Ratio Calculator
Simplify a ratio, get its decimal value and scale it to a new term.
Simplified ratio
16 : 9
Decimal 1.7778
Decimal value
1.7778
If A = 1920, B =
1,080
AI Breakdown & Smart Takeaway
Plain-English insight on your numbers
Get a personalized explanation of what these results mean — and how to improve them.
How the Ratio Calculator works
The Ratio Calculator lets you instantly simplify any ratio to its lowest terms, convert it to a decimal value, and scale either term to a target number — making it an essential tool for students, designers, engineers, cooks, and anyone who works with proportional relationships.
A ratio expresses the relative size of two quantities. When you enter a ratio like 18:24, the calculator finds the Greatest Common Divisor (GCD) of both terms and divides each by it, yielding the fully simplified form — in this case 3:4. This simplification process is mathematically equivalent to reducing a fraction and gives you the most readable, portable version of the relationship. The GCD is computed using the Euclidean algorithm, which repeatedly replaces the larger number with the remainder of dividing by the smaller until the remainder is zero.
The decimal conversion is straightforward: the calculator divides the first term (the antecedent) by the second term (the consequent), so 3:4 becomes 0.75. This single number is enormously practical because it lets you compare ratios at a glance — a 5:7 ratio (≈0.714) is slightly smaller than 3:4 (0.75) even though the raw numbers look similar. Decimal form is also required as input for many formulas in engineering, finance, and science, so having it precomputed removes a common source of error.
Scaling is where the calculator becomes especially powerful for real-world tasks. If you know one term of a proportion and need to find the other, you enter the known target value and the tool solves for the missing term using cross-multiplication: A/B = C/D, so D = (B × C) / A. For example, if a recipe uses a 2:5 ratio of oil to flour and you want to scale to 350 g of flour, the calculator instantly returns 140 g of oil. This same logic applies to map scales, architectural drawings, screen aspect ratios, and mixing paint or concrete.
The most common mistake users make is confusing the order of terms — a ratio of 3:4 is not the same as 4:3, and reversing them changes every downstream calculation. Another pitfall is applying ratio scaling to quantities that don't share a linear relationship (for example, doubling a linear dimension squares the area and cubes the volume). Always verify the units and the nature of the relationship before trusting a scaled result. When working with aspect ratios for screens or images, remember that the simplified ratio (e.g., 16:9) describes shape only — the actual pixel dimensions must also satisfy resolution requirements.
Formula
Simplify by GCD; scale via b₂ = a₂ × (b ÷ a)
Pro tips
- 16:9 and 4:3 are common screen aspect ratios.
Key terms
- Ratio
- — A ratio is a comparison of two quantities expressed as A:B, showing how many times one value contains or is contained by the other.
- Proportion
- — A proportion is an equation stating that two ratios are equal (A:B = C:D), forming the mathematical basis for scaling calculations.
- Greatest Common Divisor (GCD)
- — The largest positive integer that divides both terms of a ratio without a remainder, used to reduce the ratio to its simplest form.
- Antecedent
- — The first term in a ratio (A in A:B), representing the quantity being compared.
- Consequent
- — The second term in a ratio (B in A:B), representing the quantity to which the antecedent is compared.
- Aspect Ratio
- — A specific application of ratio that describes the proportional relationship between the width and height of a rectangle, commonly used for screens, images, and printed media.
