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Decimal to Octal Converter
Convert any decimal number to octal instantly — see every division step. Free, fast, no sign-up.
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Also equals
- Binary
- Decimal
- Octal
- Hex
Step-by-step calculation
| Division | Quotient | Remainder |
|---|
How to convert decimal to octal
- Divide the decimal number by 8 and write down the remainder.
- Divide the quotient by 8 and write down the new remainder.
- Repeat until the quotient is 0, then read the remainders from bottom to top.
Example: 125 → 125÷8=15 r5, 15÷8=1 r7, 1÷8=0 r1 → 175.
Background reading: the octal number system on Wikipedia.
Conversion table
Decimal 0–15 with the matching octal value, plus larger worked examples.
| Decimal | Octal | Calculation |
|---|---|---|
| 0 | 0 | 0 = 0₈ |
| 1 | 1 | 1 = 1₈ |
| 2 | 2 | 2 = 2₈ |
| 3 | 3 | 3 = 3₈ |
| 4 | 4 | 4 = 4₈ |
| 5 | 5 | 5 = 5₈ |
| 6 | 6 | 6 = 6₈ |
| 7 | 7 | 7 = 7₈ |
| 8 | 10 | 8 = 10₈ |
| 9 | 11 | 9 = 11₈ |
| 10 | 12 | 10 = 12₈ |
| 11 | 13 | 11 = 13₈ |
| 12 | 14 | 12 = 14₈ |
| 13 | 15 | 13 = 15₈ |
| 14 | 16 | 14 = 16₈ |
| 15 | 17 | 15 = 17₈ |
| 64 | 100 | 64 ÷ 8 = 8 r 0, 8 ÷ 8 = 1 r 0 → 100 |
| 512 | 1000 | 512 = 8³ → 1000 |
Powers of 8
| Power | Value |
|---|---|
| 80 | 1 |
| 81 | 8 |
| 82 | 64 |
| 83 | 512 |
| 84 | 4096 |
| 85 | 32768 |
Decimal to octal in code
Python
oct(64)[2:] # → '100'JavaScript
(64).toString(8); // → '100'C
#include <stdio.h>
int main(void) {
printf("%o\n", 64); /* → 100 */
return 0;
}Common values
- 64 =
100₈ - 8 =
10₈ - 15 =
17₈ - 511 =
777₈ - 0 =
0₈ - 16 =
20₈
Key takeaways
- Divide by 8 repeatedly; read remainders bottom-to-top.
- 64 = 100₈, 8 = 10₈.
- Unix file permissions (chmod 755) are written in octal.
- Octal digits never exceed 7.
Frequently asked questions
How do I convert decimal to octal?
Repeatedly divide by 8, record each remainder, and read the remainders bottom-to-top. The converter above shows every step.
What is 8 in octal?
8 in decimal equals 10 in octal.
Where is octal used?
Octal is used in Unix file permissions (e.g. chmod 755) and in some embedded systems.
What is 8 in octal?
8 = 10₈.
What is 64 in octal?
64 = 100₈ (1×64).
How do I convert decimal to octal by hand?
Repeatedly divide by 8 and read the remainders bottom-to-top.
Where is octal still used?
Unix file permissions (for example chmod 755) are the most common everyday use of octal.
Need the reverse? Try our octal to decimal converter.