🔢 Decimal to Octal Converter

By Shihab Mia · Updated 2026-07-27

Decimal number

Decimal (base 10)

100

Octal (base 8)

144

How the conversion works: repeated division by 8

Dividend	Divided by 8, quotient	Remainder (octal digit)

This decimal to octal converter turns any non-negative whole number in base 10 into its base 8 (octal) equivalent, instantly and exactly. Type a decimal number and the tool converts it using repeated division by 8, then shows every division step so you can see exactly how the remainders build the octal digits, not just the final answer. Because the conversion runs on BigInt arithmetic rather than ordinary floating-point numbers, results stay exact even for very large integers that would otherwise lose precision.

What is the Decimal to Octal Converter?

Decimal (base 10) is the counting system most people use every day, built from ten digits, 0 through 9, where each position represents a power of 10. Octal (base 8) is a positional number system built from only eight digits, 0 through 7, where each position represents a power of 8 instead. So the octal digit in the ones place counts up to 7 and then rolls over, the next position counts groups of 8, the next counts groups of 64 (8 squared), then 512 (8 cubed), and so on. Converting decimal to octal means re-expressing the same quantity using powers of 8 instead of powers of 10.

The standard manual method is repeated division by 8. Divide the decimal number by 8, write down the remainder, then divide the resulting quotient by 8 again, write down that remainder, and keep repeating until the quotient reaches 0. Each remainder is one octal digit, and because the first remainder you compute corresponds to the smallest place value (the ones place), you have to read the remainders back in reverse, from the last one you calculated to the first, to get the correct octal number. That bottom-to-top reading is the step people most often get backwards, and it is exactly what the step-by-step table above spells out for whatever number you enter.

Octal survives in computing mostly for historical and practical reasons. Older systems and instruction sets (early minicomputers, some Unix file permission notations like chmod 755, and certain embedded or legacy protocols) grouped binary bits in sets of three, since 3 bits can represent exactly one octal digit (0 to 7). That made octal a convenient shorthand for binary before hexadecimal (which groups 4 bits per digit) became the more common shorthand in modern computing. You will still see octal in Unix permission codes, some older assembly listings, certain escape sequences, and a handful of legacy data formats, which is usually why someone needs a quick, correct conversion.

One honest limitation: this tool only accepts non-negative whole numbers (no decimal points, no negative signs, no letters). Converting fractional decimals to octal is a different, less exact process (multiplying the fractional part repeatedly by 8), and negative numbers require a choice of representation (signed magnitude, two's-complement analog, and so on) that varies by context, so those cases are intentionally out of scope here to keep the result unambiguous. For plain non-negative integers, the BigInt-based math behind this converter is exact no matter how many digits you type, which is not true of calculators that rely on ordinary JavaScript or spreadsheet floating-point numbers.

When to use it

Converting Unix file permission values or legacy configuration numbers that are expressed in octal back to a readable decimal, or the reverse.
Checking homework or coursework on number systems and positional notation without redoing long division by hand.
Verifying a value produced by code (for example a language's toString(8) or printf %o output) against an independent, transparent calculation.
Understanding and double-checking octal literals or escape sequences found in older source code, scripts, or documentation.
Teaching the repeated-division method for converting between number bases, with visible, step-by-step working.
Converting very large decimal integers (beyond what a typical calculator or spreadsheet can handle precisely) to octal without rounding errors.

How to use the Decimal to Octal Converter

Type a non-negative whole decimal number into the Decimal number box (only digits 0 to 9, no letters, commas, or decimal points).
The octal result and the decimal value both update automatically as you type; click Convert if you prefer to trigger it manually.
Read the division table below the result: each row shows a dividend, the quotient after dividing by 8, and the remainder for that step.
Read the remainder column from the bottom row up to the top row to see how the octal digits are assembled in order.
Click Copy octal to place the final octal value on your clipboard for pasting elsewhere.

Formula & method

To convert a non-negative decimal integer N to octal: repeatedly divide N by 8, recording the remainder at each step, and replace N with the integer quotient. Stop once the quotient reaches 0. The octal representation is the sequence of remainders read in reverse order (from the last remainder computed to the first). Equivalently, if N = d(k) * 8^k + ... + d(1) * 8^1 + d(0) * 8^0, where each d(i) is between 0 and 7, then the octal digits are d(k) d(k-1) ... d(1) d(0). This tool computes it directly with BigInt(N).toString(8), then reconstructs and displays the same division steps for transparency.

Worked examples

Convert the decimal number 100 to octal (the tool's default example).

100 divided by 8 = 12, remainder 4 (since 8 x 12 = 96, and 100 - 96 = 4).
12 divided by 8 = 1, remainder 4 (since 8 x 1 = 8, and 12 - 8 = 4).
1 divided by 8 = 0, remainder 1 (since 8 x 0 = 0, and 1 - 0 = 1).
The quotient is now 0, so division stops. Reading the remainders from the last one computed to the first gives 1, 4, 4.

Result: 100 in decimal equals 144 in octal

Convert the decimal number 583 to octal.

583 divided by 8 = 72, remainder 7 (since 8 x 72 = 576, and 583 - 576 = 7).
72 divided by 8 = 9, remainder 0 (since 8 x 9 = 72, and 72 - 72 = 0).
9 divided by 8 = 1, remainder 1 (since 8 x 1 = 8, and 9 - 8 = 1).
1 divided by 8 = 0, remainder 1 (since 8 x 0 = 0, and 1 - 0 = 1).
Reading the remainders from the last one computed to the first gives 1, 1, 0, 7.

Result: 583 in decimal equals 1107 in octal

Decimal to octal quick reference (0 to 16)

Decimal	Octal
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	10
9	11
10	12
11	13
12	14
13	15
14	16
15	17
16	20

Octal place values (powers of 8)

Position (from the right)	Power of 8	Decimal value of that place
1st (ones)	8^0	1
2nd (eights)	8^1	8
3rd (sixty-fours)	8^2	64
4th (five-hundred-twelves)	8^3	512
5th (four-thousand-ninety-sixes)	8^4	4,096
6th (thirty-two-thousand-seven-hundred-sixty-eights)	8^5	32,768

Common mistakes to avoid

Using the digits 8 or 9 in an octal number. Octal only has eight digits, 0 through 7. A remainder or digit of 8 or 9 is a sign of a math error somewhere, since dividing by 8 can never leave a remainder of 8 or more. If you see an 8 or 9 in what should be an octal result, recheck the division.
Reading the remainders in the wrong order. The first remainder you calculate during repeated division corresponds to the smallest place value (the ones digit), not the largest. Writing the remainders down in the order you computed them, top to bottom, gives the digits backwards. Always read from the last remainder computed up to the first.
Stopping the division one step too early. The process only finishes once the quotient itself reaches 0, not once the quotient becomes a single small digit. For example, converting 8 requires one more step after the quotient reaches 1 (1 divided by 8 gives quotient 0, remainder 1), otherwise the leading digit gets dropped.
Confusing octal output with decimal or hexadecimal. An octal number like 144 is not the decimal value one hundred forty-four; it equals 100 in decimal. Octal is also easy to confuse with hexadecimal, which uses letters A through F, since neither uses the same digit meanings as decimal.

Glossary

Decimal (base 10): The everyday number system using ten digits, 0 through 9, where each position represents a power of 10.
Octal (base 8): A positional number system using eight digits, 0 through 7, where each position represents a power of 8.
Radix (base): The number of unique digits a positional number system uses, including zero. Decimal has radix 10, octal has radix 8.
Quotient: The whole-number result of a division, before considering any remainder. In repeated division by 8, the quotient becomes the next number to divide.
Remainder: What is left over after dividing one integer by another as many whole times as possible. Each remainder from dividing by 8 becomes one octal digit.
BigInt: A JavaScript numeric type that represents whole numbers of arbitrary size exactly, avoiding the precision limits of ordinary floating-point numbers used for very large integers.

Frequently asked questions

What is 100 in octal?

100 in decimal equals 144 in octal. Dividing 100 by 8 repeatedly gives remainders 4, 4, 1 (in that order), and reading them from last to first gives 144.

How do you convert decimal to octal by hand?

Divide the decimal number by 8 and note the remainder, then divide the quotient by 8 again and note that remainder too, repeating until the quotient reaches 0. Read the remainders in reverse order, from the last one computed to the first, to get the octal digits.

Why is octal used at all in computing?

Octal groups binary digits in sets of three, since 3 bits map exactly to one octal digit (0 to 7). That made it a convenient shorthand for binary values on some older computer systems. It still appears today mainly in Unix file permission notation (like chmod 755) and some legacy code or documentation.

What is the largest number this converter can handle?

Because the conversion uses BigInt arithmetic rather than ordinary floating-point numbers, there is no practical upper limit tied to precision. You can enter integers with dozens of digits and the octal result will still be exact; only extremely long inputs will have their division steps summarized in the table for readability.

Is octal the same as grouping binary digits in threes?

Yes, that is exactly the relationship. Any 3-bit group of binary digits corresponds to exactly one octal digit from 0 to 7 (for example, binary 101 equals octal 5). That is why octal was historically useful as a compact, human-readable stand-in for binary.

How do you convert octal back to decimal?

Multiply each octal digit by the power of 8 matching its position (ones place is 8^0, next is 8^1, and so on), then add the results. For example, octal 144 is (1 x 64) + (4 x 8) + (4 x 1) = 64 + 32 + 4 = 100 in decimal.