Convert octal to decimal by summing place values – each digit is multiplied by a power of 8. A permission mask like 755 becomes 493 in decimal.
Show calculation steps
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Powers of eight, summed
Octal place values run 1, 8, 64, 512 — each digit multiplies its power and the total is the decimal value. The expansion is exact, mechanical and shown in full by the steps panel for your own digits.
You need this direction whenever octal notation meets ordinary arithmetic: comparing a permission mask numerically, decoding a legacy dump, or checking a umask calculation.
Worked example
Input: 755
7×64 = 448
5× 8 = 40
5× 1 = 5
-----
493| Power | Value |
|---|---|
| 8^0 | 1 |
| 8^1 | 8 |
| 8^2 | 64 |
| 8^3 | 512 |
| 8^4 | 4096 |
| 8^5 | 32768 |
| 8^6 | 262144 |
Digit legality
Octal’s eight symbols stop at 7 — an 8 or 9 anywhere means the value is not octal, and this tool says so with the exact position rather than mis-multiplying. That validation catches the classic error of decimal numbers labelled octal, which silent converters happily corrupt.
Where you meet it
Permission masks in scripts and APIs, umask values, tar/cpio header fields (stored as octal text), old core-dump and PDP-era documentation, and C-heritage escape sequences. Octal is a niche, but a durable one — and inside the niche this conversion is constant.
Exactness and privacy
Unbounded exact expansion via BigInt; leading zeros are harmless; prefixes are validated. The octal fraction pages handle radix points. Your input is processed in-browser and never leaves the device.
How to use the Octal to Decimal Converter
- Enter the octal number (0o prefix optional; digits 0-7 only).
- Click "Convert to decimal".
- The steps multiply each digit by its power of 8 and total them.
- Copy the decimal result.
Frequently asked questions
How do octal place values work?
Powers of 8 from the right: 1, 8, 64, 512. For 755: 7×64 + 5×8 + 5×1 = 448+40+5 = 493. The steps show these products for your own digits.
Why does my permission mask decode to a weird decimal?
Because permission bits were never meant to be read in decimal – 755 → 493 has no intuitive meaning. The decimal form matters only when an API demands an integer; this tool provides the bridge.
What if my number contains an 8?
Then it is not octal, and the tool says exactly where the 8 sits instead of mis-multiplying. This commonly catches decimals mistakenly labelled octal.
Do leading zeros change anything – is 0755 different from 755?
Not as a value – both are 493. The pitfall lives in programming languages where a LITERAL starting 0 was silently octal; here the base is explicit, so no ambiguity exists.
Can this handle very long octal strings?
Yes – exact at any length via BigInt. A 30-digit octal converts to its full decimal without loss.
How is this related to binary?
Each octal digit is exactly three bits, so octal is binary shorthand. If you need the bits themselves, Octal to Binary expands per-digit with no arithmetic.
Is anything stored when I convert?
No – computation is local, and analytics record only the fact of a conversion, never the value.
