Hex to Octal Converter

Paste a hex value into the Hex Input box and the Hex to Octal Converter works out its base-8 equivalent for you, using binary as the bridge between the two. Click Convert and read the octal digits straight from the Octal Output field. If you're documenting file permissions or embedded register values in octal, the binary to octal converter converts a binary string in seconds.

Get Instant Results: Convert Hexadecimal to Octal

How to Use the Hex to Octal Converter

The hexadecimal to octal converter is built for speed and accuracy. Type or paste a hex value — using digits 0–9 and letters A–F — into the input box, and the octal result appears as soon as you type, with no button required (though a Convert button is there too). Put multiple hex values on separate lines to convert a whole batch in one pass, each line resolving independently. Use the Copy button to grab the result, the Group digits option to break a long octal string into readable chunks, and the Clear button to start over.

If you enter a character outside 0–9 and A–F, the converter shows a clear error message identifying the invalid line rather than guessing at a partial result — this hex to octal converter is built to convert whole hexadecimal integers precisely, not to silently accept malformed input.

Infographic showing how to convert hexadecimal 3D9 to octal by going through binary: expand each hex digit to 4 bits, regroup the combined bits into 3s, then convert each group to get octal 1731 — Hex to Octal Converter: 3D9 = 1731

How Hexadecimal Converts to Octal: Two Manual Methods

Method 1: Hex → Decimal → Octal

The most intuitive route for a hexadecimal to octal converter to explain by hand goes through decimal as an intermediate step. Each hex digit represents a power of 16: Enter two hex values and pick an operation in the hex bitwise calculator to see the combined result instantly.

Hexadecimal to Decimal Formula

$$Decimal = \sum_{i=0}^{n} d_i \times 16^{i}$$

Where d_i is the value of the i^th hex digit, counting from the rightmost (least significant) digit, and n is the digit count minus one.

Once you have the decimal equivalent, convert it to octal by repeated division by 8:

Divide the decimal number by 8.
Record the remainder (0 to 7) — this is the next octal digit.
Continue dividing the quotient by 8 until it reaches zero.
Write the remainders in reverse order for the final octal number.

Method 2: Hex → Binary → Octal (the Faster Route)

For most computing contexts, the fastest way to convert hexadecimal to octal is to use binary as the bridge between the two — which is exactly what this hex to octal converter does internally:

Expand each hex digit to its 4-bit binary nibble (since 16 is 2⁴) — see the hex-to-binary nibble table on the Hex to Binary Converter page for the full digit-by-digit mapping.
Re-group the resulting binary string into 3-bit chunks (since 8 is 2³), padding with leading zeros on the left if the total bit count isn't a multiple of 3.
Convert each 3-bit chunk to its octal digit to build the final octal result.

Hex → Binary → Octal Pattern

hex digit (4 bits each) → full binary string → re-grouped in 3s → octal digit per group

Worked Example: Converting 2A from Hex to Octal

Using the Decimal Bridge

Step 1 — Hex to decimal: $$2A_{16} = (2 \times 16^1) + (10 \times 16^0) = 32 + 10 = 42_{10}$$
Step 2 — Decimal to octal: $$42 \div 8 = 5\ \text{remainder}\ 2$$ $$5 \div 8 = 0\ \text{remainder}\ 5$$
Writing the remainders in reverse gives 52₈. Paste your decimal code points into the decimal to text converter and read the decoded text as soon as it updates.

Using the Binary Bridge

Step 1 — Hex to binary: 2A₁₆ = 0010 1010₂ (two nibbles, one per hex digit).
Step 2 — Re-group into 3-bit chunks from the right: 0010 1010 → 010 101 010 (padding the leftmost group with a zero to complete a 3-bit chunk).
Step 3 — Convert each chunk to octal: 010 = 2, 101 = 5, 010 = 2 → 52₈.

Both methods agree: 2A₁₆ = 52₈ — a useful check that confirms the binary-bridge shortcut produces the same result as the slower decimal route.

A Second Worked Example: ABCD to Octal

Hex to decimal: ABCD₁₆ = 43981₁₀
Decimal to octal: 43981 ÷ 8 = 5497 r5; 5497 ÷ 8 = 687 r1; 687 ÷ 8 = 85 r7; 85 ÷ 8 = 10 r5; 10 ÷ 8 = 1 r2; 1 ÷ 8 = 0 r1
Reading remainders in reverse: ABCD₁₆ = 125715₈

Hex to Octal Conversion Table (Quick Reference)

Sample Values: Common Hex to Octal Equivalents

Use this table for a quick lookup across hexadecimal, binary, octal, and decimal — the four number systems that come up most often together in programming and computer science:

Hexadecimal	Binary	Octal	Decimal
0	0000	0	0
F	1111	17	15
2A	00101010	52	42
1A3	000110100011	643	419
FF	11111111	377	255
100	000100000000	400	256

This table demonstrates how hexadecimal numbers converted to octal provide an equivalent representation of the same underlying value in a different base — useful for quick lookups when you're spot-checking a conversion by hand, such as when converting hex to octal for Unix file permission bits (e.g., a permission mode like 755 in octal).

Hexadecimal & Octal: Key Concepts

What Is Hexadecimal?

Hexadecimal (base-16) uses sixteen symbols: 0–9 and letters A–F.
Widely used in programming, debugging, memory addressing, and color codes.
Compact for representing binary data — one hex digit covers exactly four bits.

What Is Octal?

Octal (base-8) uses digits 0–7 only.
Common in legacy computing and, still today, in Unix/Linux file permission notation, where each of the three permission groups (owner, group, other) maps to one octal digit.
Octal is less compact than hex for representing the same value, but each octal digit maps cleanly to exactly three binary digits, which is why it was historically popular on machines with word sizes divisible by three bits.

Where Hex-to-Octal Conversion Shows Up

Unix and Linux file permissions: permission bits are conventionally written in octal, so converting from a hex value you've derived elsewhere often means this exact hex-to-octal step.
Assembly-level debugging: some older toolchains and debuggers display memory or register values in octal rather than hex.
Low-level file format interpretation: older binary file formats and some embedded systems still specify fields in octal.
Education: teaching how positional number systems relate to one another, and why binary is a convenient bridge between any two power-of-two bases.

Hex to Octal Conversion: Frequently Asked Questions

How do I convert a hexadecimal number to base 8?
Expand each hex digit to its 4-bit binary nibble, concatenate the bits, re-group them into 3-bit chunks (padding on the left if needed), then convert each chunk to its octal digit. This converter does exactly that automatically.
Is there a formula for hex to octal conversion?
There's no single-step formula the way there is for converting a single digit — the practical approach is always to bridge through binary (fast) or decimal (easier to explain by hand).
Can I convert more than one hex value at a time?
Yes — put each value on its own line in the input box and every line converts independently, in order.
Is this converter accurate for very large hex values?
Yes. It uses arbitrary-precision arithmetic (JavaScript BigInt), so it isn't limited to the 32-bit or 64-bit integer ranges that trip up many calculators.
What if my hex input has spaces or invalid characters?
Spaces between digits are ignored automatically. Any character outside 0–9 and A–F shows an error message telling you which line is invalid.
What's the fastest manual conversion method?
Hex → binary → octal is fastest once you know the nibble table by heart. Hex → decimal → octal is slower but often easier to follow when explaining the conversion to someone else.