Ratio Calculator – Find, Solve, and Convert Ratios
Calculate, reduce, scale, or compare ratios using the ultimate ratio calculator below.
How to Calculate Ratios
A ratio is a comparison of the size of one number to another number and can compare the size of an object, a quantity, an angle, or another unit of measure.
A ratio is expressed as one number to another number and is written in the form A:B. For example, the ratio of 3 to 2 can be written 3:2.
How to Solve a Ratio in a Proportion
Given a proportion with one ratio and one part of an equivalent ratio, it is possible to solve the proportion’s missing value. A proportion is an equation showing two equivalent ratios.
Start by finding the decimal value for the complete ratio. Do this by dividing the left side by the right side, or use our ratio to decimal calculator.
Transform the incomplete ratio into a fraction by placing the left side on top of the right side.
Next, form an equation for the proportion with the decimal on one side and the fraction on the other side.
decimal value = known valueunknown value
Finally, solve the equation to find the missing value in the second ratio of the proportion.
For example, let’s solve for x in the proportion 6:4 = 12:x
Start by converting 6:4 to decimal form
6:4 = 64 = 1.5
Then put 12:x into fraction form
12:x = 12x
Then, put the converted values into an equation representing the proportion and solve
1.5 = 12x
121.5 = x
8 = x
The resulting proportion is thus 6:4 = 12:8
How to Compare Ratios
How do you know if two ratios are equivalent or if one is larger than the other? The answer is to compare them using a few simple steps.
The first step is to convert both ratios to decimal by dividing each’s left side by the right side.
Finally, compare the decimal values to determine if the ratios are equal or if one is larger than the other.
For example, let’s compare 3:2 and 5:3
Start by converting to decimal form
3:2 = 32 = 1.5
5:3 = 53 = 1.67
Then compare the decimal values
1.5 < 1.67
Thus, 3:2 is less than 5:3
How to Reduce a Ratio
Ratios can be reduced just like a fraction can be reduced. In fact, the process of simplifying a ratio is the exact same as simplifying a fraction.
To reduce a ratio, find the greatest common factor of the left and right sides. The greatest common factor is the largest number that can be evenly divided into both the left and right sides.
Then, divide the left and right sides by the greatest common factor. The result is a reduced ratio in the simplest form that is equivalent to the original.
For example, let’s reduce 6:4
Start by finding the greatest common factor of both 6 and 4
- Factors of 6: 1, 2, 3, 6
- Factors of 4: 1, 2, 4
The greatest common factor of both 6 and 4 is 2
Divide the left and right side by the common factor
62 = 3
42 = 2
6:4 = 3:2
Thus, the reduced ratio is 3:2 shown by the proportion 6:4 = 3:2
How to Scale a Ratio
Ratios can be scaled larger or smaller in the same proportion to the original. To scale it, simply multiply the left and right sides by the scaling factor.
For example, let’s scale 7:4 by a factor of 2
Multiply the left and right side by 2
7 × 2 = 14
4 × 2 = 8
Thus the scaled ratio is 14:8
You might also be interested in our scale calculator.
Bonus: How to Convert a Ratio to a Percentage
We’ve shown how to convert a ratio to a decimal and to a fraction, but did you know that you can also convert one to a percentage? You can convert to a percentage in a few easy steps.
First, convert it to a decimal by dividing the left side by the right side.
Then, convert the decimal to percentage by multiplying it by 100. Don’t forget to add the percent symbol (%).
For example, let’s convert 3:2 to a percentage
Convert 3:2 to a decimal
3:2 = 3 ÷ 2 = 1.5
Multiply the decimal value to 100
1.5 × 100 = 150%
Thus, 3:2 converted to a percentage is 150%. You can also use our ratio to percentage conversion calculator to convert more easily.