Mathematical Tutorial
How to Convert Octal to Decimal.
Learn how to calculate standard base-10 decimal values from base-8 octal numbers.
Try it: Octal to Decimal mini-calculator
Decimal Result: 75
Positional notation method.
Octal is a base-8 positional notation system. Each column value represents a power of 8, starting with 80 on the far right and increasing by power factors as you move left.
Decimal = (d₀ × 8⁰) + (d₁ × 8¹) + (d₂ × 8²) + ...
Step-by-step example.
Convert the octal value 113 to decimal:
- Identify digit values: 1, 1, and 3.
- Apply positional weights:
- Rightmost digit (3): 3 × 80 = 3 × 1 = 3
- Middle digit (1): 1 × 81 = 1 × 8 = 8
- Leftmost digit (1): 1 × 82 = 1 × 64 = 64
- Sum the terms: 64 + 8 + 3 = 75.
Octal to Decimal Chart
| Octal | Decimal |
|---|---|
| 10 | 8 |
| 20 | 16 |
| 100 | 64 |
| 113 | 75 |