Ratio Calculator
Simplify a ratio to lowest terms, or solve a proportion for a missing value.
- A8
- B12
8 and 12 simplify down to 2:3 — same proportion, smaller numbers.
ƒShow your work
- 1GCD(8, 12) = 4 → 8/4 : 12/4
About the Ratio Calculator
Ratios compare two quantities directly — the mix of flour to water in a recipe, the aspect ratio of a photo, paint mixed at a specific proportion, a map's scale of inches to real-world miles. Anywhere something needs to be scaled up or down while keeping the same relationship between its parts, a ratio (or its close cousin, the proportion) is the tool doing the work.
This calculator covers the two most common ratio tasks: simplifying a ratio down to its smallest whole-number form (the way 8:12 is really just 2:3), and solving a proportion — filling in a missing fourth value when two ratios are set equal, like scaling a recipe that serves 4 up to serve 10.
How it’s calculated
Simplifying a ratio works exactly like simplifying a fraction: find the greatest common divisor (GCD) of the two numbers and divide both by it. 8:12 has a GCD of 4, so it simplifies to 2:3 — the same underlying proportion, expressed in smaller numbers.
Solving a proportion A:B = C:D for the missing value uses cross-multiplication: since A/B = C/D, multiplying both sides out gives D = (B × C) / A. If a recipe uses a 2:3 ratio of flour to sugar and you're using 5 cups of flour, solving 2:3 = 5:D gives D = (3 × 5) / 2 = 7.5 cups of sugar.
Frequently asked questions
How do you simplify a ratio?
Divide both numbers in the ratio by their greatest common divisor (GCD), the same way you'd simplify a fraction. A ratio of 15:25 has a GCD of 5, so it simplifies to 3:5.
What's the difference between a ratio and a fraction?
A ratio compares two separate quantities (like flour to sugar), while a fraction represents a part out of a whole (like 3 slices out of an 8-slice pizza). They're calculated the same way mathematically, but a ratio doesn't necessarily imply the two numbers add up to some meaningful total the way a fraction's numerator and denominator do.
How does cross-multiplication solve a proportion?
Setting two ratios equal, A:B = C:D, means A/B = C/D as fractions. Cross-multiplying gives A×D = B×C, and solving that equation for whichever value is unknown gives the answer — this is the standard method for scaling recipes, maps, and any other proportional relationship.
How do I scale a recipe using a ratio?
Express the recipe's key ingredients as a ratio, then set up a proportion between the original ratio and your target amount for one ingredient, and solve for the rest. If a recipe is a 1:2 ratio of butter to flour and you want to use 3 cups of butter, solving 1:2 = 3:D gives D = 6 cups of flour.
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