Octal (base-8) uses digits 0-7. It was popular in old computing because it maps nicely to 3-bit groups. Each octal digit represents 3 bits.

Unix file permissions (chmod 755), some programming languages (0o prefix in Python, JavaScript), and legacy systems. Less common than binary or hex.

How do I convert octal to decimal?

Multiply each octal digit by its corresponding power of 8 (from right, starting at 8⁰, then sum. For example, 755 = (7×8²) + (5×8¹) + (5×8⁰) = 448 + 40 + 5 = 493.

How do I convert octal to binary?

Convert each octal digit to its 3-bit binary equivalent. For example, 7 = 111, 5 = 101. 755 in octal = 111101101 in binary.

What are Unix file permissions in octal?

Unix file permissions use 3 octal digits: owner, group, others. Each digit (0-7) represents read (4), write (2), execute (1). 755 = rwxr-xr-x.

Why is octal less common than hex?

Octal uses 3-bit groups, hex uses 4-bit groups. Hex is more compact (one hex digit = 4 bits vs one octal digit = 3 bits). Hex is more widely used in modern computing.

Octal Converter

Convert octal to decimal, binary, and hexadecimal. Essential for Unix file permissions and legacy systems.

Converter

Octal (Base 8)

Result

Decimal (Base 10): -
Binary (Base 2): -
Hexadecimal (Base 16): -

Conversion Guide

Conversion

O

Octal to Decimal

Sum of (digit × 8^position)

Multiply each digit by power of 8, sum results

B

Octal to Binary

Each octal digit = 3 bits

Convert each octal digit to 3-bit binary

Step-by-Step Scenario

Example Scenario

Octal

755

1

Assign Powers

From right: 8², 8¹, 8⁰ = 64, 8, 1

Assign power of 8 to each position

2

Calculate

7 × 64 = 448
5 × 8 = 40
5 × 1 = 5

493 (decimal)

Additional Examples

File Permissions

Octal: 755

Binary

111101101

Decimal

493

Simple Value

Octal: 10

Decimal

8

Binary

1000

Characteristics of Octal

Base-8 System

Octal uses base-8 with digits 0-7. Each octal digit represents 3 bits, making it useful for 3-bit groupings.

Unix Permissions

Commonly used for Unix file permissions (chmod). Each digit represents owner, group, and others permissions.

Real-Time Conversion

Convert octal instantly as you type. All number systems are calculated simultaneously for easy comparison.

Legacy Systems

Used in legacy systems and some programming languages. Less common than binary or hex in modern computing.

Important Notes

Octal (base-8) uses digits 0-7. Each octal digit represents 3 bits, making it useful for 3-bit groupings.
To convert octal to decimal: multiply each digit by its corresponding power of 8 (from right, starting at 8⁰, then sum.
To convert octal to binary: convert each octal digit to its 3-bit binary equivalent. 7 = 111, 5 = 101, etc.
Unix file permissions use octal: 755 = rwxr-xr-x (owner: read/write/execute, group: read/execute, others: read/execute).
Octal is less common than hexadecimal in modern computing. Hex uses 4-bit groups, octal uses 3-bit groups.

Frequently Asked Questions

Find answers to common questions about octal conversion.