Ratio Calculator

Written byOleh Soloninupdated 5 October 2026

Result

x12
Simplified ratio3 : 4
Scale factor3

Cross multiplication, done for you

Solve a : b = c : x for the missing value, with the ratio reduced to its simplest form and the scale factor shown.

Proportions turn up constantly outside maths class: scaling a recipe, resizing an image without distorting it, mixing paint or fuel, reading a map scale.

The method is cross multiplication — multiply the outer pair and the inner pair, then solve. Getting the order of the terms wrong is the usual source of a wrong answer.

How to use

Enter the two known terms of the ratio.
Enter the third; the calculator finds the fourth.
Read the missing value, the ratio in lowest terms and the scale factor.

Ratio, proportion and scale

A ratio of 3 : 4 scaled three times becomes 9 : 12, and that three is the scale factor. The simplified form does not move, because a ratio describes a relationship rather than any particular pair of quantities.

The same arithmetic underlies recipes, drawing scales and dilutions. Taking a recipe from four servings to six multiplies every ingredient by 1.5, and the ratios between them stay exactly where they were.

Worked out with this calculator. Scaling never changes the simplified form: 3 : 4 in the first two rows and 16 : 9 in the third.
Ratio	Scale	Result
3 : 4	×3	9 : 12
3 : 4	×0.5	1.5 : 2
16 : 9	×120	1920 : 1080

What this calculator shows

The missing fourth term of the proportion
The ratio reduced to lowest terms
The scale factor between the two sides

What to keep in mind

Solves a : b = c : x, so the unknown is always the fourth term.
This solver does not accept zero in the first two terms; that is its own restriction, not a rule that ratios cannot contain zero.

FAQs

How does cross multiplication work?

In a : b = c : x, multiply a by x and b by c, then set them equal. Solving for x gives x = b × c ÷ a.

What is a ratio in simplest form?

One where both terms share no common factor. 12 : 16 reduces to 3 : 4, which describes the same relationship in smaller numbers.

Are ratios and fractions the same thing?

Closely related but not identical. 3 : 4 as a fraction is 3/4 when comparing part to whole, but a ratio can also compare two separate quantities that never form one total.

Where is this used in everyday life?

Map scales, screen aspect ratios, recipe scaling, fuel mixes and currency conversion are all proportion problems wearing different clothes.

What is the missing term in 3 : 4 = 9 : x?

Twelve. The scale factor is 9 ÷ 3 = 3, and the same factor applies to the second term: 4 × 3 = 12.

How is a ratio different from a fraction?

In form and in meaning. The fraction 3/4 is the number 0.75; the ratio 3 : 4 describes two quantities of any size whose quotient happens to be 0.75.

Worked example

Scaling a photo

Input: 3 : 4 = 9 : x

Output: x = 12

Note: A 3:4 image widened to 9 units must be 12 tall to keep its shape. Any other height stretches it.

Useful links

All tools in Math & Statistics

Ratio Calculator

Result

Related tools

Proportion Calculator

Percentage Calculator

Recipe scaler: adjust ingredients for more or fewer servings

Aspect Ratio Calculator

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