How to Convert Hex to Octal: Steps & Examples

To convert hex to octal, replace each hex digit with its 4-bit binary equivalent, join the groups together, then regroup the binary digits into sets of three starting from the right and convert each 3-bit group to its octal digit. For example, hex 2F becomes binary 0010 1111, which regroups into 000, 101, and 111 — octal 57. So 2F₁₆ = 57₈. This guide covers why binary works as the bridge between the two bases, both conversion tables, a repeatable step-by-step process, and several verified examples of increasing difficulty.

What Are Hexadecimal and Octal?

Hexadecimal is a base-16 number system. Once its digits run out at 9, it borrows six letters for the remaining values:

Hex	Decimal
0-9	0-9
A	10
B	11
C	12
D	13
E	14
F	15

Octal is a base-8 number system. It uses only eight digit symbols — 0 through 7 — so a digit like 8 or 9 never appears in a valid octal number.

Both are positional number systems, like decimal: each digit's value depends on where it sits, representing a power of 16 or a power of 8 rather than a power of 10.

Why Binary Makes Hex-to-Octal Conversion Easy

Hexadecimal and octal don't share an obvious relationship on their own — one is base 16, the other base 8, and neither is a power of the other. But both are powers of 2, and that's what makes binary a convenient bridge between them:

• 16 = 2⁴, so one hexadecimal digit always represents exactly 4 binary bits.
• 8 = 2³, so one octal digit always represents exactly 3 binary bits.

Converting hex straight to binary is direct digit substitution with no carrying or borrowing, since hex's sixteen possible digit values (0-F) line up exactly with the sixteen values 4 bits can hold (0000-1111). The same is true going from binary to octal: eight possible values per octal digit (0-7) line up exactly with the eight values 3 bits can hold (000-111). Chaining those two direct substitutions — hex to binary, then binary to octal — avoids doing hex-to-octal place-value math directly. For a closer look at either half individually, see How to Convert Hex to Binary; binary-to-octal grouping is covered in the steps below and in the Binary to Octal Converter.

Hexadecimal to Binary Conversion Table

Hex	Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
A	1010
B	1011
C	1100
D	1101
E	1110
F	1111

Binary to Octal Conversion Table

Binary	Octal
000	0
001	1
010	2
011	3
100	4
101	5
110	6
111	7

Together, these two tables are the entire method: look up each hex digit's 4-bit group, join them, then look up each 3-bit group's octal digit.

How to Convert Hex to Octal Step by Step

1. Write the hex number and confirm every digit is 0-9 or A-F.
2. Convert each hex digit to its 4-bit binary equivalent using the hex-to-binary table above.
3. Join the binary groups together in the same order as the original digits.
4. Regroup the combined binary digits into sets of three, starting from the right.
5. Pad the leftmost group with leading zeros if it ends up with fewer than three bits.
6. Convert each 3-bit group to its octal digit using the binary-to-octal table above.
7. Join the octal digits in the same order as their groups.

Example: Convert 2F Hex to Octal

Step 1 — Hex to binary (4 bits per digit):
Hex digit:    2      F
4-bit group: 0010   1111

Combine: 00101111

Step 2 — Regroup into 3 bits from the right:
00101111 → 00 | 101 | 111
Pad the leftmost group: 000 | 101 | 111

Step 3 — Binary to octal:
000 = 0
101 = 5
111 = 7

2F₁₆ = 057₈ = 57₈

Checking the result through decimal confirms it: 2F₁₆ = (2 × 16) + (15 × 1) = 47₁₀, and 57₈ = (5 × 8) + (7 × 1) = 40 + 7 = 47₁₀. Both sides agree: 2F₁₆ = 47₁₀ = 57₈.

More Hex to Octal Examples

Hex	Binary (Normalized)	Octal
7	111	7
A	1010	12
1A	11010	32
FF	11111111	377
100	100000000	400

A couple of these are worth walking through, since they show details the 2F example doesn't:

Hex A — a single digit is 1010 in binary (no combining needed). Grouping from the right into 3-bit sets: 1 | 010. The leftover leftmost bit isn't a complete group, so it gets padded with zeros: 001 | 010 — octal 1 and 2, or 12. This shows why padding matters even for a single hex digit: its 4 bits don't divide evenly into groups of three, so the leftover bit needs two zeros added to complete its group.

Hex 100 — digit by digit: 1 → 0001, 0 → 0000, 0 → 0000, combined as 000100000000, normalized to 100000000 (three leading zeros dropped). Regrouped from the right into 3-bit sets: 100 | 000 | 000 → octal 4, 0, 0 → 400. The internal zeros stay exactly where they are; only the non-significant leading zeros were dropped during normalization.

Every row above was cross-checked by converting the same hex value to decimal and confirming the octal result equals the same decimal number — for instance, hex FF = 255 in decimal, and octal 377 also equals (3 × 64) + (7 × 8) + (7 × 1) = 255.

If you'd rather not do the digit-by-digit lookup by hand, the Hex Converter converts any hex value to decimal, binary, and octal at once, or use the Base Converter for a general base-16-to-base-8 conversion.

Hex to Octal Reference Table

A compact 0-F table doubles as a reminder of what A-F actually represent in decimal:

Hex	Decimal	Octal
0	0	0
1	1	1
2	2	2
3	3	3
4	4	4
5	5	5
6	6	6
7	7	7
8	8	10
9	9	11
A	10	12
B	11	13
C	12	14
D	13	15
E	14	16
F	15	17

Notice that hex and octal only match for values 0-7 — once a single digit reaches 8 in decimal, its octal representation needs two digits (10₈), while hex still needs only one (8₁₆).

Alternative Method: Hex to Decimal to Octal

Binary grouping isn't the only valid route — converting through decimal works too, and it's a useful way to double-check a binary-grouping result.

Step 1: Hex to decimal. Multiply each hex digit by its power-of-16 place value and add the results:

2F₁₆ = (2 × 16¹) + (15 × 16⁰) = 32 + 15 = 47₁₀

Step 2: Decimal to octal. Divide repeatedly by 8 and read the remainders from bottom to top:

47 ÷ 8 = 5 remainder 7
 5 ÷ 8 = 0 remainder 5

Reading bottom to top: 57

47₁₀ = 57₈

Both routes agree: 2F₁₆ = 57₈. For the full hex-to-decimal method, see How to Convert Hex to Decimal; for the decimal-to-octal half, see How to Convert Decimal to Octal.

Which Method Is Better?

For manual conversion, hex-to-binary-to-octal is usually more convenient because both steps are direct digit substitution — there's no multiplication, division, or remainder tracking involved, just table lookups. The hex-to-decimal-to-octal route is equally valid and involves the same underlying math either way, but it adds an extra arithmetic step (positional multiplication, then repeated division) instead of two substitution passes. Neither method is "faster" in every situation — for a single short hex number done by hand, the binary route tends to involve less arithmetic, but the decimal route doubles as a solid way to verify a binary-grouping answer, which is exactly how the 2F example was checked above.

Common Hex-to-Octal Conversion Mistakes

• Forgetting what A-F represent. A=10 through F=15 — mixing these up produces the wrong 4-bit group even before the octal regrouping starts.
• Using an incomplete or incorrect 4-bit mapping for hex. Each digit converts independently using the hex-to-binary table; a digit written with fewer than 4 bits shifts every bit after it once the groups are joined.
• Grouping binary into 4 bits instead of 3 when producing octal. Groups of four belong to hex, not octal — the binary-to-octal step always uses groups of three.
• Regrouping binary from the left instead of the right. Octal grouping must start at the rightmost bit; grouping from the left misaligns every 3-bit group and produces a different, incorrect value.
• Padding on the wrong side. Any padding needed to complete the leftmost 3-bit group goes on the left, never the right — padding on the right changes which power of 2 each bit represents.
• Dropping zeros that aren't leading. Only the non-significant zeros at the very front of the combined binary value can be removed; zeros in the middle or at the end are significant and change the value if dropped.
• Producing an octal digit of 8 or 9. A correct 3-bit group can only map to 0-7; seeing an 8 or 9 in a result means a grouping or lookup error happened earlier.
• Confusing hex-to-octal with octal-to-hex. The two conversions use the same tables but run in opposite directions — applying the wrong direction gives a plausible-looking but incorrect result. See How to Convert Octal to Hexadecimal for the reverse direction.
• Treating hex digits as decimal place values. Hex 2F isn't "twenty-nine and a half"; it's 2 × 16 + 15 = 47 in decimal. Applying base-10 place values to a hex number gives a wrong starting point for any further conversion.
• Making arithmetic mistakes in the decimal method. A slipped multiplication or a misread remainder in the repeated-division step produces an octal answer that looks plausible but doesn't match the binary-grouping result.

How to Check a Hex-to-Octal Answer

Two reliable ways to verify a conversion by hand:

• Recheck each group. Walk back through the hex number one digit at a time, confirm its 4-bit group, re-join the bits, and confirm the 3-bit regrouping from the right — matching each group against the tables above.
• Compare decimal values. Convert both the original hex number and your octal answer to decimal, as shown in the alternative method above — if they match, the conversion is correct.

The Hex Converter shows the decimal, binary, and octal equivalents for any hex input side by side, so you can cross-check a manual answer instantly.

Frequently Asked Questions

How do you convert hex to octal? Replace each hex digit with its 4-bit binary equivalent, join the groups together, then regroup the resulting binary digits into sets of three starting from the right, padding the leftmost group with zeros if needed. Convert each 3-bit group to its octal digit and join the results. For example, hex 2F becomes binary 00101111, which regroups into 000, 101, and 111 — octal 57.

Why can binary be used to convert hex to octal? Hexadecimal is base 16 (16 = 2⁴) and octal is base 8 (8 = 2³), so both bases are powers of 2. Binary sits between them as a common bridge: one hex digit always equals exactly 4 bits, and one octal digit always equals exactly 3 bits, so converting hex to binary and then regrouping into octal avoids the positional-value math that a direct base-16-to-base-8 conversion would otherwise require.

How many binary bits represent one hexadecimal digit? Exactly 4 bits. Hexadecimal has sixteen possible digit values (0-15, written as 0-9 and A-F), and 4 binary bits can represent exactly sixteen values (0000-1111), so the ranges match perfectly.

How many binary bits represent one octal digit? Exactly 3 bits. Octal has eight possible digit values (0-7), and 3 binary bits can represent exactly eight values (000-111), so the ranges match perfectly.

What is 2F hexadecimal in octal? 2F (base 16) equals 57 in octal. Converting digit by digit gives binary 0010 and 1111, combined as 00101111. Regrouped into 3-bit sets from the right (000, 101, 111), that's octal 0, 5, and 7 — or 57 once the leading zero is dropped. Checking through decimal confirms it: 2F₁₆ = 47₁₀ = 57₈.

Can you convert hex to octal through decimal? Yes. Convert the hex number to decimal using powers of 16, then convert that decimal value to octal using repeated division by 8. It produces the same result as the binary-grouping method — for example, hex 2F converts to decimal 47, and 47 converts to octal 57 either way.

What digits are valid in octal? Only 0 through 7. Octal is a base-8 number system, so a digit like 8 or 9 is never valid and has no 3-bit binary mapping.

What do A through F mean in hexadecimal? They're the six extra digit symbols hexadecimal needs beyond 0-9, representing decimal values 10 through 15: A=10, B=11, C=12, D=13, E=14, F=15.