Perform octal (base-8) arithmetic and convert between octal, decimal, binary and hex.
Octal (base-8) uses digits 0–7. Each octal digit maps to exactly three binary digits, making it a compact notation for binary data. Arithmetic in octal works the same as decimal — carry at 8 instead of 10. To perform arithmetic, the calculator converts both operands to decimal, applies the operation, and converts the result back to octal, binary and hexadecimal.
Octal to Decimal
decimal = Σ(digit_i × 8^i) for i from 0 to n-1
Each octal digit corresponds to exactly three binary bits, so octal is a concise way to represent binary data. It is used in Unix file permissions (e.g. 755) and some legacy computing contexts.
Multiply each digit by 8 raised to its position (rightmost is position 0) and sum: 17₈ = 1×8¹ + 7×8⁰ = 8 + 7 = 15.