A ratio compares two quantities — written as A:B — telling you how much of one thing relates to another. The calculator simplifies a ratio to its lowest form, scales it up or down by a factor, or solves a proportion (A:B = C:?) when one value is missing.
What is Ratio Calculator?
Ratios appear everywhere from cooking (water to rice 2:1) to chemistry (mixing ratios), photography (aspect ratios 16:9), and finance (debt-to-equity, P/E ratio). The mathematical idea is simple — A:B can be read as 'A units of one thing per B units of another' — but the practical work is usually about simplifying, scaling, or solving proportions.
A simplified ratio uses the smallest whole numbers possible. 12:18 simplifies to 2:3 by dividing both sides by their greatest common divisor (6). Simplification makes the relationship easier to read but does not change the underlying meaning — 12:18 and 2:3 represent the same proportion.
Scaling multiplies both sides by the same factor. 2:3 scaled by 5 becomes 10:15, useful when going from a recipe that serves 4 to one serving 20, or from a small mixing batch to a large one.
Three ratio operations
Pick the operation that fits your problem. Simplify shrinks the ratio. Scale grows it. Solve fills in a missing value in a proportion (A:B = C:?).
- A, B
- Two ratio terms—the original ratio's two sides
- g
- GCD—greatest common divisor of A and B
- k
- Scaling factor—the multiplier used in scaling mode
How to use this calculator
Pick a mode, fill in the values that mode uses, read the result instantly.
Pick the mode
Simplify, scale, or solve a proportion. Each mode uses A and B; scale and solve also use C.
Enter A and B
The two terms of the ratio. For solve mode, A and B form the known ratio.
Enter C if needed
Required for scaling (the multiplier) and solve modes (the known third term in the proportion).
Read the answer
Simplified ratio, scaled ratio, or the missing term in the proportion.
Common ratio scenarios
Recipe scaling
Recipe says 2 cups rice : 4 cups water. Scaling for 6 cups rice gives 6:12 = 12 cups water.
Aspect ratios
16:9 is widescreen TV; 4:3 is older standard. Knowing the simplified form helps in image cropping.
Mixing concrete
Cement:sand:aggregate is often 1:2:4. Scale all three together when increasing the batch size.
P/E ratio in stocks
If P/E is 25 (stock price 25× earnings per share), comparing to industry average tells you if the stock is expensive.
Map scale
1:50,000 means 1 cm on the map = 50,000 cm = 500 m on the ground.
Common mistakes to avoid
Mixing up the order of terms
A:B is not the same as B:A. 2:3 (small to large) is the inverse of 3:2 (large to small). Set the order consistently.
Comparing different bases
Two ratios with the same form but different total quantities can be misleading — 1:2 of 6 items (2:4) is different from 1:2 of 12 items (4:8).
Glossary
- Ratio
- A comparison of two quantities. Can be written as A:B, A/B, or 'A to B'.
- Proportion
- An equation showing two ratios are equal. A:B = C:D.
- GCD (Greatest Common Divisor)
- The largest integer that divides both A and B without remainder. Used to simplify ratios.
- Cross multiplication
- A method to solve proportions: A × D = B × C if A:B = C:D.