Ratio Calculator
How to Simplify 2-Term and 3-Term Ratios
Ratios express the proportional relationship between two or more quantities of the same kind. In culinary recipes, gear trains, screen aspect ratios, concrete mixes, and chemical mixtures, ratios must frequently be simplified into their lowest integer terms.
Our ratio calculator supports both 2-term (A : B) and 3-term (A : B : C) ratios. If any terms contain decimals (such as 1.5 : 2.5), the engine first scales all terms by multiplying by powers of 10 until every term is a whole integer.
Next, the Euclidean algorithm determines the Greatest Common Divisor (GCD) across all terms simultaneously. Finally, every term is divided by this common divisor, yielding the simplest equivalent ratio in irreducible whole numbers.
Unlike simple fractions, ratios can compare parts to parts (e.g. 2 parts sand to 3 parts gravel) or parts to a whole (e.g. 2 parts out of 5 total parts).
Worked Concrete Mixture Example
Worked Example: Concrete Mix Proportions (3-Term Ratio)
A standard construction concrete formula specifies 250 lbs of Portland cement, 500 lbs of washed sand, and 750 lbs of gravel aggregate. Simplify this 3-term batch ratio to its simplest integer form.
- Set up the 3-term ratio: 250 : 500 : 750.
- Find the Greatest Common Divisor: GCD(250, 500, 750) = 250.
- Divide the first term: 250 ÷ 250 = 1.
- Divide the second term: 500 ÷ 250 = 2.
- Divide the third term: 750 ÷ 250 = 3.
The concrete mix ratio simplifies to 1 : 2 : 3 (1 part cement, 2 parts sand, 3 parts gravel aggregate).
Standard Aspect Ratios and Formulation Reference Table
Common ratios found across digital display resolutions, photographic prints, and engineering blends.
| Application | Raw Measurements | Simplified Ratio | Percentage Distribution | Decimal Equivalent |
|---|---|---|---|---|
| Widescreen Video (HD) | 1920 : 1080 | 16 : 9 | 64.0% : 36.0% | 1.7778 : 1 |
| Standard Monitor | 1024 : 768 | 4 : 3 | 57.1% : 42.9% | 1.3333 : 1 |
| Ultra-Wide Display | 2560 : 1080 | 21 : 9 | 70.0% : 30.0% | 2.3333 : 1 |
| Photo Print | 6 : 4 | 3 : 2 | 60.0% : 40.0% | 1.5000 : 1 |
| Mortar Blend | 50 : 150 | 1 : 3 | 25.0% : 75.0% | 0.3333 : 1 |
| Salad Vinaigrette | 3 : 1 | 3 : 1 | 75.0% : 25.0% | 3.0000 : 1 |
| 3-Term Concrete | 100 : 200 : 300 | 1 : 2 : 3 | 16.7% : 33.3% : 50.0% | — |
Common Ratio Simplification Mistakes
- Leaving decimal points in simplified ratios: An answer of 1.5 : 2 is not simplified. Multiply by 2 to yield whole integers: 3 : 4.
- Changing the order of terms: A ratio of 3 : 1 is completely different from 1 : 3. The position of each term must be preserved.
- Dividing by different numbers: Each term in the ratio must be divided by the exact same greatest common divisor.
- Confusing ratios with fractions: A ratio of 1 : 4 represents 1 part to 4 parts (a total of 5 parts), meaning the first item is 1/5 (20%) of the total, NOT 1/4 (25%).
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Frequently Asked Questions About Simplifying Ratios
How do you simplify a ratio with decimals?
Multiply all terms in the ratio by 10, 100, or 1000 until all terms become whole integers, then divide all terms by their Greatest Common Divisor (GCD).
Can a ratio have three terms?
Yes. 3-term ratios (such as 1 : 2 : 3 or 4 : 5 : 6) are common in mixing recipes, chemical compounds, and concrete formulations.
What is 12 to 16 as a ratio in simplest form?
12 : 16 simplifies to 3 : 4. Both numbers are divided by their greatest common factor of 4.
What is the difference between a ratio and a fraction?
A fraction compares a part to the whole (1/4 is 1 part out of 4). A ratio usually compares a part to another part (1:3 means 1 part of A for every 3 parts of B, totaling 4 parts).
How do you find equivalent ratios?
Multiply or divide all terms of the ratio by the same non-zero number. For example, 2 : 3 is equivalent to 4 : 6, 6 : 9, and 10 : 15.
Can ratio terms be negative or zero?
In physical measurements and standard proportions, ratio terms represent quantities and must be strictly positive non-zero numbers.