Reduce any ratio to its lowest terms, or find the missing value in A:B = C:X.
Divide both terms of the ratio by their greatest common divisor (GCD). Simplifying 8:12 — the GCD of 8 and 12 is 4, so dividing both terms by 4 gives 2:3, the lowest-terms form of the same ratio.
A proportion sets two ratios equal to each other, like A:B = C:X. Cross-multiplication gives A × X = B × C, so X = (B × C) / A. This lets you find a missing fourth value any time you already know three of the four numbers in a proportional relationship — a very common real-world task, like scaling a recipe or a map.
Related, but not identical. A fraction represents a part of a whole — 3/4 of one pizza. A ratio compares two separate quantities that don't have to add up to any single whole — a 3:2 ratio of flour to sugar in a recipe describes two different ingredients, not two parts of one total amount. Ratios are often written and calculated in fraction form, which is exactly why the two concepts get conflated, even though conceptually a ratio is a comparison and a fraction is a portion.
The Fraction Calculator handles arithmetic directly on fractions — adding, subtracting, multiplying, and dividing two fractions together. This tool instead handles ratio-specific tasks: reducing a ratio to its lowest terms, and solving a proportion for a missing value. Use the Fraction Calculator when you need to combine two fractions; use this tool when you're comparing quantities or scaling a proportion.
Worked example: simplifying 8:12 gives 2:3 (dividing both by their GCD, 4). Solving the proportion 2:3 = 10:X: X = (3 × 10) / 2 = 30/2 = 15 — check: 2:3 and 10:15 both reduce to the same 2:3 ratio.
A ratio compares quantities; a fraction expresses a part of a whole. The distinction matters more than it sounds. A 3:4 ratio means the total is divided into seven parts, not four — so 3:4 corresponds to the fractions 3/7 and 4/7, not 3/4.
Misreading this is the most frequent ratio error there is. If a recipe is 3:4 flour to water and you have 700ml total, that's 300ml flour and 400ml water.
Ratios stay equivalent when every term is multiplied or divided by the same number, so 3:4 = 6:8 = 300:400. To solve a proportion a:b = c:d for a missing term, cross-multiply: a × d = b × c.
Always simplify by the greatest common divisor to compare ratios meaningfully — 24:36 and 2:3 are the same relationship, and only the second makes that obvious at a glance.
Ratios extend to any number of terms: 2:3:5 splits a total into ten parts. Dividing £1,000 in that ratio gives £200, £300 and £500.
Inverse ratios behave in the opposite direction and catch people out. If four workers take six days, eight workers take three — the ratio of workers to days is inverse, so doubling one halves the other. Applying direct proportion here gives an answer that is wrong by a factor of four.
That last one is worth care: odds and probability are different scales, and converting between them incorrectly is common. For part-of-whole arithmetic, the Fraction Calculator is the better tool, and for percentage change use the Percentage Calculator.
For image and video dimensions specifically, the Aspect Ratio Calculator resizes without distortion and names the real ratio behind labels like "21:9".