Octal to Decimal Converter Formula
Understand the math behind the octal to decimal converter. Each variable explained with a worked example.
Formulas Used
Decimal Value
decimal_val = o4*4096 + o3*512 + o2*64 + o1*8 + o0Variables
| Variable | Description | Default |
|---|---|---|
o4 | Octal Digit 4 (4096s) | 0 |
o3 | Octal Digit 3 (512s) | 0 |
o2 | Octal Digit 2 (64s) | 1 |
o1 | Octal Digit 1 (8s) | 4 |
o0 | Octal Digit 0 (1s) | 4 |
How It Works
How to Convert Octal to Decimal
Method
Octal (base-8) uses digits 0-7. Each position represents a power of 8.
Decimal = d4×8⁴ + d3×8³ + d2×8² + d1×8¹ + d0×8⁰
For example, octal 144 = 1×64 + 4×8 + 4×1 = 64 + 32 + 4 = 100.
Worked Example
Convert octal 00144 to decimal.
o4 = 0o3 = 0o2 = 1o1 = 4o0 = 4
- 010×4096 + 0×512 + 1×64 + 4×8 + 4×1
- 02= 0 + 0 + 64 + 32 + 4
- 03= 100
Frequently Asked Questions
What is the octal number system?
Octal (base-8) uses digits 0 through 7. It was historically used in computing because each octal digit represents exactly 3 binary bits.
Where is octal used today?
Octal is used in Unix/Linux file permissions (like chmod 755) and occasionally in programming for representing groups of 3 binary bits.
How do you convert decimal to octal?
Repeatedly divide the decimal number by 8, recording the remainder at each step. Read the remainders from bottom to top.
Ready to run the numbers?
Open Octal to Decimal Converter