Ratio
A online calculator to calculate ratio of given numbers.
Ratio of given numbers will be displayed below.
A ratio is a mathematical expression that compares two or more quantities, showing how many times one quantity is contained within another. Ratios are often used in everyday life, such as in recipes (e.g., 2:1 flour to water), finance (e.g., debt-to-income ratio), or geometry (e.g., aspect ratios). They can involve two numbers (e.g., 2:3) or more (e.g., 1:2:3).
Our ratio calculator simplifies this process by allowing you to input two or three numbers, compute the simplified ratio, and even scale it larger or smaller.
A ratio compares numbers by dividing them by their greatest common divisor (GCD) to simplify the expression. For two numbers \(a\) and \(b\), the ratio is:
\( a : b = \frac{a}{\text{GCD}(a, b)} : \frac{b}{\text{GCD}(a, b)} \)
For three numbers \(a\), \(b\), and \(c\), the ratio extends to:
\( a : b : c = \frac{a}{\text{GCD}(a, b, c)} : \frac{b}{\text{GCD}(a, b, c)} : \frac{c}{\text{GCD}(a, b, c)} \)
Click Here to know how to calculate HCF or GCD.
Identify the Numbers: Gather the numbers you want to compare (e.g., 10 and 20, or 4, 8, and 12).
Divide Each Number by the GCD: This simplifies the ratio to its lowest terms.
Write the Ratio: Express the simplified numbers in the form \(a:b\) (for two numbers) or \(a:b:c\) (for three numbers).
Here, Ratio of two numbers and three numbers are calculated.
A ratio compares two or more quantities (e.g., 2:3) and can be written in different forms, such as 2 to 3. A fraction represents a part of a whole (e.g., \( \frac{2}{3} \)) and is a single number. However, a two-number ratio like 2:3 can be expressed as the fraction \( \frac{2}{3} \) for certain calculations.
Yes, our calculator handles negative numbers. However, for simplicity, the final ratio is displayed with positive values, and a note is added to indicate if the original numbers were negative (e.g., -2:-4 simplifies to 1:2 with a note).
The calculator does not allow zeros in the second or third numbers because ratios are undefined when dividing by zero. You’ll see an error message asking you to enter non-zero values for those fields.
To make a ratio larger, the calculator multiplies each part of the simplified ratio by a positive number you provide (e.g., scaling 1:2 by 3 gives 3:6). To make it smaller, it divides each part by a positive number (e.g., scaling 3:6 by 3 gives 1:2).
The greatest common divisor (GCD) is used to simplify the ratio to its lowest terms. For example, in the ratio 10:20, the GCD is 10, so dividing both numbers by 10 gives the simplified ratio 1:2, making it easier to understand and work with.