Ratio Calculator

A ratio compares two quantities without committing to units. 1920:1080 and 16:9 describe the same shape; the second is easier to reason about. The tool above does both jobs: it reduces a ratio to its lowest terms, and it solves the proportion A:B = C:x for the missing fourth value.

How it works

Simplify. Enter two values. The tool divides both by their greatest common divisor, found with Euclid's algorithm, and shows the reduced pair alongside the decimal quotient A ÷ B. Decimal inputs are handled by scaling both values up by powers of ten until they are whole numbers, so 2.5:5 correctly reduces to 1:2 rather than being rejected. A first value of zero gives 0:1; a second value of zero is refused, because a ratio against nothing is undefined.

Find an equivalent. Fill in a third value C, and the tool solves A:B = C:x as x = (B × C) ÷ A. This is the scaling question — "the recipe serves 4 with 300 g of flour, how much for 10?" — and it is also how you convert between a design mock-up and a rendered size.

Both results update as you type, and nothing leaves your browser.

Where ratios show up in engineering

Aspect ratios. A 16:9 video in a 4:3 frame has to be letterboxed, pillarboxed or cropped; there is no fourth option. Reducing the pixel dimensions of an asset to lowest terms tells you immediately which case you are in, and the equivalent-ratio mode gives you the matching height for any width you pick. Reserving that space in the layout before the image loads is what stops the page jumping around as assets arrive — HTML5 essentials covers the width/height and aspect-ratio attributes that make the browser do this for you.

Rates and error budgets. Requests per second, cache hit rate, error rate and read:write ratio are all ratios, and they are far more stable under load than absolute counts. A service handling 400 errors an hour sounds alarming until you learn it serves 40 million requests — a 0.001% rate. Sizing decisions work the same way: if your read:write ratio is 50:1, a read replica helps and sharding the writes does not. Application performance works through which of these to measure and how they drive capacity decisions.

Scaling anything. Thread pool to connection pool, memory to heap, instance count to expected load — most capacity rules of thumb are proportions, and the equivalent-ratio mode is the fastest way to apply one to a new number.

Practical notes

Order matters. 3:4 and 4:3 are different ratios. The tool preserves the order you type; it never sorts the pair for you.

A ratio is not a fraction, quite. 3:4 as a part-to-part ratio means 3 of one thing for every 4 of another — seven items in total, of which three are the first kind. Read as a fraction, 3/4 is a part-to-whole statement. Mixing the two is the most common ratio error: "3:1 in favour" means 75%, not 33%. The decimal shown by the tool is the part-to-part quotient A ÷ B.

Rounding. Reduction is exact for whole numbers. For decimal inputs the scaling step stops at a factor of one million, so values with more than six decimal places are rounded before reduction — which is the right behaviour for measurements, and worth knowing if you are feeding in raw sensor data.

To reduce the same pair as a fraction, or to add two of them, use the fraction calculator; to express one value as a share of another, the percentage calculator is the shorter route.