CalcNest

Ratio Calculator

Solve a proportion by leaving one box empty, simplify a ratio to lowest terms, and see what share of the whole each part is.

By Rachel Okafor, CPA · Last reviewed

Fill in three values and leave the one you want to find empty.

Result

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  • Proportion
  • A : B in lowest terms
  • A : B as 1 : n
  • A as share of A + B

Ratios and proportions

A ratio says how many of one thing there are for each of another — 3 cups of water to 4 cups of flour. A proportion says two ratios are equal, which is how you scale: maps, recipes, paint mixes, unit prices and similar triangles all rely on it. Because equal ratios have equal cross products, one unknown in a proportion can always be found with one multiplication and one division.

The formulas

A : B = C : D ⇔ A × D = B × C Missing C = A × D / B Missing D = B × C / A Missing A = B × C / D Missing B = A × D / C Simplest form: A : B = (A ÷ g) : (B ÷ g), g = GCF(A, B)

Worked example

A drink mix calls for 3 parts syrup to 4 parts water. For 20 cups of water, how much syrup? 3 : 4 = C : 20, so C = 3 × 20 / 4 = 15 cups.

Check: 15 : 20 simplifies (GCF 5) to 3 : 4. Syrup is 3 / (3 + 4) = 3/7 ≈ 42.86% of the mix.

Notes

  • Values can be decimals or negative; a zero in a position you divide by has no solution.
  • Results are rounded to eight significant decimals.

Sources: OpenStax, Prealgebra 2e, §6.5 Solve Proportions and their Applications.

Frequently asked questions

How do I solve a proportion?

Cross-multiply. In A : B = C : D, A × D = B × C, so any one missing value is the product of the two diagonal values divided by the remaining one. For 3 : 4 = ? : 20, the missing value is 3 × 20 / 4 = 15.

How do I simplify a ratio?

Divide both sides by their greatest common factor. 12 : 18 has a GCF of 6, so it simplifies to 2 : 3. With decimals, first multiply both sides by a power of ten to make them whole: 1.5 : 2.25 becomes 150 : 225, which simplifies to 2 : 3.

How do I scale a recipe with ratios?

Keep the ratio and change one side. A recipe that uses 2 cups of flour for 3 eggs, scaled to 5 eggs, needs 2 × 5 / 3 = 3⅓ cups of flour. Enter 2 : 3 = ? : 5.

What is the difference between a ratio and a fraction?

A ratio compares two quantities to each other (3 boys : 4 girls); a fraction compares a part to the whole (3/7 of the class are boys). The calculator shows both: for 3 : 4, the first part is 3/7 ≈ 42.9% of the total.