Decimal to Octal Converter
Free online Decimal to Octal converter with instant step-by-step division steps. Convert Base-10 to Base-8 and Octal to Decimal accurately in your browser.
Decimal to Octal Converter
| 8^2 | 8^1 | 8^0 |
|---|---|---|
| 64 | 8 | 1 |
| 7 | 5 | 5 |
| 448 | 40 | 5 |
| Step | Operation | Octal Digit | Result So Far |
|---|---|---|---|
| 1 | 493 ÷ 8 = 61 remainder 5 | 5 | 5 |
| 2 | 61 ÷ 8 = 7 remainder 5 | 5 | 55 |
| 3 | 7 ÷ 8 = 0 remainder 7 | 7 | 755 |
Overview
The ToolMono Decimal to Octal Converter is an enterprise-grade base conversion platform built for systems administrators, DevOps engineers, Linux developers, and computer science students. It converts base-10 decimal numbers into base-8 octal numbers—and vice versa—in real time with 100% client-side precision.
Featuring a built-in Unix File Permissions (chmod) Decoder, BigInt arbitrary-precision math, Bulk CSV Export, Two's Complement signed representation, dynamic step-by-step division breakdowns, and place-value visual tables, ToolMono provides the definitive reference tool for base-8 data. Explore companion tools: Binary ↔ Decimal Converter, Decimal ↔ Hex Converter, Online Calculator, Scientific Calculator, JSON Formatter, and Hash Generator.
How to Use
Type any decimal integer (e.g. 255) or octal permission string (e.g. 377 or 755) into the input box.
View live Unix chmod symbolic breakdown (rwxr-xr-x), bit width bounds, and binary/hex equivalents.
Inspect the dynamic division-by-8 mathematical step breakdown and positional place-value matrix.
Click Copy to save the formatted result or use Bulk Conversion mode to download a CSV report.
How to Convert Decimal to Octal
Converting a base-10 decimal number to base-8 octal is performed using the successive division by 8 remainder method.
- Divide the decimal number by 8 to get an integer quotient and a remainder.
- Record the remainder value (which will always be an integer between 0 and 7).
- Divide the resulting quotient by 8 again.
- Repeat the division process until the integer quotient becomes 0.
- Read the recorded remainders in reverse order (from bottom to top).
| Division Step | Integer Quotient | Remainder | Octal Digit |
|---|---|---|---|
| 255 ÷ 8 | 31 | 7 | Least Significant Digit (8⁰) |
| 31 ÷ 8 | 3 | 7 | Middle Digit (8¹) |
| 3 ÷ 8 | 0 | 3 | Most Significant Digit (8²) |
How to Convert Octal to Decimal
To convert a base-8 octal number back to base-10 decimal, apply the positional expansion method using powers of 8.
Where $d_i$ represents the octal digit at position index $i$, starting with index 0 at the rightmost character.
The leftmost digit carrying the highest positional weight power of 8 (e.g. 3 in 377₈ carries weight 8² = 64).
The rightmost digit carrying positional weight 8⁰ = 1 (e.g. rightmost 7 in 377₈).
Understanding the Octal Number System
The octal number system is a base-8 positional numeral system. While decimal (base-10) relies on ten digits (0–9) and binary (base-2) relies on two digits (0–1), octal uses eight valid symbols:
Because octal is base-8, each positional column represents a power of 8:
| Position Index | Power Notation | Decimal Multiplier Value |
|---|---|---|
| 0 | 8⁰ | 1 |
| 1 | 8¹ | 8 |
| 2 | 8² | 64 |
| 3 | 8³ | 512 |
| 4 | 8⁴ | 4,096 |
10₈ (1 × 8¹ + 0 × 8⁰). Entering digits 8 or 9 into an octal field triggers a syntax error.Octal Digit Reference Table & 3-Bit Binary Relationship
Because $8 = 2^3$, one octal digit maps directly to exactly three binary bits. This 3-to-1 relationship makes octal a convenient human shorthand for raw binary data:
| Octal Digit | Decimal Value | 3-bit Binary Equivalent |
|---|---|---|
| 0 | 0 | 000 |
| 1 | 1 | 001 |
| 2 | 2 | 010 |
| 3 | 3 | 011 |
| 4 | 4 | 100 |
| 5 | 5 | 101 |
| 6 | 6 | 110 |
| 7 | 7 | 111 |
Decimal vs. Octal Number Systems
Understanding the distinction between decimal and octal systems helps developers avoid common conversion mistakes:
Decimal System
- Base 10 ($10^n$)
- Uses ten digits:
0 1 2 3 4 5 6 7 8 9 - Positional weights: $1, 10, 100, 1000, \dots$
- Example: $255 = 2 \times 100 + 5 \times 10 + 5$
Octal System
- Base 8 ($8^n$)
- Uses eight digits:
0 1 2 3 4 5 6 7 - Positional weights: $1, 8, 64, 512, \dots$
- Example: $377 = 3 \times 64 + 7 \times 8 + 7$
Decimal to Octal Conversion Examples
Below are practical conversion examples demonstrating decimal to octal math across common values:
Decimal and Octal Reference Table
Quick lookup table converting common decimal values to octal notation:
| Decimal Value | Octal Value | Context / Note |
|---|---|---|
| 0 | 0 | Zero boundary |
| 1 | 1 | Single bit |
| 2 | 2 | Single bit |
| 3 | 3 | 2-bit max |
| 4 | 4 | Single bit |
| 5 | 5 | Read + Execute |
| 6 | 6 | Read + Write |
| 7 | 7 | 3-bit max (rwx) |
| 8 | 10 | Octal base boundary |
| 9 | 11 | Decimal 9 |
| 10 | 12 | Decimal 10 |
| 15 | 17 | 4-bit boundary |
| 16 | 20 | Base 16 boundary |
| 24 | 30 | Multiple of 8 |
| 32 | 40 | ASCII space code |
| 64 | 100 | 8² power boundary |
| 100 | 144 | Centum decimal |
| 128 | 200 | 7-bit ASCII max |
| 255 | 377 | 8-bit byte max (0xFF) |
| 512 | 1000 | 8³ power boundary |
| 1024 | 2000 | 1 KB boundary |
Where Octal Numbers Are Used
Although hexadecimal has largely superseded octal for 8-bit and 16-bit byte alignment, octal remains widely used in:
- Unix/Linux Permission Notation: Encoding Read (4), Write (2), and Execute (1) rights into 3-digit octal codes.
- Computer Science Education: Teaching positional number systems and 3-bit binary grouping.
- Legacy Hardware Architectures: Systems built around 12-bit, 18-bit, or 36-bit word sizes (e.g., PDP-8 minicomputers).
- Programming Octal Literals: Defining file mode masks (umask) and file creation modes in POSIX APIs.
Need to decode Unix permissions specifically? Use Unix chmod permission notation (e.g. 755 or 644).
Do Leading Zeros Matter in Octal?
In pure mathematics, leading zeros do not alter the value of an unsigned integer:
However, in computer programming, leading zeros carry critical syntactic meaning:
- Modern
0oPrefix: Languages such as Python, JavaScript, and Rust require the0oor0Oprefix (e.g.0o144) to explicitly declare an octal literal. - Legacy C Syntax: In C, C++, and Bash, a single leading zero (e.g.
0144) denotes an octal integer. Accidental leading zeros in C code can cause unexpected bugs if decimal numbers like08trigger syntax errors.
What About Octal Fractions?
While the primary converter on this page focuses on integers, octal can also represent fractional quantities using negative powers of 8 ($8^-1, 8^-2, \dots$):
Unix Permissions (chmod 755 / 777 / 644)
In Linux and Unix operating systems, file permissions are expressed in 3 octal digits representing Owner, Group, and Others. Each digit is a bitmask sum of Read (4), Write (2), and Execute (1):
| Octal Code | Symbolic String | Owner (User) | Group | Others | Common Usage |
|---|---|---|---|---|---|
| 755 | rwxr-xr-x | rwx (7) | r-x (5) | r-x (5) | Executable scripts & directories |
| 644 | rw-r--r-- | rw- (6) | r-- (4) | r-- (4) | Standard web server files |
| 700 | rwx------ | rwx (7) | --- (0) | --- (0) | Private SSH keys & config folders |
| 777 | rwxrwxrwx | rwx (7) | rwx (7) | rwx (7) | Full public access (Security Risk) |
Key Features
Automatically decodes 3-digit octal chmod strings into symbolic file access rights (Owner, Group, Others).
Convert numbers with hundreds or thousands of digits without encountering double-precision truncation.
Convert lists of decimal or octal values in batch mode and export structured CSV reports.
Bit Width & Integer Bounds
| Bit Width | Unsigned Max Decimal | Unsigned Max Octal | Signed Range (Two's Complement) |
|---|---|---|---|
| 8-bit (Byte) | 255 | 377 | -128 to 127 |
| 16-bit (Word) | 65,535 | 177777 | -32,768 to 32,767 |
| 32-bit (DWord) | 4,294,967,295 | 37777777777 | -2,147,483,648 to 2,147,483,647 |
| 64-bit (QWord) | 18,446,744,073,709,551,615 | 1777777777777777777777 | -9.22 × 10^18 to 9.22 × 10^18 |
Signed Numbers & Two's Complement
Negative decimal numbers are converted to octal via Two's Complement binary translation. For example, -1 in 8-bit signed two's complement binary is 11111111, which translates to octal 377.
Programming Code Examples
Reference code snippets for converting Decimal to Octal and Octal to Decimal across major programming languages:
const dec = 255; const oct = dec.toString(8); // '377' const octLiteral = '0o' + oct; // '0o377'
const oct = '377'; const dec = parseInt(oct, 8); // 255
dec_val = 255 oct_str = oct(dec_val) # '0o377'
oct_str = '0o377' dec_val = int(oct_str, 8) # 255
int dec = 255; String oct = Integer.toOctalString(dec); // "377"
String oct = "377"; int dec = Integer.parseInt(oct, 8); // 255
package main
import "fmt"
func main() {
dec := 255
oct := fmt.Sprintf("%o", dec) // "377"
}package main
import ("fmt"; "strconv")
func main() {
dec, _ := strconv.ParseInt("377", 8, 64) // 255
}#include <stdio.h>
int main() {
int dec = 255;
printf("%o\n", dec); // 377
return 0;
}#include <stdio.h>
int main() {
int dec;
sscanf("377", "%o", &dec); // 255
return 0;
}let dec = 255;
let oct = format!("{:o}", dec); // "377"let oct = "377"; let dec = i64::from_str_radix(oct, 8).unwrap(); // 255
int dec = 255; string oct = Convert.ToString(dec, 8); // "377"
string oct = "377"; int dec = Convert.ToInt32(oct, 8); // 255
$dec = 255; $oct = decoct($dec); // '377'
$oct = '377'; $dec = octdec($oct); // 255
let dec = 255 let oct = String(dec, radix: 8) // "377"
let oct = "377" let dec = Int(oct, radix: 8) // 255
val dec = 255 val oct = dec.toString(8) // "377"
val oct = "377" val dec = oct.toInt(8) // 255
-- MySQL SELECT OCT(255); -- '377'
-- MySQL
SELECT CONV('377', 8, 10); -- 255Developer & Low-Level Computer Guide
Because $8 = 2^3$, exactly 3 binary bits map to 1 octal digit. This makes octal a natural shorthand for 3-bit binary fields, such as Unix file permissions and 12-bit PDP-8 minicomputer words.
In-Depth Educational Guide
Successive Division by 8 Algorithm
To convert a decimal number to octal manually:
- Divide the decimal number by 8.
- Record the integer quotient and the remainder (0–7).
- Repeat division on the quotient until it reaches 0.
- Read the remainders in reverse order (bottom to top).
AI Overview Answers
A Decimal to Octal Converter is a mathematical web tool that converts base-10 integers (0–9) into base-8 octal numbers (0–7). Octal notation is commonly used in Unix file permissions (chmod) and computer architecture.
Frequently Asked Questions
References & Standards
IEEE 754-2019: Standard for Floating-Point Arithmetic
International standard for binary and radix conversion algorithms.
POSIX File Permission Octal Notation Specification
IEEE / Open Group standard for octal Unix file permission modes.
MDN Web Docs: parseInt() Radix Specification
Mozilla API reference for octal parsing.
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