Convert octal to and from binary, decimal and hexadecimal, including octal fractions – with 3-bit grouping explained at every step. Everything runs locally in your browser.
Binary and Octal
- Binary to Octal Converter
Convert binary to octal by splitting the bits into 3-bit groups – each group is one octal digit 0-7.
- Octal to Binary Converter
Convert octal to binary by expanding every octal digit into its 3-bit pattern.
Decimal and Octal
- Decimal to Octal Converter
Convert a decimal number to octal by repeated division by 8, with every division and remainder shown for your input.
- Octal to Decimal Converter
Convert octal to decimal by summing place values – each digit is multiplied by a power of 8.
- Octal Fraction to Decimal Converter
Convert an octal number with a fractional part (such as 7.
- Decimal Fraction to Octal Converter
Convert a decimal fraction to octal by repeated multiplication by 8, with exact repeating-digit detection instead of silent rounding.
Hex and Octal
- Hex to Octal Converter
Convert hexadecimal to octal via binary: each hex digit becomes 4 bits, and the bits regroup into 3-bit octal digits.
- Octal to Hex Converter
Convert octal to hexadecimal via binary: 3-bit octal groups merge into 4-bit hex nibbles.
Octal groups bits in threes — the shorthand of an earlier machine era that survives wherever three-bit fields matter, permissions above all. These tools expand, evaluate and regroup octal exactly, including the fraction pages for vintage-format work.
chmod arithmetic and umask puzzles resolve here with the working shown.
Octal, three bits at a time
Octal is base eight, and because 8 is 2³ each octal digit corresponds to exactly three bits. That is the entire reason octal survives in modern computing: Unix file permissions pack three permission bits — read, write, execute — into each digit, so chmod 755 literally means the bit pattern 111 101 101, or rwxr-xr-x. Converting 755 octal through these tools gives 493 in decimal and 1ED in hexadecimal, and the steps panel shows the 3-bit groups that make the conversion mechanical.
Octal also hides a classic programming trap: in C and many languages that copied it, an integer literal that starts with a zero is parsed as octal, so 011 is nine, not eleven. The octal fraction tools on this page handle digits after the point too, where each position is worth a negative power of eight — 0.4₈ is one half, and 7.4₈ is 7.5. Fractions that cannot terminate in base eight, such as one third, are reported with their exact repeating cycle instead of being rounded.
Permission modes can also carry a fourth, leading octal digit holding the setuid, setgid and sticky bits — chmod 4755 sets the setuid bit on top of rwxr-xr-x. Modern languages have moved away from the bare leading-zero syntax to the explicit 0o prefix, so 0o755 in Python is unambiguous where 0755 in C was a quiet trap for newcomers. The converters on this page accept both prefixed and bare octal input, and every result comes with its calculation steps.
