How to convert hex to octal by hand
Example 1: 1F in hex is 37 in octal
Step 1: Hex to binary: write each digit as 4 bits
Because 16 = 2⁴, every hex digit maps to exactly 4 binary digits. Drop any leading zeros at the end.
| Hex digit | Value | 4 bits |
|---|---|---|
| 1 | 1 | 0001 |
| F | 15 | 1111 |
0001 1111 → 11111
Step 2: Binary to octal: group the bits in 3s
Because 8 = 2³, every 3 bits make exactly one octal digit. Start from the right and pad the leftmost group with zeros if needed.
| 3-bit group | Value | Octal digit |
|---|---|---|
| 011 | 3 | 3 |
| 111 | 7 | 7 |
011 111 → 37
Example 2: 1ED in hex is 755 in octal
Step 1: Hex to binary: write each digit as 4 bits
Because 16 = 2⁴, every hex digit maps to exactly 4 binary digits. Drop any leading zeros at the end.
| Hex digit | Value | 4 bits |
|---|---|---|
| 1 | 1 | 0001 |
| E | 14 | 1110 |
| D | 13 | 1101 |
0001 1110 1101 → 111101101
Step 2: Binary to octal: group the bits in 3s
Because 8 = 2³, every 3 bits make exactly one octal digit. Start from the right and pad the leftmost group with zeros if needed.
| 3-bit group | Value | Octal digit |
|---|---|---|
| 111 | 7 | 7 |
| 101 | 5 | 5 |
| 101 | 5 | 5 |
111 101 101 → 755
Hex to Octal conversion table
| Hex | Octal | Decimal |
|---|---|---|
| 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 | 10 | 8 |
| 9 | 11 | 9 |
| A | 12 | 10 |
| B | 13 | 11 |
| C | 14 | 12 |
| D | 15 | 13 |
| E | 16 | 14 |
| F | 17 | 15 |
| 10 | 20 | 16 |
| 20 | 40 | 32 |
| 40 | 100 | 64 |
| 64 | 144 | 100 |
| 80 | 200 | 128 |
| FF | 377 | 255 |
| 100 | 400 | 256 |
| 200 | 1000 | 512 |
| 3E8 | 1750 | 1000 |
| 400 | 2000 | 1024 |
Where this conversion comes up
- C and C++ character escapes: '\x41' and '\101' are both the letter A, one written in hex and one in octal.
- Coursework that asks you to convert between hex and octal without going through decimal.
Frequently asked questions
What is the quickest way to convert hex to octal by hand?
Go through binary. Write each hex digit as 4 bits, then regroup the bits in threes from the right and write each group as an octal digit. It avoids any long division.
Can I convert negative numbers?
Yes. Put a minus sign in front and it is kept in the result, for example -1F becomes -37. The converter does not produce two's complement.
Is there a limit on how big the number can be?
No practical limit. The conversion uses arbitrary precision integers, so long values stay exact. The step-by-step working is shown for numbers up to 24 digits.
Can I convert fractions?
Not with this tool. It converts whole hex numbers to whole octal numbers.
Other number converters
Going the other way? Use the Octal to Hex Converter. To see a number in every base at once, try the all-in-one number converter.