Decimal to Octal Converter

Going the other way? Convert octal back to decimal →

How do you convert decimal to octal?

Decimal to octal conversion divides the number by 8 over and over, keeping each remainder, then reads the remainders from the last one back to the first.

1. Divide the number by 8 and write down the remainder. 156 ÷ 8 leaves 4.
2. Divide the quotient by 8 again and keep that remainder too.
3. Repeat until the quotient reaches 0.
4. Read the remainders from bottom to top: 156 = 234.

Decimal to Octal Conversion Table

One hexadecimal digit equals exactly 4 bits (16 = 2⁴); one octal digit equals exactly 3 bits (8 = 2³). Hex and octal are therefore converted by grouping bits, and hex ↔ octal passes through binary. That is the whole method, so the table below is the only thing you need: every group of 3 bits has exactly one octal digit, and the mapping never changes. Binary writes values on the digit set 0, 1 with each place worth 2ⁿ, and a value marked 0b is binary; octal values are marked 0o.

Each base is defined by three things: which digits it uses, how a value is marked, and what each position is worth.

Worked Example: 156 to Octal

One value, converted the long way so the working is visible. This is the same grid the converter shows when you turn on "show steps".

Divide by 8 and keep the remainder, then divide the quotient again, until the quotient reaches 0. For 156 that runs: 156 / 8 = 19 remainder 4; 19 / 8 = 2 remainder 3; 2 / 8 = 0 remainder 2.

The remainders come out least significant first, so they are read from the bottom of the list back to the top: 234. Reading them the other way is the single most common error, and it gives a number that looks plausible and is wrong. The check is quick — expand the result back and it must return 156.

Check it in reverse

The value returns unchanged. Convert 234 back and you get 156, because a base change rewrites the digits without touching the quantity they stand for. That is the whole test: if the round trip differs, a digit was misread. To check it by hand, convert the decimal value back to octal and compare it with the number you started from.

Worked examples: decimal to octal

Each example gives the value first, then the working. Click a value to load it in the converter.

Every example above reverses exactly — expand the same octal digits into a decimal value.

What About Padding, Fractions and Width?

Leading zeros and width

A number carries no leading zeros unless a width is fixed. 234 and 0234 are the same value, so the converter writes the short form. Fixed widths belong to bytes and registers, not to arithmetic. converting between binary, octal, decimal and hexadecimal covers where width does matter.

Fractions and the point

Digits after a point convert by the same rule with negative powers, so the first place after the point is worth 1/8. Many fractions that end neatly in decimal repeat forever in binary, which is where rounding creeps in.

Negative values

A minus sign is kept in front of the digits. Fixed-width binary encodes sign differently, using two's complement, and that is a separate rule from the base change itself.

How large a value can be

The method has no ceiling; each extra decimal digit multiplies the range by 10. Practical limits come from the width a machine stores the value in, not from the conversion.

Decimal to Octal in Code

The same rule in one line. Both divide repeatedly and return the digits in order.

Python: format(156, 'o')

JavaScript: (156).toString(8)

Common Mistakes

• Reading the remainders top to bottom. They come out in reverse, so the digits land backwards.
• Using a digit the base does not have — an 8 in octal, or a 2 in binary. The value cannot be read at all.
• Grouping bits from the left. Groups are counted from the right, and the leftmost group is the one that gets padded.
• Treating the result as a character code. 65 is a number here, not the letter A.

Frequently Asked Questions

Related Conversions

• Decimal also converts to hex by the same route — dec to hex with A-F remainders.
• Decimal also converts to binary by the same route — decimal to binary by repeated division.
• Decimal also converts to text by the same route — dec to ASCII code lookup.
• If your input is binary rather than decimal, convert binary to octal instead.
• If your input is hex rather than decimal, change a hex number into octal via binary instead.
• If your input is hex rather than decimal, work out the decimal value of a hex number instead.

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