Ratio Calculator

Simplify ratios to lowest terms, solve proportions of the form a:b = c:x, and find missing values in a ratio equation. A free ratio and proportion calculator for recipes and scales.

How to Use

  1. Enter the ratio

    Input the known values of the proportion. Leave the unknown field empty.

  2. Choose calculation type

    Select proportion solving or ratio simplification.

  3. View result

    Click Calculate to see the missing value or the simplified ratio.

What is a ratio?

A ratio compares the relative sizes of two numbers and is written in the form a:b. Read as 'a to b', it tells you how many times larger a is than b. For example, the screen ratio 16:9 means the width is 16/9 times the height.

Two core ratio operations

  • Simplifying a ratio: dividing a ratio of large numbers like 1920:1080 by the greatest common divisor to reduce it to the simplest integer ratio, such as 16:9.
  • Solving a proportion: finding the unknown x in the equation a:b = c:x, where two ratios are equal.

It is widely used in everyday situations that involve 'so many to so many' relationships, such as ingredient amounts in recipes, the aspect ratio of photos and videos, map scales, and diluting solutions.

Calculation formula

Simplifying a ratio divides both numbers by their greatest common divisor (GCD).

simplified ratio = (a ÷ GCD) : (b ÷ GCD)

Example) 1920:1080 → the GCD is 120, so 1920÷120 : 1080÷120 = 16:9

Solving a proportion follows from the property that the product of the outer terms equals the product of the inner terms (a×x = b×c).

a:b = c:x → x = (b × c) ÷ a

Example) 2:3 = 4:x → x = (3 × 4) ÷ 2 = 6

Here a and b are the reference ratio, c is the matching value, and x is the unknown you want to find.

Frequently Asked Questions

What is a ratio?
A ratio is a way of expressing the relative sizes of two numbers. Written as a:b, it shows how large a is compared to b. For example, the screen ratio 16:9 means the width is 16/9 times the height.
Can a ratio be reduced to its simplest form?
Yes, the entered ratio is automatically divided by the greatest common divisor (GCD) to give the simplest integer ratio. For example, 1920:1080 divided by the GCD of 120 becomes 16:9, and 12:8 reduces to 3:2.
How do I find the unknown in a proportion?
In a:b = c:x, calculate x = b×c/a. For example, if 2:3 = 4:x then x = 3×4/2 = 6. Enter the three values and the remaining one is found automatically.
Can decimal or fractional ratios be simplified too?
Yes, a ratio containing decimals such as 1.5:2.5 is converted to integers by multiplying by a power of 10 matching the number of decimal places, then reduced by the greatest common divisor. So 1.5:2.5 simplifies to 3:5.
What does the decimal ratio mean?
The decimal ratio expresses a÷b as a real number, which is useful when you want to see the ratio as a single scale factor. For example, the decimal ratio of 16:9 is about 1.7778, calculated to six decimal places.
How is solving a proportion different from simplifying a ratio?
Simplifying a ratio reduces a single ratio a:b to a simpler integer ratio, while solving a proportion finds the missing value x in the relationship a:b = c:x where two ratios are equal. You can select the mode to perform either calculation.
What happens if the denominator b is 0 or a is 0?
Since you cannot divide by 0 in a ratio, if a is 0 no meaningful ratio can be formed and it is treated as 0:0. To compute x = b×c/a when solving a proportion, the reference value a must be a non-zero number.
Where are ratio calculations used in real life?
Proportions are used to scale recipe ingredient ratios to the number of people, to convert real distances using a map scale, to fit photos and videos to aspect ratios such as 16:9 or 4:3, and to dilute solutions at a fixed ratio.
Verified 2026 formulas

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