Introduction / overview

The Decimal to Octal Converter switches a number between base 10 and base 8. Type a decimal such as $6521$ and you immediately get its octal form $14571_8$ ; flip the mode and the same tool reads an octal value such as $3241_8$ back into decimal $1697$ .

One tool, two directions: “decimal to octal” is the default, and the “octal to decimal” mode runs the conversion the other way. Both output fields are read-only — the result always follows from whatever you type.

This is the tool to reach for when you are studying number systems, decoding an octal value from documentation, checking a permission code, or just want to confirm what a base-8 representation looks like. Conversions are exact, and the calculator handles negative and fractional values too — so you can convert $-6521$ to $-14571_8$ or $0.5$ to $0.4_8$ in the same way.

How to use / quick start

1

Keep “decimal to octal” selected

This is the default mode under Convert…, so you can usually skip this step.

2

Type the decimal number

For example, enter $6521$ into the (Decimal input)₁₀ field.

3

Read the octal result

The (Octal output)₈ field shows $14571$ — the same value written in base 8. Each place now stands for a power of 8 rather than 10.

4

Convert the other way when needed

Choose octal to decimal, type an octal value such as $3241_8$ , and the (Decimal output)₁₀ field returns $1697$ .

Worked example — why 6521 becomes 14571

Divide by 8, keep the remainder, and repeat with the quotient. The remainders, read from last to first, are the octal digits:

6521 \div 8 = 815

\text{ r }

1

815 \div 8 = 101

\text{ r }

7

101 \div 8 = 12

\text{ r }

5

12 \div 8 = 1

\text{ r }

4

1 \div 8 = 0

\text{ r }

1

Reading the remainders upward gives $14571_8$ . You never have to do this by hand — the calculator shows it instantly — but knowing the pattern makes it easy to sanity-check the result.

Calculation method

Decimal to octal — repeated division by 8

To convert a decimal value, divide it by 8 and record the remainder as the rightmost octal digit. Then divide the quotient by 8 again, and keep going until the quotient reaches zero. The remainders, collected in reverse order, are the octal digits:

d_i = N \bmod 8,\qquad N \gets \left\lfloor \frac{N}{8} \right\rfloor

Because 8 is larger than 10, octal digits appear less often than decimal ones — every three decimal digits usually compress into fewer octal digits, which is part of why octal is handy for compact output.

Octal to decimal — positional expansion

Going back, each octal digit $d_i$ sits at a position worth $8^i$ , starting from the right at $i = 0$ :

N_{10} = \sum_{i=0}^{n-1} d_i \cdot 8^i

For $3241_8$ , that works out to:

3 \times 8^3 + 2 \times 8^2 + 4 \times 8^1 + 1 \times 8^0

=

1536 + 128 + 32 + 1

=

1697

The two modes are exact mirrors of each other, so you can check either direction and get the same value back.

What about fractions?

The same idea extends past the decimal point. Multiply the fractional part by 8, take the whole part as the next octal digit, and repeat. For example, $0.5$ becomes $0.4_8$ because $0.5 = \frac{4}{8}$ .

Octal and binary

Octal is base 8, so it uses only the digits $0$ through $7$ — there is no 8 or 9. Its close cousin is binary (base 2), and the two are tightly linked because $8 = 2^3$ .

One octal digit is exactly three binary bits

Since each octal digit covers the same range as three bits, you can group binary digits in threes and read them straight across to octal. For example, $6521_{10}$ is $1100101111001_2$ , and grouping $001\;100\;101\;111\;001$ gives $1\,4\,5\,7\,1$ — octal $14571$ again. If you want to work directly at the bit level, the binary converter shows fixed-width bit patterns for both positive and negative values.

You will most often meet octal in computing. Unix-style file permissions are conventionally written as octal codes such as $755$ , and some legacy file formats and embedded systems still express values in octal because of how conveniently it packs binary. If you are decoding a permission value, the chmod calculator turns those octal codes into the readable $rwx$ permission letters.

Frequently asked questions

Why is an input like 18 rejected?

Because octal only has the digits $0$ through $7$ . A number such as $18$ contains an 8, which does not exist in base 8, so the calculator flags it. The decimal $18$ is fine — it just converts to octal $22$ .

Does it handle negative or fractional numbers?

Yes. Negative values keep their sign, so $-6521$ becomes $-14571_8$ . Fractions convert too — $0.5$ is $0.4_8$ , and $12.4_8$ reads back as $10.5$ .

How large a number can I convert?

The octal side accepts up to 16 digits, so the largest value is $7777777777777777_8 = 281,474,976,710,655$ . The decimal side accepts magnitudes below $999,999,999,999,999,999$ . If you need hexadecimal or any base between 2 and 64, the integer base converter is a more general tool.

Limitations

This converter works with base 10 and base 8 only. The octal input accepts just the digits $0$ to $7$ and at most 16 digits, and the decimal input must be smaller than $999,999,999,999,999,999$ in magnitude. Integer conversions are exact. For fractional values that do not terminate in base 8 — such as $0.1$ , which repeats as $0.06314631463146314631\ldots_8$ — the result is shown to a practical number of digits rather than an endless string. For hexadecimal or other bases, use a dedicated base converter instead.

Decimal to Octal Converter

Introduction / overview

How to use / quick start

Calculation method

Decimal to octal — repeated division by 8

Octal to decimal — positional expansion

Frequently asked questions

Why is an input like 18 rejected?

Does it handle negative or fractional numbers?

How large a number can I convert?

Limitations

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