Octal to Decimal Converter
Convert octal numbers (base 8) to decimal numbers (base 10) with this free converter. Octal uses digits 0 through 7, whilst decimal uses 0 through 9. Enter your octal value below to see the decimal equivalent instantly.
Quick Conversions
Click any button below for instant conversion of common octal values.
Octal to Decimal Conversion Table
This table shows common octal numbers and their decimal equivalents.
| Octal (Base 8) | Decimal (Base 10) | Octal (Base 8) | Decimal (Base 10) |
|---|---|---|---|
| 0 | 0 | 20 | 16 |
| 1 | 1 | 21 | 17 |
| 2 | 2 | 22 | 18 |
| 3 | 3 | 23 | 19 |
| 4 | 4 | 24 | 20 |
| 5 | 5 | 30 | 24 |
| 6 | 6 | 40 | 32 |
| 7 | 7 | 50 | 40 |
| 10 | 8 | 60 | 48 |
| 11 | 9 | 70 | 56 |
| 12 | 10 | 77 | 63 |
| 13 | 11 | 100 | 64 |
| 14 | 12 | 144 | 100 |
| 15 | 13 | 200 | 128 |
| 16 | 14 | 377 | 255 |
| 17 | 15 | 777 | 511 |
Conversion Formula and Method
The octal system operates on base 8, which means each position represents a power of 8. Converting from octal to decimal requires multiplying each digit by its positional value.
The Formula
Where d represents each octal digit, and n represents the position from right to left (starting at 0).
Step-by-Step Method
Follow these steps to convert any octal number to decimal:
- Write down the octal number – Identify each digit from right to left
- Assign position values – Starting from 0 on the right, number each position
- Calculate powers of 8 – Work out 80=1, 81=8, 82=64, etc.
- Multiply each digit – Multiply each octal digit by its corresponding power of 8
- Sum the results – Add all the products together to get your decimal answer
Worked Example: Convert 754₈ to Decimal
Step 1: Identify the digits: 7, 5, 4
Step 2: Assign positions (right to left): 4 is position 0, 5 is position 1, 7 is position 2
Step 3: Calculate the powers: 80 = 1, 81 = 8, 82 = 64
Step 4: Multiply: (7 × 64) + (5 × 8) + (4 × 1)
Step 5: Sum: 448 + 40 + 4 = 492
Answer: 754₈ = 492₁₀
Another Example: Convert 123₈ to Decimal
Breakdown: 1 × 82 + 2 × 81 + 3 × 80
Calculation: (1 × 64) + (2 × 8) + (3 × 1) = 64 + 16 + 3 = 83
Answer: 123₈ = 83₁₀
Number System Conversions
Octal is part of a family of number systems used in computing and mathematics. Here’s how octal compares with other common bases.
| Binary (Base 2) | Octal (Base 8) | Decimal (Base 10) | Hexadecimal (Base 16) |
|---|---|---|---|
| 0000 | 0 | 0 | 0 |
| 0001 | 1 | 1 | 1 |
| 0010 | 2 | 2 | 2 |
| 0011 | 3 | 3 | 3 |
| 0100 | 4 | 4 | 4 |
| 0101 | 5 | 5 | 5 |
| 0110 | 6 | 6 | 6 |
| 0111 | 7 | 7 | 7 |
| 1000 | 10 | 8 | 8 |
| 1001 | 11 | 9 | 9 |
| 1010 | 12 | 10 | A |
| 1111 | 17 | 15 | F |
| 10000 | 20 | 16 | 10 |
| 11111111 | 377 | 255 | FF |
Where Octal Numbers Appear
Whilst octal isn’t as common today as hexadecimal, it still pops up in various computing contexts. Understanding when you might encounter octal helps contextualise why this conversion matters.
Unix File Permissions
Unix and Linux systems use octal notation for file permissions. The familiar “chmod 755” command sets read, write, and execute permissions using octal values. Each digit represents permissions for owner, group, and others.
Early Computing Systems
Older computer systems, particularly those with 12-bit, 24-bit, or 36-bit word sizes, favoured octal because these word lengths divide evenly by three. Each octal digit represents exactly three binary bits.
Digital Electronics
Some digital circuit designs and embedded systems documentation use octal notation to represent binary states more compactly than binary itself, whilst remaining more readable than hexadecimal for certain applications.
FAQs
An octal number is a number expressed in base 8, using only the digits 0 through 7. Each position in an octal number represents a power of 8, similar to how each position in decimal represents a power of 10.
Octal provides a more compact way to represent binary numbers compared to binary itself. Three binary digits convert directly to one octal digit, which historically made octal popular in computing before hexadecimal became the standard.
Octal numbers only contain digits 0-7. If you see an 8 or 9, it’s not octal. In programming, octal numbers often have a leading zero (like 0755) or are marked with a subscript 8 (like 755₈) in mathematical notation.
Yes, octal numbers can represent fractional values. The digits after the octal point represent negative powers of 8 (8-1, 8-2, etc.). For example, 0.4₈ equals 0.5₁₀ because 4 × 8-1 = 4/8 = 0.5.
The largest single digit in octal is 7. This is because octal is base 8, so it uses eight digits total (0, 1, 2, 3, 4, 5, 6, 7). The next number would be 10₈, which equals 8 in decimal.
Octal and binary have a direct relationship. Each octal digit corresponds to exactly three binary digits. For example, 7₈ = 111₂, 5₈ = 101₂, and 3₈ = 011₂. This makes conversion between octal and binary straightforward.
Octal is less common than hexadecimal in modern computing, but it’s still used in Unix/Linux file permissions and occasionally in embedded systems. Most contemporary programming languages support octal literals for backwards compatibility.
You can’t convert 89 from octal because octal only uses digits 0-7. The digits 8 and 9 don’t exist in base 8. If you see these digits, the number is either decimal, hexadecimal, or another base system.