Octal to Decimal Converter

What is Octal to Decimal Conversion?

Octal to decimal conversion changes a base-8 number (octal) into its base-10 equivalent (decimal). Octal uses eight digit symbols, 0 through 7, while decimal uses ten, 0 through 9. This conversion comes up most often when reading Unix/Linux file permissions, since chmod values such as 755 or 644 are written in octal.

For example, octal 52 equals decimal 42: 5×8¹ + 2×8⁰ = 5×8 + 2×1 = 40 + 2 = 42. For the reverse operation, see the Octal to Binary Converter. For the related base-16 conversion, see Hex to Decimal. Want to learn how to convert octal to decimal manually? Read the full step-by-step guide.

How to Convert Octal to Decimal Manually

The standard manual method uses base-8 positional notation:

Worked example: convert 52 to decimal

52₈

Position:   1   0
Octal digit: 5   2

5 × 8¹ = 5 × 8 = 40
2 × 8⁰ = 2 × 1 = 2

40 + 2 = 42

Result: 52₈ = 42₁₀

Manual multiplication works for short octal strings, but it is easy to make an arithmetic error on longer numbers — the converter above returns the exact result for any size of input.

Octal Digit Reference (0-7)

Octal is base 8, so each digit position can hold eight possible values, 0 through 7. Unlike hexadecimal, octal never needs letters — every digit already matches its decimal value.

Octal to Decimal Conversion Table

A quick reference for common octal values and their decimal equivalent:

Octal to Decimal in Unix/Linux File Permissions

The most common practical use of this conversion is reading chmod permission values. Each of the three octal digits covers owner, group, and others, where the bits stand for read (4), write (2), and execute (1):

Where Octal to Decimal Conversion Is Used

• Unix/Linux permissions: converting chmod values to decimal to understand their numeric size or compare them programmatically.
• System programming: some APIs and system calls expect a decimal value even when documentation states it in octal.
• Legacy systems: older computer architectures and file formats sometimes use octal notation that needs decimal interpretation.
• Computer science education: octal-to-decimal conversion is a standard example for teaching positional number systems.

For the related base-2 conversion, see the Octal to Binary Converter.

Negative Numbers and Two's Complement

This converter accepts octal integers without a sign. Simply writing a minus sign in front of an octal string (for example, -17) isn't how computers represent negative numbers, and it isn't a fixed, unambiguous format on its own.

Machines represent negative numbers using two's complement, which requires choosing a fixed bit width (such as 8, 16, or 32 bits) before the value's sign can be determined. Use the Two's Complement Calculator to interpret a signed value at a specific bit width.

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Frequently Asked Questions