Convert a decimal number to octal by repeated division by 8, with every division and remainder shown for your input. The classic use is Unix permission masks.
Show calculation steps
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Division by eight
The change-of-base algorithm with divisor 8: repeatedly divide, collect remainders 0–7, read bottom-up. No letters are needed — octal is the largest common base whose digits stay within decimal symbols — which historically made it printer-friendly shorthand.
The steps panel lists each division for your input, doubling as a worked tutorial in the method that generalises to every base.
Worked example
Input: 493 493 ÷ 8 = 61 r 5 61 ÷ 8 = 7 r 5 7 ÷ 8 = 0 r 7 Read upward: 755
| Power | Value |
|---|---|
| 8^0 | 1 |
| 8^1 | 8 |
| 8^2 | 64 |
| 8^3 | 512 |
| 8^4 | 4096 |
| 8^5 | 32768 |
| 8^6 | 262144 |
The permissions round trip
That example is no accident: 493 is what stat() returns in decimal for mode 755. APIs that expose permissions as plain integers force exactly this conversion on developers — in both directions — and getting it wrong produces silently mis-permissioned files. The pairing page (Octal to Decimal) closes the loop.
Sizing rule
Each octal digit covers three bits, so digit count ≈ bit count / 3: values under 512 need three digits, under 4096 four. Compare hex’s four bits per digit — octal is one notch less dense, one notch more keyboard-friendly.
Exactness and privacy
BigInt-exact at any magnitude; fractions route to the Decimal Fraction to Octal page where repeat detection lives. Digits are validated with positions. Local computation only — nothing transmitted.
How to use the Decimal to Octal Converter
- Enter the decimal number.
- Click "Convert to octal".
- The steps show each division by 8 and its remainder – read bottom-up for the answer.
- Copy the octal result.
Frequently asked questions
How does division by 8 produce octal digits?
Each division extracts the number of 8s and a leftover 0-7; the leftover is the next digit from the right. 493 ÷ 8 = 61 r 5, 61 ÷ 8 = 7 r 5, 7 ÷ 8 = 0 r 7 → read up: 755.
Why is 493 = 755 octal a famous pair?
Because chmod 755 – the standard permission set rwxr-xr-x – IS decimal 493. Tools that display permissions in decimal produce exactly this confusion, which the converter untangles.
How many octal digits will a number need?
Roughly one per three bits: numbers to 511 fit three octal digits (9 bits), to 4095 four digits. It is the same bound as binary, grouped in threes.
Does the converter handle huge decimals?
Yes – the division loop runs in BigInt, so any length stays exact. There is no float involved at any point.
What about a decimal with a fraction like 7.5?
Use the Decimal Fraction to Octal converter – fractions need the multiplication method and can repeat; this page is exact integers only and says so rather than rounding.
How can I verify the result?
Recompute the last digit: your number mod 8 must equal it (493 mod 8 = 5 ✓). Or round-trip through the Octal to Decimal converter, which sums place values back.
Where does the arithmetic run?
In your browser. Values are never transmitted – the steps you see were generated on your device.
