Convert hexadecimal numbers to octal instantly. Enter any hex value and get the exact octal, decimal, and binary equivalents with step-by-step conversion shown.
✓
Verified: IEEE — Positional Number Systems (Base 8 and Base 16) — April 2026
0x
Please enter a valid value.
Enter hex digits: 0-9 and A-F (case insensitive)
Convert hexadecimal numbers to octal instantly. Enter any hex value and get the exact octal, decimal, and binary equivalents with step-by-step conversion shown.
Octal Result
—
Was this calculator helpful?
✓ Thanks for your feedback!
Sources & Methodology
✓ Formulas and reference data verified against authoritative sources listed below.
NIST reference for mathematical constants and number system conversions
Methodology: Hex to Octal via binary bridge: each hex digit converts to 4 binary bits (nibble). Binary string is then grouped into 3-bit groups from the right, each group becoming one octal digit. Alternatively: Hex to Decimal = sum(digit x 16^n), Decimal to Octal = repeated division by 8.
⏱ Last reviewed: April 2026
How to Convert Hexadecimal to Octal
Converting hexadecimal (base 16) to octal (base 8) is most cleanly done via binary as an intermediate step. Since one hex digit = 4 binary bits, and one octal digit = 3 binary bits, converting through binary avoids messy arithmetic. The process: hex to binary (nibble table), then binary to octal (triplet grouping).
Step 1 — Hex to Binary (Nibble Method)
Each hexadecimal digit maps to exactly 4 binary bits. Replace each hex digit with its 4-bit equivalent: 0=0000, 1=0001... 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111. Concatenate all nibbles to form the full binary string.
Step 2 — Binary to Octal (Triplet Method)
Group the binary string into groups of 3 bits from the right, padding with leading zeros if needed. Each 3-bit group maps to one octal digit: 000=0, 001=1, 010=2, 011=3, 100=4, 101=5, 110=6, 111=7. Concatenate the octal digits for the final result.
Octal (base 8) was historically used in early minicomputers and Unix/Linux file permissions. Unix chmod permissions use 3-digit octal: 777 means rwxrwxrwx (all permissions), 644 means rw-r--r-- (owner read/write, others read-only). Each octal digit represents 3 permission bits exactly.
Hex to Binary (nibble table) → Group binary into 3-bit groups → Each triplet = one octal digit
Example: 0x1A = 0001 1010 (binary) = 00 011 010 (triplets) = 032 (octal). Verify: 3x8 + 2 = 26 = 0x1A. Alternatively: hex to decimal via positional values, then decimal to octal via repeated division by 8.
Hex to Octal Quick Reference
Hex
Binary
Octal
Decimal
0x0F
0000 1111
017
15
0x1A
0001 1010
032
26
0x3F
0011 1111
077
63
0xFF
1111 1111
377
255
0x100
0001 0000 0000
0400
256
0x1FF
0001 1111 1111
0777
511
0x200
0010 0000 0000
01000
512
0xFFF
1111 1111 1111
07777
4095
💡 Unix Permissions Tip: Linux/Unix file permissions use octal notation: chmod 755 means 7=111 (rwx owner), 5=101 (r-x group), 5=101 (r-x others). Each octal digit is exactly 3 binary bits for read (r=4), write (w=2), execute (x=1). Converting chmod values: hex is rarely used for permissions, but the binary bridge to octal makes the permission bits visible.
Frequently Asked Questions
The easiest method: convert hex to binary using the nibble table (each hex digit = 4 bits), then group binary into triplets from the right (each triplet = one octal digit). Example: 0xAF = 1010 1111 (binary) = 010 101 111 = 257 (octal).
0x100 = 0400 in octal = 256 in decimal. Binary: 0001 0000 0000. Triplets: 001 000 000 000 = 1000 octal. Written as 0400 with the leading zero octal prefix convention.
Direct hex-to-octal arithmetic requires dividing and tracking remainders which is error-prone. Going through binary is easier because the nibble (4 bits = 1 hex digit) and triplet (3 bits = 1 octal digit) relationships make conversion mechanical and verifiable.
Octal numbers are prefixed with 0 or 0o depending on context. In C and Unix: 0377 means octal 377. In Python 3: 0o377. In assembly: 377Q or 377O. The leading zero convention comes from C, where any integer literal starting with 0 is interpreted as octal.
One hex digit (4 bits) does not map evenly to octal digits (3 bits each). Two hex digits (8 bits) map to approximately 2.67 octal digits, so the conversion is not 1-to-1. This is why the binary bridge method is preferred.
Binary (base 2): uses 0 and 1, the native language of computers. Octal (base 8): uses digits 0-7, was popular in early computing for its easy mapping to 3-bit groups. Hexadecimal (base 16): uses 0-9 and A-F, is the modern standard for representing binary data compactly (1 hex digit = 4 bits).
Convert your octal result back to decimal: multiply each octal digit by 8 raised to its position power. Then verify it equals the decimal value of your original hex number. Example: 0x2B = 43 decimal. Octal = 053. Verify: 5x8 + 3 = 43. Correct.