Decimal to Octal Converter

How to convert decimal to octal by hand

Octal is base 8, so it has eight digits: 0, 1, 2, 3, 4, 5, 6 and 7. Converting a decimal number means asking, over and over, how many groups of 8 fit and what is left over. Divide the number by 8, write down the remainder, then divide the quotient by 8 again. Stop when the quotient reaches 0 and read the remainders from bottom to top.

Take 156. Dividing by 8 gives 19 with a remainder of 4, then 19 divided by 8 gives 2 with a remainder of 3, then 2 divided by 8 gives 0 with a remainder of 2:

Read the remainder column upward and 156 in decimal comes out as 234 in octal. The check is to expand the digits back: 2 x 64 + 3 x 8 + 4 = 156. One more quick example: 100 divides by 8 to give 12 remainder 4, then 12 divides to 1 remainder 4, then 1 divides to 0 remainder 1, which reads upward as 144.

The calculator above runs this ladder for any number you type and shows every division step, so you can compare your handiwork line by line.

Decimal to octal chart and place values

Every position in an octal number is worth a power of 8, counting from the right:

With those place values in hand, the small numbers become a lookup instead of a calculation. Digits 0 through 7 stay the same in both bases; from 8 upward the octal reading jumps ahead:

The jumps look odd at first: 8 decimal is already "10" in octal, and 64 decimal is "100". That is the same thing that happens when a decimal odometer rolls over at 9, except this one rolls over at 7.

Reading octal back as decimal

Running the conversion in reverse needs no division at all. Multiply each octal digit by its place value and add the products. Reading 234 in octal: the 2 sits in the 64s place, the 3 in the 8s place and the 4 in the 1s place, so the value is 2 x 64 + 3 x 8 + 4 = 156.

The same expansion checks bigger numbers. Read 1750 in octal as 1 x 512 + 7 x 64 + 5 x 8 + 0 = 1000, which confirms the chart entry above. Read 377 in octal as 3 x 64 + 7 x 8 + 7 = 255, the largest value three octal digits can hold, in the same way that 999 is the largest three decimal digits can hold.

Spot-check digits as you go: if any digit you wrote down is an 8 or a 9, the conversion went wrong somewhere, because those digits do not exist in base 8. That one rule catches most slips instantly, and it is also why certain real-world codes, covered below, never contain an 8 or a 9.

Converting decimal fractions to octal

Whole numbers divide by 8; fractional parts multiply by 8 instead. Multiply the fraction by 8, write down the whole-number part of the result as the next octal digit, then repeat with whatever fraction remains.

Take 0.25. Multiplying by 8 gives exactly 2, so 0.25 in decimal is 0.2 in octal, and the process ends because nothing remains. Take 0.75: 0.75 x 8 = 6, so the octal form is 0.6, again terminating after one digit.

Most fractions do not end so neatly. Converting 0.1 gives the digits 0, 6, 3, 1, 4 and then the same block repeats: 0.06314631... in octal. Just as 1/3 becomes the repeating decimal 0.333..., a decimal fraction that terminates in base 10 can repeat forever in base 8. Converters handle this by rounding after several digits, which is why two tools may show slightly different trailing digits for the same input.

When a number has both parts, convert each side separately: 156.25 in decimal is 234.2 in octal, built from the ladder for 156 and the single digit for 0.25.

Where octal shows up today

Octal survives in a handful of places where grouping bits in threes is natural, and the digit rule (no 8s, no 9s) is the tell that a number is octal:

The permission connection is the one most people meet first. Each digit of a chmod mode is three bits, one bit each for read, write and execute, and three bits make exactly one octal digit: 4 for read, 2 for write, 1 for execute, added together. That is why modes like 644 (owner read and write, others read) and 600 (owner only) are written in octal, and why the chmod manual documents the numeric modes in base 8.

Transponder codes work the same way from the other end: a controller who assigns "squawk 4573" is reading four octal digits, which is why you will never hear an 8 or a 9 in a code assignment.

The binary shortcut: three bits per digit

Because 8 is 2 cubed, every octal digit corresponds to exactly three binary digits. That gives a second route from decimal to octal: convert to binary first, then slice the bits into groups of three from the right and translate each group by eye.

The number 156 in binary is 10011100. Pad it on the left to a multiple of three bits, which gives 010 011 100, and each group reads as an octal digit: 2, 3, 4. Same answer as the division ladder, reached without any division at all.

The shortcut cuts both ways, and it is the fastest method whenever one of the two bases is already in hand. Our binary to octal converter shows the grouping step in detail if you are starting from bits rather than from decimal.

Octal compared with hexadecimal

Hexadecimal is the other base that computer people keep around, and the two fill different niches. Hex groups bits in fours, so one byte, which is 8 bits, becomes exactly two hex digits. Octal groups bits in threes, which lines up with 12-bit and 36-bit machine words from older architectures and with the 9-bit read-write-execute permission triad, but a byte needs up to three octal digits and the top digit can only reach 3.

That is why hex took over most of computing: bytes are the unit modern machines trade in, and two hex digits describe one byte with no padding. Both bases are built into the tools you already use, from the parseInt radix argument in JavaScript to the base-aware int() constructor documented for Python. Octal kept the domains where threes fit better, notably Unix permissions and a few hardware and aviation conventions.

The two bases do agree on one thing: any octal digit expands to a clean binary group, and so does any hex digit, so converting between octal and hex through binary takes seconds. For instance, 64 in decimal is 100 in octal and 40 in hex, and both spellings unpack to the same six bits, 1000000.

Common mistakes and quick checks

Decimal to octal conversion goes wrong in a few predictable ways. Each has a fast fix:

• Writing an 8 or a 9. If either digit appears in your answer, a division step went wrong. Every octal digit is 0 through 7, no exceptions.
• Reading remainders top down. The remainders come out of the ladder in reverse. Reading 156's ladder downward gives 432, which is wrong; upward gives 234.
• Stopping one step early. Keep dividing until the quotient is 0, even if it feels repetitive. Skipping the final step drops the leading digit.
• Assuming fractions terminate. In base 8, many decimal fractions repeat forever, so treat trailing digits beyond a few places as rounded.
• Mixing up octal with hex. Both look like plain numbers. Check for the digits 8 and 9, which can only appear in hex or decimal, and confirm which base the source document is using.

The one-check-fits-all move is to expand your answer back: multiply each digit by its place value, add the products, and confirm you land on the number you started with. If 2 x 64 + 3 x 8 + 4 = 156, then 234 is a correct octal reading and you are done.