Hexadecimal ↔ Octal Converter
Convert between hexadecimal (base 16) and octal (base 8) instantly
Hexadecimal and octal are both compact representations of binary data. Hexadecimal is used in memory addressing and color codes; octal is used in Unix/Linux file permissions (chmod). This converter helps you switch between these two number systems instantly.
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How It Works
The Hex-Octal Formula
How to convert between hexadecimal and octal
Formula
Hex → Decimal → Octal | Octal → Decimal → Hex
Variables
Convert to Decimal First
Both conversion directions use decimal as an intermediate step. Hex → Decimal → Octal, or Octal → Decimal → Hex. This ensures 100% accuracy.
Hexadecimal Digits
Hexadecimal uses digits 0-9 and letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15).
Octal Digits
Octal uses digits 0 through 7 only.
Note: Converting directly between hex and octal is possible by first converting to binary, then to the target base, but the decimal intermediate method is more straightforward for mental calculation.
Step-by-Step Example
Converting hexadecimal DEAD to octal
Convert hex DEAD to decimal
D=13, E=14, A=10, D=13
Apply powers of 16
D (13) × 16³ = 13 × 4096 = 53,248
E (14) × 16² = 14 × 256 = 3,584
Add: 53,248 + 3,584 = 56,832
A (10) × 16¹ = 10 × 16 = 160
Add: 56,832 + 160 = 56,992
D (13) × 16⁰ = 13 × 1 = 13
Add: 56,992 + 13 = 57,005 decimal
Convert decimal 57,005 to octal
57,005 ÷ 8 = 7,125 remainder 5
7,125 ÷ 8 = 890 remainder 5
890 ÷ 8 = 111 remainder 2
111 ÷ 8 = 13 remainder 7
13 ÷ 8 = 1 remainder 5
1 ÷ 8 = 0 remainder 1
Read remainders bottom to top: 1,5,7,2,5,5
Hexadecimal DEAD = Octal 157255
DEAD (hex) = 157255 (octal)
Reference Guide
| unit | value | note |
|---|---|---|
| Hex: FF | Octal: 377 | 255 decimal |
| Hex: DEAD | Octal: 157255 | 57,005 decimal |
| Hex: FACE | Octal: 175316 | 64,206 decimal |
| Hex: ABCD | Octal: 125674 | 43,981 decimal |
| Hex: 100 | Octal: 400 | 256 decimal |
| Hex: BEER | Octal: 137361 | 48,881 decimal |
| Hex: CAFE | Octal: 145376 | 51,966 decimal |
Understanding Hexadecimal and Octal
Why both number systems exist in computing
Hexadecimal uses 16 digits: 0-9 and A-F. Each hex digit represents exactly 4 binary bits. This makes it the most compact human-readable representation of binary data. One byte (8 bits) is represented by exactly 2 hex digits.
Best for: Memory addresses, color codes (RGB: #FF5733), assembly language, debugging, character encoding (Unicode)
Octal uses 8 digits: 0-7. Each octal digit represents exactly 3 binary bits. In early computing, when systems used 12-bit, 24-bit, or 36-bit word sizes, octal was more natural than hex because bits divided evenly into 3-bit groups.
Best for: Unix/Linux file permissions (chmod), PDP-11 and other legacy systems, when working with 3-bit groups
Hexadecimal is dominant in modern computing because byte-based architectures (8, 16, 32, 64 bits) divide cleanly into 4-bit groups. Octal remains relevant primarily for Unix file permissions (each permission set is 3 bits).
Best for: Use hex for memory, colors, and modern programming. Use octal for chmod and legacy systems.
Why Both Hexadecimal and Octal Are Used in Computing
Computers operate in binary, but binary is long and difficult for humans to read. Hexadecimal and octal provide a bridge: they are compact enough to be readable while maintaining a direct, exact relationship to binary. Why Hexadecimal Works So Well: A single hex digit represents exactly 4 binary bits (since 2⁴ = 16). Modern computers use 8-bit bytes (2 hex digits), 16-bit words (4 hex digits), 32-bit (8 hex digits), and 64-bit (16 hex digits). This perfect alignment is why hex became the standard. Why Octal Still Exists: Octal became important because some early computers (notably the PDP-11, which heavily influenced Unix) used 12-bit and 36-bit word sizes, where grouping by 2 bits (hex) didn't fit evenly but grouping by 3 bits (octal) did. Dennis Ritchie and Ken Thompson built Unix on the PDP-11, and the octal permission system stuck. Octal in chmod: File permissions in Unix are represented as three bits per user class: read (4), write (2), execute (1). Three bits conveniently fit into one octal digit (0-7). So 755 means read+write+execute for owner (7), read+execute for group (5), read+execute for others (5). Converting between hex and octal requires going through decimal (or binary) because they don't share a direct power relationship. This converter does the math automatically, giving you accurate results every time.
Key Features
💡 Pro Tips
- →Each hex digit = 4 bits, each octal digit = 3 bits. To convert quickly: hex to binary to octal, or octal to binary to hex.
- →In programming, hex is often prefixed with 0x (e.g., 0xDEADBEEF). Octal is sometimes prefixed with 0 in some languages (e.g., 0755 for chmod).
- →Web colors (CSS) are always hexadecimal (#FF5733). chmod file permissions are always octal (0755). This is a consistent convention across computing.
- →Memory addresses in debuggers (GDB) are displayed in hex. File permissions in Unix/Linux are displayed in octal when using commands like stat.
- →If you see a number with digits only 0-7 starting with 0, it's likely octal. If it contains A-F, it's hex. This is a quick way to identify the number system.
Common Mistakes
Using digits A-F in octal numbers
Octal only uses digits 0 through 7. Letters A-F are not valid in octal numbers. The converter will show an error if you try this.
Using digits 8-9 in octal numbers
Octal digits are only 0-7. Digits 8 and 9 are not valid in octal. Always check your octal input for these digits.
Assuming every number starting with 0 is octal
In some programming languages, a leading zero indicates octal (e.g., 0755). But in JavaScript and many other languages, leading zeros are ignored. Always check the context.
Confusing hex digit 'A' (10) with letter 'A'
In hex, A has a numeric value of 10. You cannot treat it as a letter — it must be included in the calculation as a digit.
Research & Citations
All factual claims on this page are sourced from peer-reviewed research
- [1]
Ritchie, D., Thompson, K. (1974). The UNIX Time-Sharing System. Communications of the ACM, 17(7), pp. 365–375.
Original Unix paper explaining octal permissions and number system choices
- [2]
Bell Laboratories (1972). PDP-11 Processor Handbook. Digital Equipment Corporation.
Documentation for the PDP-11 — the computer that made octal the default for Unix systems
- [3]
IEEE (1985). IEEE Standard for Binary Floating-Point Arithmetic (IEEE 754). IEEE.
Standard that cemented hexadecimal as the primary representation for binary data in computing
This calculator is a reference tool and does not constitute medical advice. For personalised sleep health guidance, consult a qualified healthcare provider.
Last updated: January 10, 2025
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Frequently Asked Questions
How do I convert hex to octal?
Convert hex to decimal first, then convert that decimal to octal. Or convert hex to binary (each hex digit = 4 bits), then group the binary into 3-bit groups and convert to octal. Our calculator does the work instantly.
How do I convert octal to hex?
Convert octal to decimal first, then convert that decimal to hex. Or convert octal to binary (each octal digit = 3 bits), then group the binary into 4-bit groups and convert to hex. Our calculator handles both directions instantly.
Why do we need both hex and octal?
Hexadecimal is used in modern computing because it aligns perfectly with 4-bit nibbles and 8-bit bytes. Octal is still used because Unix/Linux file permissions (chmod) are based on 3-bit groups, and octal digits fit that perfectly. Both have their place in computing history and practice.
Is there a direct conversion between hex and octal?
Yes — through binary. Hex → Binary (4 bits per digit) → group into 3-bit groups → Octal. Or Octal → Binary (3 bits per digit) → group into 4-bit groups → Hex. This is the most efficient direct method without using a calculator.
What is chmod 0755 in hex?
chmod 0755 (octal) is 1ED in hex. But chmod is always expressed in octal; you will never see chmod using hex. The octal representation is the standard because each digit directly encodes one of the three permission sets (owner, group, others).
What is hex DEADBEEF in octal?
DEADBEEF (hex) is 33653337357 in octal. This is a famous hex value used in debugging to mark uninitialised memory. Converting to octal produces a longer number because each hex digit (4 bits) expands to approximately 1.33 octal digits.