Octal is base 8 — a number system using digits 0 through 7. It was widely used in early computing because 3 binary bits map exactly to one octal digit. Today its most common use is Unix/Linux file permissions: chmod 755 means rwxr-xr-x (owner: 7=111₂, group: 5=101₂, others: 5=101₂).

How do you convert octal to decimal?

Multiply each digit by its power of 8 and sum the results. Example: 17₈ = 1×8 + 7×1 = 8 + 7 = 15₁₀ Place values from right: 8^0=1, 8^1=8, 8^2=64, 8^3=512, 8^4=4096...

How do you convert octal to binary?

Each octal digit maps directly to exactly 3 binary bits: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111 Example: 377₈ → 3=011, 7=111, 7=111 → 011111111₂ = 11111111₂ = 255₁₀

What is chmod 755 in binary?

chmod 755 = 7, 5, 5 in octal. 7 = 111₂ = rwx (read, write, execute) 5 = 101₂ = r-x (read, no write, execute) 5 = 101₂ = r-x So 755 means: owner has full access, group and others can read and execute but not write. 777 = full access for everyone (111 111 111₂).

Why did computers use octal instead of hex?

Early computers (PDP-8, IBM mainframes) used word sizes that were multiples of 3 bits (6, 12, 24, 36 bits), making octal the natural grouping — each octal digit represents exactly 3 bits. Later architectures moved to 8, 16, 32, 64-bit words, making hexadecimal (4 bits per digit) more convenient. Both are still used today.

Octal Mega — Convert Any Octal Number Instantly

The Octal Mega Calculator converts any octal number (base 8) to decimal, binary, and hexadecimal instantly. Enter any sequence of digits 0–7 — the result appears immediately with a place value breakdown, all base conversions, and a colour swatch for values up to 255. Octal is most commonly seen in U...

ENTER OCTAL NUMBER

OCTAL (digits 0–7 only)

0o

QUICK EXAMPLES

CONVERSIONS

DECIMAL (base 10)

BINARY (base 2)

1010₂

HEX (base 16)

0xA

PLACE VALUE BREAKDOWN

1 × 8 (8^1) + 2 × 1 (8^0) = 10

CSS GREYSCALE #0A0A0A

#0A0A0A

rgb(10, 10, 10)

OCTAL DIGIT TABLE (0–7)

oct

= 0

oct

= 1

oct

= 2

oct

= 3

oct

= 4

oct

= 5

oct

= 6

oct

= 7

Octal uses digits 0–7 only. Digit 8 and 9 do not exist in base 8.

BASE CONVERSION SUMMARY

Octal (8)12₈

Decimal (10)10₁₀

Binary (2)1010₂

Hex (16)0xA

OCTAL QUICK REFERENCE

7₈ = 7₁₀Max single octal digit

10₈ = 8₁₀8 decimal = 10 in octal

77₈ = 63₁₀2-digit max

100₈ = 64₁₀= 8² (power of 8)

377₈ = 255₁₀= 0xFF one byte

3 bits = 1 octalEach octal digit = 3 bits

Created with❤️byeaglecalculator.com

HOW TO USE

1
Type any octal number using only digits 0–7 into the input box. The 0o prefix is shown automatically. Any digit 8 or 9 is blocked — they don't exist in base 8.
2
The result panel shows the decimal value in green, binary in red, and hex in gold — all updating instantly as you type.
3
The place value breakdown shows each octal digit multiplied by its power of 8 (1, 8, 64, 512...). This confirms the conversion: digit × 8^position, summed from right to left.
4
For values up to 255, a CSS greyscale colour chip shows rgb(n,n,n). Click COPY for the full result string. Click SHARE for a ?n= URL that pre-loads your octal number for anyone who opens it.

WORKED EXAMPLE

Convert 377₈ to decimal, binary, and hex: 3×64 + 7×8 + 7×1 = 192 + 56 + 7 = 255₁₀ 255₁₀ = 11111111₂ = FF₁₆ 377₈ is the octal representation of one full byte at maximum value (255). Unix chmod 777 = read+write+execute for all = 7×64 + 7×8 + 7×1 = 511₁₀.

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Last updated: April 29, 2026 · Verified by EagleCalculator team

Octal Mega — Convert Any Octal Number Instantly

ENTER OCTAL NUMBER

HOW TO USE

WORKED EXAMPLE

FREQUENTLY ASKED QUESTIONS

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