Decimal to Octal Converter

Convert decimal (base-10) numbers to octal (base-8) instantly with a step-by-step division breakdown. Supports batch conversion and reverse direction.

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Decimal → Octal

Common Decimal to Octal Values

8
= 10
63
= 77
64
= 100
100
= 144
255
= 377
420
= 644
493
= 755
511
= 777
512
= 1000
1023
= 1777
2047
= 3777
4095
= 7777

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Bidirectional

Convert decimal to octal and octal back to decimal. Click the Swap button to switch direction instantly.

Step-by-Step

See the full division-remainder method showing each step of converting a decimal number to its octal representation.

Batch Conversion

Convert multiple decimal values at once. Enter space or comma-separated values for fast bulk conversion.

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Frequently Asked Questions

How do I convert decimal to octal?
Divide the decimal number by 8 repeatedly, recording each remainder. Read the remainders from bottom to top. For example, 125: 125 ÷ 8 = 15 remainder 5, 15 ÷ 8 = 1 remainder 7, 1 ÷ 8 = 0 remainder 1. Reading bottom-to-top: 175 in octal.
What is the octal equivalent of decimal 255?
Decimal 255 in octal is 377. This is significant in computing as 255 is the maximum value of an unsigned 8-bit byte. In Unix permissions, chmod 377 would mean write+execute for owner, and full permissions for group and others.
Why is octal used in computing?
Each octal digit maps to exactly 3 binary bits, making it a compact way to represent binary data. It's commonly used in Unix/Linux file permissions (chmod 755, chmod 644), older programming languages, and some assembly code. It provides a human-readable shorthand for groups of 3 binary digits.
What are common Unix permission values in octal?
Common permissions: 755 (rwxr-xr-x, directories & executables), 644 (rw-r--r--, regular files), 777 (rwxrwxrwx, full access), 600 (rw-------, private files), 700 (rwx------, private directories). Each digit represents owner, group, and others respectively.
Can I convert octal back to decimal?
Yes! Click the "Swap Direction" button to switch to Octal → Decimal mode. To manually convert, multiply each octal digit by 8 raised to the power of its position (starting from 0 on the right), then sum all values. For example, octal 175 = (1×64) + (7×8) + (5×1) = 125.