Enter any octal number (base-8) into the Octal Input field and get the decimal equivalent (base-10) back immediately. The converter also shows the full step-by-step calculation — each digit multiplied by its power of 8 — so you can see exactly how the conversion works.
Decimal Value (Base-10)
--
Step-by-Step Calculation
--
Binary Equivalent (Base-2)
--
Hexadecimal Equivalent (Base-16)
--
Number of Octal Digits
--
Multiply each digit of the octal number by 8 raised to the power of its position, counting from right starting at 0. Then add all the products together. For example, 345₈ = (3×8²) + (4×8¹) + (5×8⁰) = 192 + 32 + 5 = 229₁₀.
The octal system is base-8, meaning it only uses eight symbols: 0 through 7. Just as decimal (base-10) has no single digit for ten (it uses two digits '10'), octal has no single digit for eight — it becomes '10' in octal notation.
Octal is commonly used in computing and programming contexts, especially for Unix/Linux file permissions (e.g. chmod 755). Converting to decimal helps you work with standard numeric values in everyday calculations or when interfacing with systems that use base-10.
Octal numbers are often written with a leading zero (e.g. 0345) or followed by a subscript 8 (e.g. 345₈). A number containing only digits 0–7 could be either octal or decimal, so context or explicit notation is needed to distinguish them.
The largest single octal digit is 7, which equals 7 in decimal. The two-digit octal number 77₈ equals 63 in decimal, and 777₈ equals 511 in decimal.
Octal became popular in early computing because each octal digit maps directly to exactly three binary bits. This made it a compact shorthand for reading and writing binary data in 6, 12, 24, and 36-bit computer architectures that were common in the mid-20th century.
Yes. Octal is still widely used for Unix file permission codes (read=4, write=2, execute=1), certain network protocols, and some embedded systems. It appears in programming languages like C, Python (prefix 0o), and JavaScript (prefix 0o).
The formula is: decimal = d₀×8⁰ + d₁×8¹ + d₂×8² + … + dₙ×8ⁿ, where d₀ is the rightmost digit and dₙ is the leftmost digit. Each digit is multiplied by 8 raised to the power of its zero-based position from the right.