Guide
From octal to decimal using powers of eight
Reading an octal number as an ordinary decimal quantity is a small calculation, but it is easy to get wrong when the digits look like something you know. A string such as 755 or 644 is a number in decimal and a mode in octal. Here you choose the base, type the digits, and get the decimal value with the sum laid out.
The positional sum
The rightmost octal digit counts ones, the next counts eights, then sixty-fours, then five-hundred-and-twelves. In general the position n (counting from zero on the right) is worth 8 to the power n. Multiply each digit by its worth and add them. For 3062 octal that is 3 × 512 + 0 × 64 + 6 × 8 + 2, which equals 1,586.
What the working displays
The numbered lines show each digit, its power of eight and the product, and finish with the total. The box beneath gives the same number in binary, hexadecimal and base 36. Because each octal digit is three bits, the binary line is a handy check: it should be the three-bit patterns of your digits joined together.
Where octal still appears
Octal turns up in Unix file permissions, in escape sequences within C strings such as \033 for the escape character, in tar headers, and in manuals for older computers. If you are decoding one of those, convert the digits and keep in mind that the number often stands for a set of flags rather than a quantity. In a permission mode the decimal value is rarely meaningful by itself.
Edge cases
An 8 or a 9 cannot occur in octal, so the page stops and names the offending character. Fractions are accepted: octal 0.4 is 4/8, or 0.5. Negative numbers keep a minus sign. A long octal string is no problem because the page does not use floating-point numbers, but the working is long, so switch it off if you only want the result. Leading zeros are allowed and ignored, so 0755 and 755 give the same answer here.
A worked example
The Sample button loads 755. The terms are 7 × 8² = 448, 5 × 8¹ = 40 and 5 × 8⁰ = 5, and the sum is 493. In binary this is 111101101, and in hexadecimal it is 1ED. If you need to read it as a permission mode, ignore the 493: it is just the number seven hundred fifty-five written in base 8, and the useful reading is owner rwx, group r-x, others r-x.
Limits
The page is arithmetic only. It does not know whether you are decoding a mode, a character escape or a quantity, and it does not warn about leading zeros that might mean something in another language. Verify the interpretation against the documentation of the system that produced the number. For permission work the chmod calculator is a better fit than a base converter.
Checking your answer
There are two quick checks for any conversion on this page. First, the size of the result: a three-digit octal number lies between 64 and 511 in decimal, a four-digit one between 512 and 4,095, and so on, because each added digit multiplies the range by eight. Second, the parity: an octal number is odd exactly when its last digit is odd, because every higher place value is even. Both checks take seconds and catch most slips made when converting by hand.
Related tools
- Decimal to Octal converts back with the division chain.
- Octal to Binary expands each digit into three bits.
- Octal to Hex regroups the bits into fours.
- Chmod Calculator turns octal modes into permission descriptions.
Checked against the current version of the Octal to Decimal on .