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Octal to Decimal Converter

Convert octal (base 8) numbers to decimal. Interpret Unix chmod values like 755.

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ASCII Letter A

Convert the ASCII code for uppercase A (65) across all bases.

Key values: Decimal 65 · Binary 1000001 · Hex 41

Byte Maximum

The largest value a single byte can hold (255).

Key values: Decimal 255 · Binary 11111111 · Hex FF

Hex Color Code

Convert a common hex color code (deep sky blue) to other bases.

Key values: Hex 00BFFF · Decimal 49151 · Binary nibbles

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Enter a number in any base to see it converted to binary, octal, decimal, hexadecimal, and any custom base 2-36.

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The Octal Number System

Octal (base-8) uses digits 0–7. Each position represents a power of 8:

(d_n d_{n-1} \ldots d_1 d_0)_8 = \sum_{i=0}^{n} d_i \times 8^i

Worked Example

Convert $755_8$ to decimal:

7 \times 8^2 + 5 \times 8^1 + 5 \times 8^0 = 448 + 40 + 5 = 493

Unix File Permissions

The most common modern use of octal is Unix file permissions. The command chmod 755 file sets three octal digits — one each for owner, group, and others:

Octal	Binary	Permissions
0	`000`	No access
1	`001`	Execute only
2	`010`	Write only
4	`100`	Read only
5	`101`	Read + execute
6	`110`	Read + write
7	`111`	Read + write + execute

So chmod 755 means: owner gets full access (7 = rwx), group gets read+execute (5 = r-x), others get read+execute (5 = r-x).

Why octal works here: Each permission group has 3 bits (read, write, execute), and $8 = 2^3$ — so one octal digit maps perfectly to one 3-bit permission group. This is the same reason hex maps to 4-bit nibbles.

Octal ↔ Binary Shortcut

Just as hex groups 4 bits, octal groups 3 bits:

755_8 \to \underbrace{111}_{7}\;\underbrace{101}_{5}\;\underbrace{101}_{5} = 111101101_2

This 3-bit grouping is why octal was popular on machines with 12-bit, 24-bit, or 36-bit word sizes (all multiples of 3). Modern 32-bit and 64-bit machines favor hex (4-bit grouping) instead.

Historical Context

Octal was the dominant shorthand for binary in early computing (1950s–1970s). The PDP-8 and other DEC machines used 12-bit words, which divide evenly into four octal digits. The C programming language's octal literal syntax (0755) dates from this era. Hex eventually replaced octal for most purposes as 8-bit bytes and 16/32-bit words became standard.

Frequently Asked Questions

How do you convert octal to decimal?

Multiply each octal digit by its positional power of 8 and sum. For example, 755 in octal = $7 \times 8^2 + 5 \times 8^1 + 5 \times 8^0 = 448 + 40 + 5 = 493$ in decimal.

What does chmod 755 mean in Unix?

Each digit represents permissions for owner, group, and others. 7 (binary 111) = read+write+execute, 5 (binary 101) = read+execute. So chmod 755 gives the owner full access and read+execute access to group and others.

Why is octal used for Unix file permissions?

Each permission group has 3 bits (read, write, execute), and $8 = 2^3$ , so one octal digit maps perfectly to one 3-bit permission group. This is the same reason hex maps to 4-bit nibbles.

How do you convert between octal and binary?

Each octal digit corresponds to exactly 3 binary digits. For example, 755 in octal becomes 111 101 101 in binary. Just convert each digit independently using the 3-bit groups.

Why has hexadecimal largely replaced octal in modern computing?

Modern computers use 8-bit bytes and 16/32/64-bit words, which are all multiples of 4 (not 3). Hex groups 4 bits per digit, aligning perfectly with byte boundaries. Octal was more natural for older machines with 12-bit or 36-bit word sizes.

Octal to Decimal Converter

Convert octal (base 8) numbers to decimal. Interpret Unix chmod values like 755.

Try an Example

ASCII Letter A

Byte Maximum

Hex Color Code

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Related conversion Variants

Binary to Decimal

Decimal to Binary

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ASCII Letter A

Byte Maximum

Hex Color Code

Convert a Number

The Octal Number System

Worked Example

Unix File Permissions

Octal ↔ Binary Shortcut

Historical Context

Frequently Asked Questions

How do you convert octal to decimal?

What does chmod 755 mean in Unix?

Why is octal used for Unix file permissions?

How do you convert between octal and binary?

Why has hexadecimal largely replaced octal in modern computing?