Decimal to Octal
Convert decimal (base-10) numbers to octal (base-8) instantly. Handles integers and fractions, shows step-by-step division, and maps chmod permissions — with optional leading-zero prefix. Free, no signup.
Why We Built the Decimal to Octal Converter
A single slip in a decimal-to-octal conversion can set the wrong file permission or misconfigure a legacy system. We built a converter that shows every division step, maps octal digits to chmod bits, and handles fractions and prefixes — so you can trust the result. It's fast, accurate, and completely free with no signup.
Convert Decimal to Octal in Three Steps
Enter your decimal number and the converter repeatedly divides it by 8, recording each remainder. It reads those remainders from bottom to top to build the octal result, and for fractions it multiplies the decimal part by 8 to the precision you choose. You get a full step-by-step breakdown, a chmod permission view, and an optional leading-zero prefix for use in code.
Convert Decimal to Octal in Three Steps
Enter your decimal number and the converter repeatedly divides it by 8, recording each remainder. It reads those remainders from bottom to top to build the octal result, and for fractions it multiplies the decimal part by 8 to the precision you choose. You get a full step-by-step breakdown, a chmod permission view, and an optional leading-zero prefix for use in code.
Common Mistakes to Avoid
❌ Writing 8 or 9 in an octal number
✓ Solution:
Octal only uses digits 0–7. Decimal 8 becomes octal 10 (8 ÷ 8 = 1 remainder 0), not 8. If a result shows an 8 or 9, the conversion went wrong — the tool always outputs valid octal digits.
❌ Forgetting the leading-zero prefix in code
✓ Solution:
In many languages, a leading 0 marks a number as octal. 755 is decimal, but 0755 is octal 755, which equals decimal 493. Dropping or adding the prefix by accident causes serious calculation and permission errors, so match the format your language expects.
❌ Mapping permission bits incorrectly
✓ Solution:
Each octal digit is read (4) + write (2) + execute (1). To get the permission you want, add the values: 7 = rwx, 6 = rw-, 5 = r-x, 4 = r--. Guessing instead of adding is how chmod settings end up granting the wrong access.
❌ Confusing octal place values with decimal
✓ Solution:
Octal 100 equals decimal 64, not 100, because each position is a power of 8. Reading an octal number as if it were decimal — or vice versa — can misinterpret a value badly. Always confirm the base and the place values before trusting a number.
❌ Mishandling the fractional part
✓ Solution:
Fractions don't use division-by-8; they use multiplication-by-8, recording the integer part each round. Reusing the integer method on the fraction, or stopping at the wrong precision, gives a wrong or truncated result. Set your desired precision, since some fractions don't terminate in octal.
Frequently Asked Questions
Divide the number by 8, record the remainder (0–7), then repeat with the quotient until it reaches 0. Read the remainders from bottom to top for the octal result. Example: 132 → 132÷8=16 r4, 16÷8=2 r0, 2÷8=0 r2 → 204 octal. The tool shows every step.
Multiply the fractional part by 8 and record the integer part each time, repeating until you hit zero or your chosen precision. Example: 0.75 × 8 = 6.0 → 0.6 octal. Some fractions don't terminate, so the tool lets you set how many octal digits to keep.
Each octal digit covers three permission bits — read (4), write (2), execute (1) — for owner, group, and others. Add the values for the access you want: rw-r--r-- is 6, 4, 4 → 644. The tool's permission mode maps digits to bits so you can build the right chmod value quickly.
Octal shines wherever data groups in threes. Unix permissions use three bits each for owner, group, and others, so three octal digits map perfectly and read more intuitively than hex or decimal. Legacy systems like the PDP-8 and PDP-11 were built around 3-bit groupings, and that tradition persists.
Yes. The same division-by-8 method scales to any size. Example: 1000 → 1000÷8=125 r0, 125÷8=15 r5, 15÷8=1 r7, 1÷8=0 r1 → 1750 octal. The tool handles large integers without error, so it's fine for big values, device encoding, or legacy computing work.
Decimal to Octal Converter: Turn Base-10 Into Octal With Step-by-Step Division — Free & Instant
The Decimal to Octal Converter turns everyday base-10 numbers into their base-8 equivalents in an instant. Enter a value and get the octal result along with a full step-by-step breakdown showing each division by 8, the remainder at every stage, and how those remainders read bottom-to-top to form the answer.
It covers both whole numbers and fractions. Integers use the repeated division-by-8 method, while decimal fractions use multiplication-by-8 with configurable precision — so 0.75 becomes 0.6 octal cleanly. A special permission mode maps each octal digit to its read (4), write (2), and execute (1) bits, making it easy to work out chmod values for owner, group, and others. You can also toggle the leading-zero prefix (like 0755) that programming languages use to mark octal.
It's built for the places octal still matters: Unix/Linux file permissions, legacy and mainframe systems documented in octal, embedded hardware, and computer science coursework. Everything runs in your browser, works on any device, and needs no download or account.
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