Octal to Decimal Converter
Free online tool to instantly convert octal (Base 8) to decimal (Base 10). Includes quick conversion tables and step-by-step mathematical explanations.
How to convert Octal to Decimal
Converting from Octal (Base 8) toDecimal (Base 10) involves positional value evaluation.
Convert Octal to Decimal
Multiply each digit of the octal number by 8 raised to the power of its position index (starting from position 0 on the right). Sum all products together to obtain the decimal equivalent.
Octal to Decimal Quick Conversion Table
Common values converted between Octal (Base 8) and Decimal (Base 10):
| Octal (8) | Decimal (10) |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 7 |
| 10 | 8 |
| 11 | 9 |
| 12 | 10 |
| 13 | 11 |
| 14 | 12 |
| 15 | 13 |
| 16 | 14 |
| 17 | 15 |
| 20 | 16 |
| 40 | 32 |
| 100 | 64 |
| 144 | 100 |
| 377 | 255 |
Octal to Decimal Frequently Asked Questions
Common questions and step-by-step mathematical answers about converting Octal (Base 8) to Decimal (Base 10).
1How do you convert octal to decimal?↓
Start from the rightmost digit with 8⁰=1, the next with 8¹=8, 8²=64, etc. Multiply each digit by its positional weight and add all values.
2What is the formula for octal to decimal conversion?↓
Decimal = dₙ·8ⁿ + dₙ₋₁·8ⁿ⁻¹ + ... + d₁·8¹ + d₀·8⁰.
3How do you convert octal numbers to decimal manually?↓
Example with 247₈: (2 × 64) + (4 × 8) + (7 × 1) = 128 + 32 + 7 = 167₁₀.
4What is 10 in decimal from octal?↓
(1 × 8¹) + (0 × 8⁰) = 8 + 0 = 8₁₀.
5What is 25 in decimal from octal?↓
(2 × 8¹) + (5 × 8⁰) = 16 + 5 = 21₁₀.
6What is 100 in decimal from octal?↓
(1 × 8²) + (0 × 8¹) + (0 × 8⁰) = 64 + 0 + 0 = 64₁₀.
7How does octal place value work?↓
Moving from right to left, each position is 8 times larger than the previous one.
8How do you convert octal fractions to decimal?↓
Example: 0.4₈ = 4 × 8⁻¹ = 4 / 8 = 0.5₁₀.
9What digits are used in the octal number system?↓
Digits 8 and 9 do not exist in octal. Any number containing 8 or 9 is invalid in base-8.
10What is the difference between octal and decimal?↓
Octal rolls over to the next place value at 8 (so 7 + 1 = 10₈), whereas decimal rolls over at 10 (9 + 1 = 10₁₀).