Ratio Calculator
Simplify ratios and solve proportions — find the missing term in A:B = C:D for cooking, scaling recipes, maps, and mixing ratios.
What is Ratio Calculator?
The ratio calculator does two common jobs: it simplifies a ratio like 18:24 to its lowest terms (3:4), and it solves a proportion A:B = C:D when one value is missing.
Useful for scaling recipes, mixing paint or concrete, reading map scales, converting currency at a fixed rate, and any time two quantities need to grow together in lock-step.
Formula
Simplify a ratio a:b by dividing both sides by the greatest common divisor (GCD).
Solve the proportion a:b = c:d for the missing term by cross-multiplying: a × d = b × c.
- Solve for D: D = (B × C) ÷ A
- Solve for C: C = (A × D) ÷ B
- Solve for B: B = (A × D) ÷ C
- Solve for A: A = (B × C) ÷ D
Worked example
A recipe serves 4 with 3 cups of flour. How much flour for 9 servings?
- Proportion: 3 cups : 4 servings = X : 9 servings
- A = 3, B = 4, C = 9, D = ?
- D = (4 × 9) ÷ 3 = 12
You need 12 cups of flour for 9 servings.
How to use this calculator
- Enter the known ratio as A:B (e.g., 3:4).
- Enter C with the value you know from the second pair, and leave D blank to solve.
- The calculator also shows A:B in simplified form plus decimal and percentage equivalents.
Frequently asked questions
What is the difference between a ratio and a proportion?
A ratio compares two quantities (3:4). A proportion states that two ratios are equal (3:4 = 9:12). You can only solve a proportion when three of the four values are known.
Can ratios have decimals?
Yes. 1.5:2 is valid (equivalent to 3:4). However, ratios are usually written as whole numbers in lowest terms for clarity.
Why does it matter that A:B be in the same order as C:D?
Order defines the meaning. "3 cups flour : 4 servings" is not the same as "4 servings : 3 cups flour" — the units flip. Keeping the order consistent on both sides of the proportion is how cross-multiplication stays valid.
How is ratio used in construction?
Concrete mixing ratios (e.g., 1:2:3 cement:sand:gravel) and mortar ratios (e.g., 1:3 cement:sand) scale by total volume. The ratio calculator helps convert a known volume to ingredient amounts.