How does octal convert to decimal?

Octal is base 8, so each digit's value is the digit multiplied by 8 raised to the power of its position, counting from zero at the rightmost digit. Summing all those terms gives the decimal value.

Which digits are valid in octal?

Only the digits 0 through 7. There is no digit 8 or 9 in octal, just as there is no single digit for ten in decimal.

Where is octal still used?

Octal is most common in Unix and Linux file permissions, where modes like 755 or 644 are octal. It groups three bits per digit, which suits the read/write/execute permission triplets.

Why is 10 in octal equal to 8 in decimal?

In octal, the number after 7 rolls over to 10, just as decimal rolls over after 9. So octal 10 means one eight plus zero ones, which is 8 in decimal.

Can it handle large octal numbers?

Yes. The converter uses exact big-integer arithmetic, so even very long octal strings convert to decimal without any rounding error.

What is the Octal to Decimal Converter?

Convert octal (base-8) integers to decimal (base-10) using exact positional expansion. Each digit is multiplied by its power of 8 and summed, with the full term breakdown shown. Runs entirely in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

Octal to Decimal Converter

Name: Octal to Decimal Converter
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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Converting octal to decimal is a frequent need for anyone working with Unix file permissions, older computing systems or low-level data, since octal packs neatly into groups of three bits. This converter evaluates a base-8 number positionally and shows the full working so you can follow the math.

How it works

Octal is a base-8 positional system using the digits 0 through 7. The value of a number is the sum of each digit multiplied by 8 raised to the power of that digit’s position, where positions are counted from zero starting at the rightmost digit. So the rightmost digit is multiplied by 8 to the power 0 (which is 1), the next by 8 to the power 1 (which is 8), the next by 64, and so on.

The tool walks the string from right to left, computes each digit’s place value as a power of 8, multiplies, and accumulates the total using exact big-integer arithmetic.

Powers of 8 reference

Position	Power of 8	Decimal value
0 (rightmost)	8⁰	1
1	8¹	8
2	8²	64
3	8³	512
4	8⁴	4,096
5	8⁵	32,768

Unix permission example

The most common real-world use of octal: Unix file permission modes from chmod. Each octal digit encodes three bits for one of the permission triplets — owner, group, others — where 4 = read, 2 = write, 1 = execute.

For example, convert the permission mode 755:

7 × 8² + 5 × 8¹ + 5 × 8⁰
= 7 × 64 + 5 × 8 + 5 × 1
= 448 + 40 + 5
= 493

So octal 755 is decimal 493. In permission terms, 7 = rwx (owner), 5 = r-x (group), 5 = r-x (others) — typical for executable programs.

Another common mode: 644 (files that should be readable but not executable):

6 × 64 + 4 × 8 + 4 × 1 = 384 + 32 + 4 = 420

Octal 644 is decimal 420, meaning rw-r--r--.

Additional examples

Octal	Decimal	Common meaning
`0`	0	No permissions
`7`	7	Full permissions for one role
`10`	8	Execute bit in the next group
`17`	15	(combine)
`777`	511	Full permissions for everyone

Tips

If you enter a digit of 8 or 9 the tool flags an error, since those are not valid octal digits — only 0 through 7 exist in base-8. For large octal strings (like 64-bit addresses printed in octal by some debuggers), the converter uses exact big-integer arithmetic so no rounding occurs. All processing runs locally in your browser; nothing leaves your device.