Octal Calculator
Perform arithmetic operations in Octal number system. Enter two octal numbers and select an operation.
About Octal Calculator
The Octal Calculator allows you to perform addition, subtraction, multiplication, and division operations directly in the octal number system without converting to decimal first.
How the Octal Calculator Works
An octal calculator performs arithmetic on base-8 numbers, which use digits 0 through 7. Octal arithmetic carries at 8 instead of 10. Each octal digit corresponds to exactly 3 binary bits, making octal a convenient shorthand for binary in certain computing contexts — particularly Unix/Linux file permissions.
- Enter two octal numbers (digits 0–7 only)
- Select an operation: +, −, ×, or ÷
- The result is displayed in octal format
Octal Arithmetic Rules
Addition: Add digit values. If sum ≥ 8, write (sum − 8) and carry 1.
Example: 7 + 3 = 10 → write 2, carry 1 (since 10₁₀ = 12₈)
Subtraction: If top digit < bottom digit, borrow 8 from next column.
Example: 3 − 5 → borrow to get 11 − 5 = 6 (in octal: 13₈ − 5₈ = 6₈)
Multiplication: Multiply digit values, carry when product ≥ 8.
Division: Long division in base-8.
Worked Example: 755 + 22 (Octal)
755₈ (493 in decimal)
+ 22₈ (18 in decimal)
------
Column 0: 5 + 2 = 7
Column 1: 5 + 2 = 7
Column 2: 7 + 0 = 7
Result: 777₈ = 511₁₀
Verification: 493 + 18 = 511 ✓
Technical Details
Octal was widely used in early computing (PDP-8, UNIVAC, IBM mainframes) because their word sizes were multiples of 3 bits, making octal a natural fit. Today, octal's primary use is in Unix/Linux file permissions: each permission set (owner, group, others) is a 3-bit value (read=4, write=2, execute=1), and the three sets form a 3-digit octal number. For example, chmod 755 means owner=rwx (7), group=r-x (5), others=r-x (5). In C and C++, octal literals are prefixed with 0 (e.g., 0755). This calculator performs integer arithmetic with floor division.
Frequently Asked Questions
What is 777 + 1 in octal?
777₈ + 1₈ = 1000₈. In decimal: 511 + 1 = 512. The carry propagates through all three columns, similar to 999 + 1 = 1000 in decimal.
Why is octal used for file permissions?
Each permission (read, write, execute) is one bit, and each user class (owner, group, others) has 3 permissions — exactly one octal digit. This makes octal a perfect fit: 7 = rwx, 5 = r-x, 4 = r--, 0 = ---.
What digits are valid in octal?
Only 0, 1, 2, 3, 4, 5, 6, and 7. The digits 8 and 9 do not exist in base-8. If you enter 8 or 9, the input is invalid.
How does octal relate to binary?
Each octal digit maps to exactly 3 binary bits: 0=000, 1=001, 2=010, 3=011, 4=100, 5=101, 6=110, 7=111. So octal 755 = binary 111 101 101.