Best uses
- Convert base-10 values into base-8 notation.
- Practice number systems for programming or computer science.
- Check examples related to permissions or older computing systems.
Number converters
Decimal to Octal Converter
Convert decimal numbers to octal online, read remainders upward, and review examples, invalid octal digits, FAQs, and conversion checks.
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Converting Steps of Decimal to Octal:
How to convert decimal to octal?
To convert the whole-number part of a decimal value to octal, divide by 8 and read the remainders in reverse order. For the fractional part, multiply by 8 repeatedly and record each whole-number result until the fraction becomes 0 or reaches the precision you need. The example below shows the process:
Example of decimal to octal conversion.
(210.625)10 = (?)8
For 210:
| Divided by 8 | Quotient | Remainder | Flow |
|---|---|---|---|
| 210 / 8 | 26 | 2 | ↑ |
| 26 / 8 | 3 | 2 | ↑ |
| 3 / 8 | 0 | 3 | ↑ |
For .625:
| Multiply by 8 | Result | Non-Fractional Part | Flow |
|---|---|---|---|
| .625 * 8 | 5.00 | 5 | ↓ |
Result is = (322.5)8
When decimal to octal is useful
Decimal to octal conversion is useful for learning base systems and for reading examples where values are grouped by powers of 8. You may still see octal in file permission examples, older computing material, and number-system exercises where binary values are grouped into sets of three.
Things to remember
- Octal uses only the digits 0, 1, 2, 3, 4, 5, 6, and 7.
- A remainder of 8 or 9 is not possible in base 8.
- Read division remainders from bottom to top for the whole-number part.
- For decimal fractions, the result may stop or may need a limited number of digits.
Decimal to Octal conversion table:
| Decimal | Octal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 8 | 10 |
| 9 | 11 |
| 10 | 12 |
| 11 | 13 |
| 12 | 14 |
| 13 | 15 |
| 14 | 16 |
| 15 | 17 |
| 16 | 18 |
| 17 | 19 |
| 18 | 20 |
| 19 | 21 |
| 20 | 22 |
Use remainders and grouping as independent checks
Repeated division by 8 gives the octal whole number directly: keep each remainder and read the remainders from the final division upward. You can verify the same result by converting the decimal value to binary and grouping bits in threes from the radix point. Agreement between the two methods is a useful way to catch a reversed remainder or a copied digit.
Digits 8 and 9 can appear in the decimal input but never in the octal answer. Fractional values use repeated multiplication by 8, and some expansions do not terminate. Preserve the requested number of octal places, state when rounding was used, and convert the rounded result back to decimal when accuracy matters.
Decimal to octal guide
Decimal to octal conversion uses repeated division by 8. The remainders, read from bottom to top, become the octal number.
Quality checks
- Divide by 8 until the quotient is zero.
- Read remainders in reverse order.
- Remember every octal digit must be between 0 and 7.
Common mistakes
- Using digits 8 or 9 in the octal answer.
- Reading remainders in the original order.
- Confusing octal with hexadecimal grouping.
Quick answers
Why can octal not use 8 or 9?
Octal is base 8, so its digits are only 0 through 7.
What is 210 in octal?
210 in decimal is 322 in octal.