Octal Calculator
Perform octal (base-8) arithmetic and convert between octal, decimal, binary and hex.
Inputs
An octal integer (digits 0-7 only).
Second operand (ignored for convert-only).
Result (Octal)
24
Result (Decimal)
20
Result (Binary)
10100
Result (Hex)
14
Step by step
Operation
17₈ + 5₈
Decimal values
A = 15, B = 5
Result (decimal)
= 20
Result (octal)
= 24
How it works
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.
Formula
Octal to Decimal
decimal = Σ(digit_i × 8^i) for i from 0 to n-1
- digit_i
- The ith octal digit (from the right, 0-indexed)
- i
- Position index
Frequently Asked Questions
Why is octal useful?
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.
How do I convert octal to decimal by hand?
Multiply each digit by 8 raised to its position (rightmost is position 0) and sum: 17₈ = 1×8¹ + 7×8⁰ = 8 + 7 = 15.