Decimal to Octal Converter

Octal is base 8. It uses only the digits 0 through 7 — there is no 8 and no 9, because in base 8 the value eight is written 10, exactly as ten is written 10 in decimal. Each place is worth eight times the one to its right: 1, 8, 64, 512, and so on.

Octal exists because 8 is 2 cubed, which means one octal digit corresponds to exactly three binary digits. That made it valuable in early computing, when machine word sizes were often multiples of three bits. Modern machines settled on 8-bit bytes, which divide evenly into hexadecimal's 4-bit digits but not into octal's 3-bit ones, and hex largely displaced octal as a result. Octal survives mainly in Unix file permissions and a handful of legacy formats.

Converting from decimal is the awkward direction. Ten is not a power of eight, so unlike binary-to-octal — which is pure regrouping — decimal-to-octal requires real arithmetic: repeated division for whole numbers, repeated multiplication for fractions.

1. Divide the decimal number by 8.
2. Write down the whole-number quotient and the remainder. The remainder will always be 0-7.
3. Replace the number with the quotient and repeat from step 1.
4. Stop when the quotient reaches 0.
5. Read the remainders from the bottom up. That string is your octal number.

Reading bottom-to-top is not arbitrary. Each division peels off the least significant digit first, so the first remainder you produce is the last digit of the answer. Writing the remainders top-to-bottom instead gives you the number backwards, which is the most common error in this conversion — and it is silent, because the reversed string is usually still a valid octal number.

Worked example: 100 in octal

100 divided by 8 is 12 with a remainder of 4. Then 12 divided by 8 is 1 with a remainder of 4. Then 1 divided by 8 is 0 with a remainder of 1, and the quotient has hit zero, so we stop. Reading bottom-to-top gives 1, 4, 4 — so 100 in decimal is 144 in octal. Check it by expanding: (1 x 64) + (4 x 8) + (4 x 1) = 64 + 32 + 4 = 100.

Worked example: 255 in octal

255 divided by 8 is 31 remainder 7. Then 31 divided by 8 is 3 remainder 7. Then 3 divided by 8 is 0 remainder 3. Bottom-to-top: 377. So 255 decimal is 377 octal — the largest value a single byte can hold, which is why 377 was the conventional octal byte ceiling on older Unix systems before hex took over.

The reverse is positional expansion and it is easier than the division method. Number the octal digits from right to left starting at zero, multiply each digit by 8 raised to its position, then add the results. There are no letter digits to translate first, which makes octal simpler to expand by hand than hexadecimal.

Take 144. The rightmost 4 sits at position 0, contributing 4 x 1 = 4. The middle 4 is at position 1, contributing 4 x 8 = 32. The leading 1 is at position 2, contributing 1 x 64 = 64. Adding: 64 + 32 + 4 = 100. Take 755: (7 x 64) + (5 x 8) + (5 x 1) = 448 + 40 + 5 = 493 — a number worth remembering, for reasons the file-modes section below makes clear.

Fractions invert the method. Instead of dividing the whole number by 8 and collecting remainders, you multiply the fractional part by 8 and collect the integer parts — and you read those digits top-to-bottom, the opposite direction to the integer half. Getting this backwards is easy and no page currently ranking for this term covers fractional conversion at all.

Take 0.75. Multiply by 8 and you get 6.0. The integer part is 6 and the leftover fraction is 0, so the process stops: 0.75 decimal is 0.6 octal. Check it — 6/8 is indeed 0.75. Take 0.125: multiplied by 8 that is 1.0, so the answer is 0.1 octal, since 1/8 is 0.125.

Most decimal fractions, though, never terminate in octal. 0.1 is the clearest case: multiplying repeatedly gives 0, 6, 3, 1, 4, 6, 3, 1, 4 and onward forever, so 0.1 decimal is 0.0631463146... octal with '6314' repeating. This is the same phenomenon as one-third being 0.333... in decimal — the fraction simply has no exact representation in the target base. The converter above flags repeating expansions rather than truncating them silently.

Almost nobody converts decimal to octal for its own sake. The situation that produces the query is nearly always the same one: a program returned a file permission as a plain decimal integer, and permissions are conventionally written in octal, so the number looks wrong until you convert it.

Python's os.stat() is the classic source. Ask it for a file's mode and you get something like 33261, which is meaningless until you convert it — 33261 in octal is 100755. The trailing three digits, 755, are the permission bits you recognise from chmod: read, write and execute for the owner, read and execute for everyone else. The leading 100 is the file-type field, which marks it as a regular file rather than a directory or a symlink. Node's fs.statSync, Go's os.FileMode and Ruby's File.stat all behave the same way.

This is why 493 is a number worth recognising. It is 755 in octal, so a permission value stored or logged as 493 is the standard executable-and-directory permission set. Likewise 420 is 644, the ordinary file default. If you have ever seen a config file or a Terraform plan with a mode of 420 and assumed something had gone wrong, this is the explanation.

For how each octal digit expands into the rwx permission bits themselves, see the binary to octal converter, which covers the three-bits-per-digit mapping in full.

One further trap: a leading zero means octal in several languages. In Python 3 you must write 0o755 and a bare 0755 is a syntax error, which is a deliberate guard. In older Python 2, C and pre-ES6 JavaScript, 0755 silently meant octal 755, while 755 meant decimal 755 — two very different permission sets. If a config value behaves differently after a language upgrade, a lost leading zero is worth checking early.

Backend developers and DevOps engineers

Reading file modes returned as decimal integers from stat calls, deployment tooling, container manifests and infrastructure-as-code plans. The decimal-mode table above is built for exactly this lookup, and the permalink means a specific value can be pasted into a ticket or a code review.

Computer science students

Repeated-division base conversion is standard coursework and it is marked on method, not just answer. The working panel prints the division trace for your own number, so you can compare your steps rather than only your result — including the fractional case, which is where most people lose marks.

Embedded and legacy systems engineers

Some older architectures, instruction encodings and datasheet conventions are octal-native, particularly PDP-descended designs. Register fields that split into three-bit chunks are easier to read in octal than in hex, because the field boundaries align with the digits.

Anyone debugging a leading-zero bug

A number written with a leading zero being silently read as octal is a classic source of wrong values in C, older JavaScript and Python 2. Converting both interpretations quickly is usually the fastest way to confirm whether a literal is being read as base 8 or base 10.

How do you convert decimal to octal?

Divide the number by 8, note the remainder, then divide the quotient by 8 and note that remainder, repeating until the quotient is zero. Read the remainders from the bottom up to get your octal number. The converter above shows every division step for your own value.

What is 100 in octal?

100 in decimal is 144 in octal. The working is three divisions: 100/8 = 12 remainder 4, then 12/8 = 1 remainder 4, then 1/8 = 0 remainder 1. Expanding 144 back gives (1 x 64) + (4 x 8) + 4 = 100.

What is 255 in octal?

255 in decimal is 377 in octal. It is the largest value a single byte holds, which is why 377 was the conventional octal byte ceiling on early Unix systems. In binary it is 11111111 and in hex it is FF.

Why does Python show a file's permissions as 33261?

Because os.stat() returns the mode as a decimal integer, and 33261 in octal is 100755. The trailing 755 is the permission set you know from chmod, and the leading 100 is the file-type field marking it as a regular file. Convert the number to octal and it becomes readable.

What is 493 in octal, and why does it keep appearing?

493 in decimal is 755 in octal, which is the standard permission set for directories and executable scripts. Tools that store or log permissions as plain integers will show 493 where you expected 755, so recognising it saves a lot of confusion.

How do I convert octal back to decimal?

Multiply each octal digit by 8 raised to its position, counting from the right starting at zero, then add the results. For 144: (1 x 64) + (4 x 8) + (4 x 1) = 100. Or type the octal value into the right-hand field of the converter, since both fields are live.

Why aren't 8 and 9 allowed in octal?

Because base 8 has exactly eight digits, 0 through 7. The value eight is written as 10, in the same way that ten is written 10 in decimal. A digit 8 or 9 in an octal number means it is not a valid octal number.

What if my decimal number has a fractional part?

The method inverts: multiply the fraction by 8 repeatedly and read the integer parts top-to-bottom, rather than dividing and reading bottom-up. So 0.75 x 8 = 6.0, giving 0.6 octal. Many decimal fractions never terminate in octal and repeat instead.

How do I convert a negative decimal to octal?

The converter accepts a leading minus and applies it to the result, so -100 gives -144. Note this is sign-and-magnitude; if you are reading a negative value out of a fixed-width register, convert the two's-complement bit pattern as an unsigned number instead.

What's the difference between octal and hexadecimal?

Octal is base 8 and maps to three binary digits per character; hexadecimal is base 16 and maps to four. Hex became dominant because a byte is eight bits, which divides evenly into two hex digits but not into octal digits. Octal survives mainly in Unix file permissions.

Is octal still used today?

Yes, though narrowly. File permissions and umask values on Unix and Linux are its most common surviving use, alongside some embedded architectures and octal literals in languages where a leading zero or 0o prefix signals base 8.