Octal to Decimal
Convert octal (base-8) numbers to decimal (base-10) instantly using the weighted power-of-8 method, with full step-by-step working shown. Supports integers, fractional octal numbers, and a built-in reference for common Unix/Linux chmod permission values.
What is Octal to Decimal Conversion?
The Octal to Decimal Converter is a free, browser-based tool that converts octal (base-8) numbers into decimal (base-10) using the weighted power-of-8 method. It supports integer and fractional octal numbers, displays the full step-by-step calculation, and includes a built-in reference table for common Unix/Linux chmod permission values (755→493, 644→420, 777→511, and more).
How It Works
- Enter your octal number (digits 0–7 only), including a decimal point if you need a fractional conversion.
- The tool multiplies each digit by 8 raised to its position's power, counting from 0 at the rightmost digit.
- For fractional numbers, digits after the point are multiplied by negative powers of 8.
- All results are summed to produce the final decimal value.
- View the full step-by-step breakdown, or check the built-in chmod reference table for common permission values.
Common Mistakes to Avoid
❌ Including invalid digits (8 or 9)
✓ Solution:
which aren't valid in octal and signal invalid input.
❌ Misreading position order
✓ Solution:
always count positions from 0 at the rightmost digit.
❌ Forgetting negative powers for fractional parts
✓ Solution:
which use 8⁻¹, 8⁻², and so on rather than positive powers.
❌ Manually miscalculating chmod values
✓ Solution:
which can create real security vulnerabilities by granting unintended access.
Frequently Asked Questions
Multiply each digit by 8 raised to its position's power, counting from 0 on the right, then sum the results. Octal 347 converts to 231 decimal this way.
chmod permissions are written in octal, but some scripts expect decimal values. chmod 755 converts to 493, and chmod 644 converts to 420.
Octal 777 equals decimal 511. This grants full read, write, and execute access to everyone, often considered insecure for most files.
Yes. The integer part uses positive powers of 8 and the fraction uses negative powers. Octal 12.34 converts to decimal 10.4375.
Octal maps to 3 binary bits per digit; hexadecimal maps to 4. Decimal is for human counting, and binary is the native language of computer hardware.
Octal to Decimal Converter: Convert Numbers with Step-by-Step Solutions
You're looking at a chmod permission value, a legacy PDP-era memory address, or a homework problem in octal, and you need the actual decimal number — not a rough guess. Manual conversion is simple in concept but easy to slip up on once fractional digits or larger numbers are involved. This converter handles it instantly and shows the full calculation so you can verify it yourself.
What Is Octal to Decimal Conversion?
Octal-to-decimal conversion translates a base-8 number — using digits 0 through 7 — into its base-10 equivalent. Each octal digit represents a power of 8 based on its position, counting from 0 at the rightmost digit. To convert, multiply each octal digit by 8 raised to its position's power, then sum the results. For example, octal 347 converts to decimal as: (3×8²) + (4×8¹) + (7×8⁰) = (3×64) + (4×8) + (7×1) = 192 + 32 + 7 = 231.
Why Convert Octal to Decimal
Understand Unix/Linux file permissions. chmod permissions are written in octal (755, 644, 777), but some older scripts, system calls, and configuration files expect decimal values instead. Converting chmod 755 to its decimal equivalent, 493, is essential for compatibility with these systems — and an incorrect conversion when manually setting permissions can create real security vulnerabilities.
Maintain legacy hardware and mainframes. Early computers (PDP-8, PDP-11, DEC-10, and various IBM mainframes) documented memory addresses, registers, and configuration settings in octal, since their 12-bit, 24-bit, and 36-bit word sizes divide evenly into octal digits. Converting this documentation to decimal helps administrators calculate memory ranges and configure emulators.
Work with industrial control systems. Some programmable logic controllers (PLCs) and industrial control systems use octal addressing for I/O modules. Converting these addresses to decimal helps engineers understand channel numbers during troubleshooting.
Learn or teach number systems. The weighted-sum conversion method is a foundational computer science concept, and step-by-step results make the underlying logic clear for students and self-learners alike.
How the Conversion Works
Integer conversion: multiply each digit by 8 raised to its position's power (counting from 0 at the rightmost digit), then sum the results.
Worked example — octal 347: (3×8²) + (4×8¹) + (7×8⁰) = (3×64) + (4×8) + (7×1) = 192 + 32 + 7 = 231
Worked example — chmod 755: (7×8²) + (5×8¹) + (5×8⁰) = (7×64) + (5×8) + (5×1) = 448 + 40 + 5 = 493
Fractional octal numbers convert the integer and fractional parts separately. Fractional digits use negative powers of 8 (8⁻¹=0.125, 8⁻²=0.015625, 8⁻³=0.001953125).
Worked example — octal 12.34: Integer part: (1×8¹)+(2×8⁰) = 8+2 = 10. Fractional part: (3×0.125)+(4×0.015625) = 0.375+0.0625 = 0.4375. Combined: 10.4375
Quick Mental Conversion for Small Octal Numbers
Memorize the key powers of 8: 8⁰=1, 8¹=8, 8²=64, 8³=512, 8⁴=4,096. For a 1-digit octal number (0–7), the decimal value is identical. For a 2-digit number (10–77), decimal = (first digit × 8) + second digit — for example, 47 octal = (4×8)+7 = 39. For a 3-digit number, decimal = (first digit × 64) + (second digit × 8) + third digit.
Common Mistakes and How to Fix Them
Including invalid digits (8 or 9). Octal only uses digits 0–7. An 8 or 9 anywhere in the number signals invalid input, not a valid octal value.
Misreading position order. Always count positions starting from 0 at the rightmost digit, the least significant position (worth 8⁰=1). Counting from the left instead reverses the place values and produces an incorrect result.
Forgetting negative powers for fractional parts. Digits after the octal point use negative powers of 8 (8⁻¹=0.125, 8⁻²=0.015625, and so on) — treating them the same as integer-side digits gives a wrong result.
Manually miscalculating chmod values. An incorrect conversion when manually setting file permissions can create a real security vulnerability by granting broader access than intended. Cross-check against a known reference value (755=493, 644=420, 777=511) whenever precision matters.
Final Checklist for Octal to Decimal Conversion
- Confirm the input contains only valid octal digits (0–7, plus a decimal point for fractions)
- Count positions starting from 0 at the rightmost digit
- Multiply each digit by 8 raised to its position's power
- For fractions, use negative powers of 8 for digits after the point
- Sum all results to get the final decimal value
- Cross-check chmod conversions against known reference values
- Use the step-by-step breakdown to verify any manual calculation
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