Octal converter: convert octal numbers to decimal, binary, and hexadecimal, or back the other way, instantly and accurately. Free, private, in-browser.
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Last verified July 2026
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Octal converter: convert octal numbers to decimal, binary, and hexadecimal, or back the other way, instantly and accurately. Free, private, in-browser.
Base conversion is exact, not approximate: 255 = 377 in octal = 11111111 in binary = FF in hexadecimal.
Decimal 73 becomes octal 111 by dividing by 8 and reading remainders up.
Formula & evidence
How this calculator works
Reviewed 2026-09-20 · BoringToolsKit Editorial Team
Formula
Octal (base 8) = the decimal value regrouped into powers of 8: divide by 8 repeatedly and read the remainders upward. The same value is also shown in binary (base 2) and hexadecimal (base 16).
Sources support the method, terminology, or planning context. Editable assumptions remain your responsibility.
Assumptions to verify
Inputs are treated as exact decimal values.
Standard (not historical or survey) unit definitions are used.
The calculation uses the factors at the precision shown in the formula panel; rounding beyond that is display-only and adds no accuracy.
Frequently asked questions
Is an octal conversion exact?
Yes. Base conversion only regroups the same quantity, so it does not round. The limit is the input: whole numbers from 0 to 2^53 convert exactly; beyond that JavaScript cannot represent every integer exactly and the tool rejects it.
BoringToolsKit. “Octal Converter.” boringtoolskit.com/octal-converter/ (reviewed 2026-09-20). Free to reference in articles, syllabi, and answer posts with a link.
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Worked example: converting 73 step by step
Take decimal 73. To get octal directly, divide by 8 and track remainders: 73 / 8 = 9 remainder 1, then 9 / 8 = 1 remainder 1, then 1 / 8 = 0 remainder 1. Reading the remainders bottom-up gives 111 in base 8. Check it: 1x64 + 1x8 + 1x1 = 73.
The same digits line up in binary because 8 is 2 cubed. 73 in binary is 1001001 (64 + 8 + 1). Pad it to a multiple of 3 bits: 001 001 001. Each group of three binary digits is one octal digit: 001 = 1, 001 = 1, 001 = 1, so octal 111. Hex works the other way, with groups of four: 0100 1001 becomes 49 in base 16.
This is why the calculator can emit all three bases at once from one integer: JavaScript stores the value as a single 64-bit float, then toString(2), toString(8) and toString(16) just re-print the same magnitude in different groupings. No rounding happens anywhere because 73 and every input up to 9007199254740991 is exactly representable.
Where octal actually shows up
Unix and Linux file permissions are the daily use. A mode of 644 means owner read+write (4+2), group read-only (4), others read-only (4). The calculator makes the arithmetic visible: 755 decodes to rwxr-xr-x, which is 7 = 4+2+1 for the owner, 5 = 4+0+1 for group and others. A common mistake is setting 777 to fix a permission error; that hands write access to every user on the system, and chmod 600 on an SSH private key is literally enforced by ssh, which refuses keys looser than that.
Two edge cases worth knowing. First, the upper bound: 2^53-1 = 9007199254740991 converts to octal 777777777777777777777, fifteen octal digits, and past that floating-point inputs silently round, so the tool rejects non-integers outright. Second, leading zeros in source code: in JavaScript and C, 011 is octal 9, not decimal 11, a legacy trap that has bitten config parsing for decades. When copying a number out of this tool into code, state the base explicitly or use the 0o prefix.
