Decimal to Octal Converter
Convert a decimal integer to octal instantly with an exact base-10 to base-8 converter. Enter any non-negative whole number to get its octal representation, digit count, repeated-division steps, and verified examples.
What Is a Decimal to Octal Converter?
A decimal to octal converter changes a number written in the familiar decimal number system (base 10) into the equivalent octal number system (base 8). Decimal uses digits 0 through 9, while octal uses only the digits 0 through 7.
The octal system is a positional number system. Its place values are powers of eight: 1, 8, 64, 512, 4096, and so on. This means each octal digit represents a multiple of a power of 8.
BinaryCon performs integer conversion using arbitrary-size integer arithmetic, so very large decimal values can be converted exactly without the floating-point rounding problems that affect ordinary JavaScript Number calculations.
Decimal — Base 10
Uses digits 0–9 with place values based on powers of ten.
Octal — Base 8
Uses digits 0–7 with place values based on powers of eight.
How to Use the Decimal to Octal Converter
Type a non-negative whole number such as 45.
BinaryCon calculates the exact base-8 representation automatically.
The main result card shows the complete octal number using only digits 0–7.
For smaller values, the calculator shows repeated division by 8 and the remainders that form the octal digits.
Use the octal value for programming, Unix permissions, digital systems, coursework, or another conversion.
How Decimal to Octal Conversion Works
The standard manual method is repeated division by 8. Divide the decimal integer by 8, record the remainder, then divide the quotient by 8 again. Continue until the quotient becomes zero.
Because octal has eight digits, each remainder will be between 0 and 7. Read the remainders from the final division back to the first division to obtain the octal number.
Worked Example: Convert Decimal 45 to Octal
Another Example: Convert Decimal 255 to Octal
| Division | Quotient | Remainder |
|---|---|---|
| 255 ÷ 8 | 31 | 7 |
| 31 ÷ 8 | 3 | 7 |
| 3 ÷ 8 | 0 | 3 |
Reading the remainders from bottom to top gives
377. Therefore 255₁₀ = 377₈.
Decimal to Octal Conversion Table
| Decimal | Octal | Decimal | Octal |
|---|---|---|---|
| 0 | 0 | 8 | 10 |
| 1 | 1 | 9 | 11 |
| 2 | 2 | 10 | 12 |
| 3 | 3 | 11 | 13 |
| 4 | 4 | 12 | 14 |
| 5 | 5 | 13 | 15 |
| 6 | 6 | 14 | 16 |
| 7 | 7 | 15 | 17 |
| 16 | 20 | 32 | 40 |
| 63 | 77 | 64 | 100 |
| 127 | 177 | 128 | 200 |
| 255 | 377 | 256 | 400 |
| 511 | 777 | 512 | 1000 |
Important Powers of Eight
Octal place values are powers of 8. Learning a few common powers helps verify decimal-to-octal conversions.
| Power | Decimal Value | Octal Representation |
|---|---|---|
| 8⁰ | 1 | 1 |
| 8¹ | 8 | 10 |
| 8² | 64 | 100 |
| 8³ | 512 | 1000 |
| 8⁴ | 4,096 | 10000 |
| 8⁵ | 32,768 | 100000 |
| 8⁶ | 262,144 | 1000000 |
Why Octal Uses Only Digits 0 Through 7
The base of a positional number system determines how many digit values are available before carrying into the next position. Decimal is base 10, so its digits range from 0 through 9. Octal is base 8, so its digits range from 0 through 7.
There is no valid octal digit 8 or 9. When a value reaches decimal 8, octal moves to the next position:
Decimal 8 = Octal 10
Decimal 9 = Octal 11
Decimal 64 and 512 as Useful Octal Benchmarks
Decimal 64 equals 8², so it becomes 100₈.
Decimal 512 equals 8³, so it becomes 1000₈.
512₁₀ = 1000₈
These values are useful checkpoints because powers of the base always appear as a 1 followed by zeros in that number system.
Decimal to Octal vs Decimal to Binary
Decimal-to-octal and decimal-to-binary conversion follow the same general repeated-division idea, but the divisor changes with the target base.
| Target | Base | Repeated Division By | Allowed Digits |
|---|---|---|---|
| Binary | 2 | 2 | 0–1 |
| Octal | 8 | 8 | 0–7 |
| Hexadecimal | 16 | 16 | 0–9, A–F |
Why Octal Is Closely Related to Binary
Octal and binary have a convenient mathematical relationship because 8 = 2³. Every octal digit therefore corresponds exactly to three binary bits.
| Octal | Binary |
|---|---|
| 0 | 000 |
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
This relationship made octal a convenient compact shorthand for binary patterns in some computing systems.
Where Decimal to Octal Conversion Is Used
Unix permissions
Numeric permission values such as 644 and 755 are commonly written in octal because each octal digit maps naturally to three permission bits.
Programming
Some programming languages and system tools support octal literals, file modes, escape values, or legacy numeric formats.
Digital systems
Octal provides a compact way to represent binary bit groups when hexadecimal is not the chosen notation.
Computer science education
Decimal-to-octal exercises help students understand positional bases, repeated division, and relationships among binary, octal, and decimal.
Common Decimal to Octal Conversion Mistakes
Octal contains only digits 0 through 7. Any output containing 8 or 9 is not a valid octal numeral.
With repeated division by 8, the octal digits are obtained by reading remainders from the last division back to the first.
The target number system is base 8, so repeated division must use 8.
Octal 100₈ equals decimal 64 because it represents
1 × 8².
Related BinaryCon Tools
Reverse the conversion or convert the same decimal value into binary, hexadecimal, or BCD using these related tools.
Decimal to Octal Converter FAQs
How do you convert decimal to octal?
Divide the decimal integer repeatedly by 8 and record each remainder. Continue until the quotient reaches zero, then read the remainders from bottom to top. Those remainders form the octal result.
What is decimal 10 in octal?
Decimal 10 equals 12₈. Dividing 10 by 8 gives quotient 1 and remainder 2, then 1 divided by 8 gives quotient 0 and remainder 1. Reading upward gives 12.
What is decimal 45 in octal?
Decimal 45 equals 55₈. Since 5 × 8 + 5 = 45, the octal digits are 5 and 5.
What is decimal 255 in octal?
Decimal 255 equals 377₈. In positional form, 3 × 64 + 7 × 8 + 7 = 192 + 56 + 7 = 255.
What is decimal 512 in octal?
Decimal 512 equals 1000₈ because 512 = 8³. A power of the base is written as 1 followed by the corresponding number of zeros.
Why does octal stop at digit 7?
Octal is base 8, so it has exactly eight digit values: 0 through 7. The next value after 7 is written 10₈, just as decimal moves from 9 to 10.
Is octal 10 equal to decimal 10?
No. Octal 10₈ equals decimal 8 because the left digit
occupies the 8¹ place. Decimal 10 is written 12₈.
Why is octal related to binary?
Because 8 = 2³. Each octal digit corresponds exactly to three binary bits, so binary and octal can be converted directly in 3-bit groups.
Can this decimal to octal converter handle large integers?
Yes. The calculator uses JavaScript BigInt for integer conversion, allowing very large non-negative whole numbers to be converted exactly without ordinary floating-point safe-integer rounding.
Can I convert a negative decimal number to octal?
This page converts non-negative decimal integers to unsigned octal magnitude. Negative values require a defined signed representation or application-specific convention, especially when a fixed bit width is involved.
Does this converter support decimal fractions?
This tool is designed for whole numbers. Fractional decimal-to-octal conversion uses repeated multiplication of the fractional portion by 8, and some decimal fractions produce repeating octal expansions.
What is octal commonly used for today?
One of the most familiar current uses is Unix-style file permissions, where values such as 755 and 644 compactly represent groups of three permission bits. Octal also appears in programming, legacy systems, digital logic, and computer science education.
Is decimal-to-octal conversion exact?
Yes for integers. A whole number has an exact positional representation in octal, so no rounding is required. The converted octal numeral represents exactly the same integer quantity as the original decimal value.
Convert Decimal Numbers to Octal Instantly
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