Ratio Calculator
Simplify a ratio and scale it proportionally.
Optional — finds the matching B at this scale.
Results update as you type.
How it works
A ratio compares two quantities by showing how many units of one correspond to units of the other, written with a colon as A to B. Two jobs come up constantly with ratios: reducing them to their simplest whole-number form and scaling them up while holding the proportion fixed. The ratio calculator does both, and also expresses the relationship as a single decimal for quick comparison. Simplifying divides both terms by their greatest common divisor, which leaves 16 : 9 unchanged but collapses 1920 : 1080 to the same 16 : 9. Scaling answers the practical question of what B must be if A becomes a given value. The tool keeps A to B constant, so setting A to 1920 against an original 16 : 9 returns B equal to 1920 times 9 divided by 16, which is 1080. Because the proportion never shifts, a ratio calculator lets you resize recipes, mixes, screen dimensions or map distances without recomputing the relationship from scratch. Designers matching aspect ratios, cooks and chemists holding a mixture's proportions, and model builders scaling plans all lean on this ratio calculator to simplify and rescale two-part relationships reliably.
Divide both terms by their GCD; scale via A : B = newA : newB
Dividing both terms of a ratio by their greatest common divisor removes the factor they share without disturbing their relationship, so 1920 : 1080 shrinks to 16 : 9. Scaling relies on the proportion A to B staying equal to newA to newB; solving that equality for the missing term gives newB as newA times B divided by A. Setting A to 1920 therefore returns B as 1920 times 9 divided by 16, or 1080.
Source:Standard arithmetic
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter value a and value b.
- 2
Adjust the options
Adjust scale a to if they apply — sensible defaults are already set.
- 3
Read your result
Simplified ratio updates instantly as you type — no button to press.
Frequently asked questions
How do I simplify a ratio?
Divide both numbers by their greatest common divisor, the largest value that goes into each with no remainder. For 1920 : 1080 that divisor is 120, and dividing both terms by it leaves 16 : 9. The ratio still describes the same relationship, only with smaller numbers. If the two terms already share no common factor, the ratio is fully simplified as it stands.
What is a ratio as a decimal?
It is the first term divided by the second, which turns the comparison into one plain number. A 16 : 9 ratio equals 16 divided by 9, about 1.78, meaning the first quantity is roughly 1.78 times the second. Decimals make ratios easy to rank and compare at a glance, and they slot directly into further calculations that expect a single value rather than a two-part expression.
How does scaling a ratio work?
Scaling holds the proportion fixed while you change one term. Set a new value for A, and the calculator finds the B that keeps A to B equal to the original ratio. With a 16 : 9 ratio and A set to 1920, it returns 1080, because 1920 times 9 divided by 16 is 1080. This is how a single aspect ratio expands to any resolution without distorting the shape.
What is the difference between a ratio and a fraction?
A fraction expresses a part of a single whole, while a ratio compares two separate quantities that may or may not belong to the same whole. A 16 : 9 ratio can be written as the fraction 16/9, and the arithmetic of simplifying is the same, but ratios often describe relationships like width to height or one ingredient to another, where thinking of a single whole would be misleading.
Can I use a ratio to find a missing value?
Yes, that is exactly what the scaling field does. Given a known ratio and one new term, the calculator solves for the other so the proportion stays intact. Enter A as 1920 with an original 16 : 9 ratio and it returns B as 1080. The same cross-multiplication finds a missing first term if you know the second, which is how proportion problems in recipes and maps are solved.