Ratio Calculator

A online calculator to calculate ratio of given numbers.


Result

Ratio of given numbers will be displayed below.

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Understanding Ratio Calculation

What is a Ratio?

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.

Formula for Calculating a Ratio

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:

\( a : b : c = \frac{a}{\text{GCD}(a, b, c)} : \frac{b}{\text{GCD}(a, b, c)} : \frac{c}{\text{GCD}(a, b, c)} \)

Pro Tip

Click Here to know how to calculate HCF or GCD.

Steps to Calculate a Ratio

1

Identify the Numbers: Gather the numbers you want to compare (e.g., 10 and 20, or 4, 8, and 12).

2

Divide Each Number by the GCD: This simplifies the ratio to its lowest terms.

3

Write the Ratio: Express the simplified numbers in the form \(a:b\) (for two numbers) or \(a:b:c\) (for three numbers).

Examples to find Ratio

Here, Ratio of two numbers and three numbers are calculated.

Two Numbers Example

Example: Calculate the ratio of 10 and 20.
- Step 1: Numbers are 10 and 20.
- Step 2: Find the GCD of 10 and 20. The GCD is 10.
- Step 3: Divide each number by the GCD: \( 10 \div 10 = 1 \), \( 20 \div 10 = 2 \).
- Step 4: The simplified ratio is 1:2.
So, the ratio of 10 to 20 is 1:2.

Three Numbers Example

Example: Calculate the ratio of 4, 8, and 12.
- Step 1: Numbers are 4, 8, and 12.
- Step 2: Find the GCD of 4, 8, and 12. The GCD is 4.
- Step 3: Divide each number by the GCD: \( 4 \div 4 = 1 \), \( 8 \div 4 = 2 \), \( 12 \div 4 = 3 \).
- Step 4: The simplified ratio is 1:2:3.
So, the ratio of 4, 8, and 12 is 1:2:3.

Frequently Asked Questions (FAQ)

What is the difference between a ratio and a fraction?

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.

Can I calculate a ratio with negative numbers?

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).

What happens if I enter a zero in the second or third number?

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.

How does the calculator make a ratio larger or smaller?

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).

Why is the GCD important in ratio calculation?

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.