Octal to Decimal Converter – With Expansion Steps
Octal <> Decimal Engine
High-precision base-8 to base-10 numerical trans-translator with expansion mapping
Quick answer
To convert octal to decimal, multiply each digit by 8 raised to its position (counting from 0 on the right) and add the results. For 755: 7 × 8² + 5 × 8¹ + 5 × 8⁰ = 448 + 40 + 5 = 493. Octal digits can only be 0 to 7.
Our free octal to decimal converter shows this expansion for every digit, so you can follow and check the maths. Switch to Decimal to Octal to go the other way. It is especially handy for Unix and Linux file permissions (chmod 755, 644), older computing systems and computer science homework.
What Is the Octal Number System?
Octal is base 8. It uses the digits 0 to 7, and each place is worth eight times the place to its right: 1, 8, 64, 512, 4096 and so on. Because 8 is 2³, each octal digit maps neatly to three binary bits, which made octal popular in early computers. Today you mostly meet it in file permissions, where each digit sets read (4), write (2) and execute (1) for one group of users.
Octal to Decimal Formula
For an octal number with digits dn…d1d0: decimal = dn × 8n + … + d1 × 8 + d0.
| Digit | Position | Calculation | Value |
|---|---|---|---|
| 7 | 2 | 7 × 64 | 448 |
| 5 | 1 | 5 × 8 | 40 |
| 5 | 0 | 5 × 1 | 5 |
| Total | 493 | ||
How to Use the Octal to Decimal Converter
Step 1: Select Octal to Decimal
Make sure the Octal to Decimal tab is active. Choose Decimal to Octal instead if you are starting from a base-10 number.
Step 2: Enter the Octal Number
Type your base-8 number using digits 0 to 7 only. We enter 755, a common file permission.
Step 3: Click Convert Base
Press Convert Base. If the number contains 8 or 9, the octal to decimal tool shows a validation error because those digits do not exist in base 8.
Step 4: Read the Decimal Value and Steps
The result shows 493 with a Copy Result button. The Expansion Steps Matrix lists each digit, its power of 8 and its value, ending with the total.
Octal to Decimal Chart
| Octal | Decimal | Octal | Decimal |
|---|---|---|---|
| 7 | 7 | 177 | 127 |
| 10 | 8 | 377 | 255 |
| 12 | 10 | 644 | 420 |
| 17 | 15 | 755 | 493 |
| 20 | 16 | 777 | 511 |
| 52 | 42 | 1000 | 512 |
| 77 | 63 | 100 | 64 |
Octal and Unix File Permissions
| chmod | Owner | Group | Others | Decimal |
|---|---|---|---|---|
| 755 | read, write, execute | read, execute | read, execute | 493 |
| 644 | read, write | read | read | 420 |
| 777 | all | all | all | 511 |
Decimal to Octal
To go back, divide the decimal number by 8 repeatedly and read the remainders from bottom to top. 493 ÷ 8 = 61 r 5, 61 ÷ 8 = 7 r 5, 7 ÷ 8 = 0 r 7, so 493 = 755 in octal. The Decimal to Octal tab does this for you.
Common Mistakes to Avoid
- Using 8 or 9. They are not valid octal digits.
- Counting positions from the left. Position 0 is always the rightmost digit.
- Reading 10 as ten. In octal, 10 means eight.
- Ignoring prefixes. Some languages write octal as 0o755 or 0755. Remove the prefix before using the octal to decimal tool.
Frequently Asked Questions
How do I convert octal to decimal?
Multiply each digit by 8 to the power of its position from the right (starting at 0), then add. 52 = 5 × 8 + 2 = 42.
What is 755 in decimal?
755 in octal is 493 in decimal.
What is 777 octal in decimal?
777 in octal is 511 in decimal.
Why can't octal numbers have 8 or 9?
Base 8 only has eight digits, 0 to 7. After 7 the count rolls over to 10.
Can this tool convert decimal to octal?
Yes. Click Decimal to Octal, enter a base-10 number and convert.
Is this octal to decimal converter free?
Yes. It is free, needs no sign-up, and runs entirely in your browser.