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Ratio Calculator

Simplify any ratio and solve proportions a : b = c : x

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How to use

  1. 1.Choose a mode: Simplify to reduce a ratio, or Solve proportion to find a missing term.
  2. 2.Enter your numbers — a : b (add an optional third term), or three of the four values in a : b = c : x, leaving the unknown box blank.
  3. 3.Read the result instantly: the simplest-form ratio with its decimal and percentage, or the solved unknown value.

About Ratio Calculator

A ratio compares two or more quantities, telling you how much of one thing there is relative to another. It is written with a colon, like 16 : 9, and read as "sixteen to nine". This ratio calculator does the two jobs people need most: it simplifies a ratio to its lowest terms, and it solves a proportion when one value is missing. Everything runs instantly in your browser, with no sign-up and nothing uploaded to a server.

To simplify a ratio you divide every term by the same number until they share no common factor. The largest number you can divide by is the greatest common divisor (GCD), so simplifying 8 : 12 means dividing both sides by 4 to get 2 : 3. The calculator finds the GCD with the Euclidean algorithm and reduces the ratio in one step, whether it has two terms or three (handy for aspect ratios such as 1920 : 1080, which reduces to 16 : 9). Decimals are welcome too: enter 0.5 : 0.25 and it scales both numbers up to whole numbers before reducing, returning 2 : 1.

A ratio is closely related to a fraction. The ratio a : b is the same comparison as the fraction a/b, so the simplest-form ratio is exactly the fraction reduced to lowest terms. That is why the tool also shows the equivalent decimal (a divided by b) and the percentage, letting you move freely between a ratio, a fraction, a decimal and a percent. For 3 : 4 you instantly see 0.75 and 75%.

The second mode solves a proportion. A proportion is a statement that two ratios are equal, written a : b = c : x. When three of the four values are known, the missing one is found by cross-multiplication: a times x equals b times c. Leave any single box empty and the calculator rearranges the equation for you, so 2 : 3 = 10 : x gives x = 15, and 4 : 5 = c : 20 gives c = 16. If a required divisor works out to zero, it explains the problem instead of showing a broken answer.

Ratios and proportions show up everywhere in daily life. Recipes scale up and down by proportion, so doubling a 2 : 3 flour-to-sugar mix keeps the taste identical. Map and model scales, like 1 : 50, tell you real distances. Screen and photo aspect ratios such as 16 : 9 or 4 : 3 decide how an image fits without stretching. Mixing paint, fuel, fertiliser or cocktails relies on getting the ratio right, and finance uses ratios for odds, gearing and unit prices.

Use the simplify mode to reduce a ratio, convert a ratio to a fraction or read off its percentage, and switch to the proportion mode whenever you need to scale a ratio up, scale it down, or find an unknown term. Type your numbers and the answer updates as you go.

Frequently asked questions

How do I simplify a ratio?
Divide every term of the ratio by their greatest common divisor (GCD) until no common factor is left. For example, 8 : 12 share a GCD of 4, so dividing both by 4 gives the simplest form 2 : 3. This calculator finds the GCD with the Euclidean algorithm and reduces the ratio for you in one step.
How do I solve a proportion like a : b = c : x?
Use cross-multiplication: in a : b = c : x the products across the equals sign are equal, so a × x = b × c. Rearrange to find the missing term — x = (b × c) ÷ a. For 2 : 3 = 10 : x that gives x = (3 × 10) ÷ 2 = 15. Leave any one box empty and the tool solves for it automatically.
What is a ratio in simplest form?
A ratio is in simplest (or lowest) form when its terms are whole numbers that share no common factor other than 1. For instance 50 : 100 simplifies to 1 : 2, and 1920 : 1080 simplifies to 16 : 9. A ratio like 7 : 13 is already in simplest form because 7 and 13 are coprime.
What is the difference between a ratio and a fraction?
A ratio compares quantities (a : b) while a fraction expresses a part of a whole (a/b), but numerically the ratio a : b equals the fraction a/b. So the ratio 3 : 4 is the fraction 3/4, which equals the decimal 0.75 and 75%. This calculator shows the equivalent decimal and percentage alongside the simplified ratio.
How do I scale a ratio up or down?
Multiply or divide every term by the same number so the comparison stays the same. To scale 2 : 3 up by 5 you get 10 : 15; to scale 16 : 9 for a wider image, multiply both terms by 120 to get 1920 : 1080. To find one scaled value when you know the target for another term, use the Solve proportion mode.

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