Octal to Decimal Converter

Octal to Decimal Converter

Convert octal numbers to decimal format. This tool provides step-by-step calculation showing how each octal digit is multiplied by powers of 8 to get the decimal equivalent.

What is octal to decimal conversion?

Octal to decimal conversion is the process of converting a base-8 number to a base-10 number. Each digit is multiplied by 8 raised to the power of its position, starting from the rightmost digit (8⁰).

How do you convert octal to decimal?

To convert octal to decimal:
1. Write down the octal number
2. Multiply each digit by 8 raised to the power of its position (from right to left, starting with 0)
3. Add all the results together

Example: 17₈ = 1×8¹ + 7×8⁰ = 8 + 7 = 15₁₀

What is the formula for octal to decimal conversion?

The formula is: Decimal = dₙ×8ⁿ + dₙ₋₁×8ⁿ⁻¹ + ... + d₁×8¹ + d₀×8⁰

Where dₙ is the nth digit from the right, and n is the position (starting from 0).

Why use octal instead of decimal?

Octal is useful in computing because:
- Easy conversion to binary (3 octal digits = 9 binary digits)
- More compact than binary
- Used in Unix file permissions
- Common in some programming contexts

Octal to Decimal Conversion Table