Octal Converter Formula

Understand the math behind the octal converter. Each variable explained with a worked example.

Use the Octal Converter

Formulas Used

Decimal Value

decimal = o5 * 32768 + o4 * 4096 + o3 * 512 + o2 * 64 + o1 * 8 + o0

Variables

VariableDescriptionDefault
o5Octal Digit 5 (32768s)0
o4Octal Digit 4 (4096s)0
o3Octal Digit 3 (512s)0
o2Octal Digit 2 (64s)7
o1Octal Digit 1 (8s)5
o0Octal Digit 0 (1s)5

How It Works

Octal to Decimal Converter

How It Works

Octal (base-8) uses digits 0-7. Each position represents a power of 8:

  • Digit 0: 8^0 = 1
  • Digit 1: 8^1 = 8
  • Digit 2: 8^2 = 64
  • Digit 3: 8^3 = 512
  • Digit 4: 8^4 = 4096
  • Digit 5: 8^5 = 32768

    • Multiply each digit by its place value and sum all the results.

    Worked Example

    Convert octal 755 to decimal.

    o5 = 0o4 = 0o3 = 0o2 = 7o1 = 5o0 = 5
    1. 017×64 + 5×8 + 5×1
    2. 02= 448 + 40 + 5
    3. 03= 493 in decimal

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