It's the equality of two ratios. In A:B = C:X the ratios A/B and C/X are equal. Knowing three values, we find the fourth by cross-multiplication.
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Solve A:B = C:X and simplify ratios to lowest terms.
A ratio compares two quantities (A:B), and a proportion is the equality of two ratios: A:B = C:X, the same as A/B = C/X. The key property is cross-multiplication: A/B = C/X is equivalent to A·X = B·C, meaning the product of the extremes equals the product of the means. When three of the four values are known, this tool isolates the missing term with the right formula, for example X = (B·C) ÷ A when the fourth term is blank, and shows the steps. In simplify mode it reduces an integer ratio to lowest terms by dividing both terms by their greatest common divisor (GCD): 18:24 becomes 3:4 because GCD(18, 24) = 6. Proportions turn up constantly in map and blueprint scales, recipe scaling, unit conversion, mixtures, proportional discounts and resizing images without distorting their shape. Everything is computed locally in your browser.
Every proportion A:B = C:X can be rewritten as the equality of the fractions A/B = C/X. Cross-multiplying yields A·X = B·C: the product of the extremes (A and X) equals the product of the means (B and C). From that single identity, any of the four terms is isolated simply by dividing by the opposite term.
That is exactly what the tool does once it detects which field you left blank. If the first term is missing, A = (B·C) ÷ X; if the second is missing, B = (A·X) ÷ C; and so on. In simplify mode the path is different: it computes the GCD of the two integers and divides both by it, leaving the ratio in its smallest equivalent form.
Example 1, solve: 3:5 = 12:X. Here A = 3, B = 5, C = 12 and the fourth term is blank, so X = (B·C) ÷ A = (5 × 12) ÷ 3 = 60 ÷ 3 = 20. Thus 3:5 = 12:20, and you can check that 3 ÷ 5 = 0.6 equals 12 ÷ 20 = 0.6.
Example 2, simplify: 45:60. The greatest common divisor is GCD(45, 60) = 15, so we divide both terms by 15: 45 ÷ 15 = 3 and 60 ÷ 15 = 4. The simplified ratio is 3:4, equivalent to the decimal 45 ÷ 60 = 0.75.
The order of the terms matters: 3:4 (= 0.75) is not the same relationship as 4:3 (≈ 1.333), so keep the correspondence consistent across both sides. When solving, the term acting as the divisor cannot be zero, that is why the tool warns 'division by zero' when it happens. Simplification, since it relies on the GCD, requires whole nonzero numbers; to reduce a ratio with decimals, first multiply both sides until they become integers.
In practice, proportions scale ingredients when you double a recipe, convert a map's 1:50000 scale into real distances, keep an image's aspect ratio when resizing, split amounts into proportional parts and compare performance as a rate (for example, miles per gallon).
Paste the code into your HTML and the tool shows up on your page, without J-Kit's navigation and ads. It still runs in the browser of whoever visits your site.
<iframe
src="https://jkit.tools/embed/en-US/ratio-calculator"
width="100%"
height="600"
style="border:0"
loading="lazy"
title="Ratio Calculator"
></iframe>These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
It's the equality of two ratios. In A:B = C:X the ratios A/B and C/X are equal. Knowing three values, we find the fourth by cross-multiplication.
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