantities that shows how much of one exists relative to the other. It is written as A:B, A to B, or A divided by B. Ratios appear in cooking, finance, construction, and proportion problems across all levels of math.
To simplify a ratio, divide both terms by their greatest common divisor (GCD). For 18:12, the GCD is 6. Dividing each term by 6 gives the simplified form 3:2. Use the Simplify tab above to do this automatically with any inputs.
To scale a ratio, multiply or divide both terms by the same number. The ratio 2:3 scaled by 4 becomes 8:12. The Scale Ratio tab asks for the original ratio and the multiplier, then shows the scaled result and simplified form.
To convert a ratio A:B to percentages, divide each term by the total (A plus B) and multiply by 100. For the ratio 1:3, the total is 4. A becomes 1 divided by 4 times 100 = 25%, and B becomes 3 divided by 4 times 100 = 75%.
A ratio compares two quantities of the same kind, such as 2 apples to 3 apples. A rate compares two quantities of different kinds, such as 60 miles per hour. Both use the same mathematical structure but describe different real-world relationships.
To check if ratios A:B and C:D are equivalent, compare A divided by B with C divided by D. If both equal the same decimal, the ratios are equivalent. You can also verify using cross multiplication: A times D must equal B times C. Use the Compare tab above for instant results.