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Ratio Calculator

Simplify ratios, scale them up or down, or solve for a missing value in a proportion (A:B = C:D) — handy for recipes, mixing, finance, and design work.

Enter your values

Result

Simplified Ratio
2 : 3
Original
12 : 18
Quick answer

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:?).

Formula
Simplify: A:B → A/g : B/g where g = GCD(A, B) Scale: A:B by k → A×k : B×k Solve: If A:B = C:? then ? = (B × C) / A
A, B
Two ratio termsthe original ratio's two sides
g
GCDgreatest common divisor of A and B
k
Scaling factorthe multiplier used in scaling mode
Worked example
ModeSolve A:B = C:?
A3
B5
C12
? = (B × C) / A = (5 × 12) / 3
? = 60 / 3 = 20
3:5 = 12:20

How to use this calculator

Pick a mode, fill in the values that mode uses, read the result instantly.

  1. Pick the mode

    Simplify, scale, or solve a proportion. Each mode uses A and B; scale and solve also use C.

  2. Enter A and B

    The two terms of the ratio. For solve mode, A and B form the known ratio.

  3. Enter C if needed

    Required for scaling (the multiplier) and solve modes (the known third term in the proportion).

  4. 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.
Disclaimer: Results are estimates based on the inputs you provide. They are not professional advice. For consequential decisions — financial, tax, medical, or legal — verify with a qualified professional.

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