How this calculator works
A ratio compares two quantities of the same kind, like 4 cups of flour to 8 cups of water. This calculator covers the three tasks people most often need: reducing a ratio to its simplest whole-number form, solving a proportion where two ratios are set equal and one term is unknown, and scaling a ratio up or down by a factor while keeping the same proportion.
Ratios and fractions follow the same reduction rule, which is why 4:8 and 4/8 both simplify to the same lowest terms, 1:2. A proportion — two ratios set equal to each other — is solved by cross-multiplication, the same technique used for equivalent fractions.
The formulas
Simplify: a:b → (a ÷ g):(b ÷ g), where g = gcd(a, b)Proportion: if a:b = c:x, then x = (b × c) ÷ aScale: a:b × k → (a × k):(b × k)Scaling a ratio by any positive factor k never changes the proportion it represents — only how large the two sides are written.
Worked example: solving 2:3 = 10:x
- Set up the proportion 2:3 = 10:x, where x is unknown.
- Cross-multiply: 2 × x = 3 × 10, so 2x = 30.
- Divide both sides by 2: x = 15.
- Check: 2:3 and 10:15 both reduce to the same simplified ratio, 2:3, confirming the answer.
Frequently asked questions
What is the difference between a ratio and a fraction?
A ratio compares two separate quantities (4 apples to 8 oranges), while a fraction usually represents a part of a whole (4 out of 8 total apples). The reduction arithmetic is identical, but they answer different kinds of questions.
How do I scale a recipe or mixture using a ratio?
Multiply both terms of the ratio by the same scale factor. A 2:1 concrete mix scaled by a factor of 5 becomes 10:5 — five times as much of each ingredient, in the same proportion.
Can a ratio have more than two terms?
Yes, ratios like 2:3:5 compare three or more quantities at once. This calculator handles two-term ratios; extend the same idea by dividing every term by the shared greatest common divisor.
Why do simplified ratios only use whole numbers?
A ratio in lowest terms is conventionally written with the smallest possible whole numbers, the same way a fraction is fully reduced. If your original values are decimals, this calculator scales them up to whole numbers before reducing.
Is a ratio the same as a rate?
Not quite. A ratio compares two quantities of the same kind, like 4 cups of flour to 8 cups of water. A rate compares two quantities in different units, like 60 miles per hour. Both simplify by dividing out a shared common factor, but a rate's units don't cancel the way a same-kind ratio's do.