Octal to Decimal Converter - MathCalculators

Octal to Decimal converter is an online tool to convert the given input octal number to Decimal equivalent. You can use the below converter now!

What is Octal?

Octal number system is a base-8 numeral system that uses eight digits: from 0 to 7. Each position in an octal number represents a power of 8, starting from the right.

Example: 173 (octal)

Each octal digit can be represented as a sum of powers of 8:

173₈ = 1×8² + 7×8¹ + 3×8⁰ = 64 + 56 + 3 = 123₁₀

What is Decimal?

Decimal number system is a base-10 system that uses ten digits: from 0 to 9. It is the most widely used number system in human activities, from counting to finance and engineering. Each digits of decimal number counts a power of 10.

Example: 123 (decimal)

Each decimal digit is a sum of powers of 10, making it the most familiar way to express quantities.

123 = 1×10² + 2×10¹ + 3×10⁰

How to Convert Octal to Decimal ?

To convert an octal number to decimal equivalent, each digit in the octal number is multiplied by the appropriate power of 8, depending on its position. Starting from the rightmost digit, the powers of 8 increase from 0 upwards.

Decimal = (Octal Digit) * 8ⁿ

Where n is the position of the digit, starting from 0.

Steps to Convert Octal to Decimal

Write the octal number and note the position of each digit, starting from 0 on the rightmost digit.
Multiply each digit by (8^n) based on its position.
Add all the products to get the decimal equivalent.

Example Conversions

Let’s see a few examples to better understand how to convert numbers.

Example 1: How to convert 173 from octal to decimal number.

List the powers of 8 for each digit:
- (1 × 8² = 1 × 64 = 64)
- (7 × 8¹ = 7 × 8 = 56)
- (3 × 8⁰ = 3 × 1 = 3)
Add the results: (64 + 56 + 3 = 123)

So, 173 is equal to 123 (decimal).

Example 2: Convert 45 (octal) to decimal.

List the powers of 8 for each digit:
- (4 × 8¹ = 4 × 8 = 32)
- (5 × 80 = 5 × 1 = 5)
Add the results: (32 + 5 = 37)

So, 45 is equal to 37 (decimal).

Example 3: Convert 377 (octal) to decimal.

List the powers of 8 for each digit:
- (3 * 8² = 3 * 64 = 192)
- (7 * 8¹ = 7 * 8 = 56)
- (7 * 8⁰ = 7 * 1 = 7)
Add the results: (192 + 56 + 7 = 255)

So, 377 is equal to 255 (decimal).

Octal to Decimal Conversion Table/Chart

The table showing common octal numbers converted to their decimal equivalents:

Octal	Decimal
1	1
2	2
3	3
4	4
5	5
6	6
7	7
10	8
11	9
12	10
20	16
25	21
50	40

Online Octal to Decimal Converter

Online converter tool can help you to make the conversion fast and easy. It is useful while working with larger numbers or multiple conversions.

Steps to Use an Online Converter

Enter the octal number in the input field.
This tool will display the equivalent decimal number.