How do you convert octal to decimal?

Multiply each digit of the octal number by 8 raised to the power of its position index (starting from 0 on the far right), then sum up all the resulting products.

What is octal 113 in decimal?

Octal 113 converts to 75 in decimal. Calculation: (1 * 8²) + (1 * 8¹) + (3 * 8⁰) = 64 + 8 + 3 = 75.

Mathematical Tutorial Updated July 2026

Octal to Decimal Converter — 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

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