Octal Calculator
An octal calculator is an online tool designed to perform math operations like addition, subtraction, multiplication, and division on base 8 numbers. In the octal system, numbers only use eight digits from 0 to 7. This calculator allows you to compute octal math problems instantly and automatically converts the results into decimal, binary, and hexadecimal formats for fast verification.
Allowed digits: 0, 1, 2, 3, 4, 5, 6 and 7
Expand each number by place value
Apply the operation in decimal
Convert back to octal by dividing by 8
| 130 | ÷ 8 = | 16 | remainder 2 |
| 16 | ÷ 8 = | 2 | remainder 0 |
| 2 | ÷ 8 = | 0 | remainder 2 |
Reading the remainders bottom to top gives 202.
Column by column, without leaving base 8
Each column carries once it reaches 8, not 10.
Created by Ethan Park
Last updated: September 13, 2026
What Is the Octal Number System?
The octal number system, also called base 8, is a positional numeral system that relies on eight unique digits: 0, 1, 2, 3, 4, 5, 6, and 7. Unlike the standard decimal system that uses ten digits from 0 to 9, octal never includes the digits 8 or 9. When counting in octal, the number that comes right after 7 is 10, which represents the value of eight in our daily counting system.
Every digit position in an octal value represents a power of 8. The rightmost digit sits in the 8^0 (ones) place, the next digit to the left is in the 8^1 (eights) place, followed by the 8^2 (sixty-fours) place, and so on. Because each octal digit maps directly to three binary bits, programmers often use a binary calculator to quickly interpret low-level computer data.
How to Use the Octal Calculator
Using this tool to solve base 8 equations requires only a few steps:
- Enter your first base 8 value into the first input box. Make sure you only use digits from 0 through 7.
- Select your desired math operation from the menu. You can pick addition, subtraction, multiplication, or division.
- Enter your second base 8 value into the second input box.
- Click the Calculate button to view your final answer, full step-by-step working, and base conversions.
If you work with other number bases, you can switch to the Converter tab above, or use the hexadecimal calculator for base 16 operations.
How Octal Arithmetic Works
Performing math in base 8 follows the exact same principles as regular decimal arithmetic, but you regroup whenever a value reaches or exceeds 8.
Octal Addition
When adding two octal digits, any sum of 8 or higher triggers a carry to the next column. For example, adding 7 + 1 in decimal equals 8, but in octal, it equals 10. If you need to verify simple conversions beforehand, the Converter tab above can help simplify the process.
Octal Subtraction
When subtracting, if the top digit is smaller than the bottom digit, you must borrow from the column to the left. When you borrow 1 from a neighboring column in octal, it adds 8 to the current column rather than 10.
Octal Multiplication and Division
Multiplication involves multiplying the digits, converting intermediate products that exceed 7 into base 8, and summing the results. For long division, you divide using octal multiples. If you want to convert whole values to standard base 10 before multiplying, the Converter tab above covers the manual steps.
Why Are Octal Numbers Used in Computing?
Octal was widely popular in early computing systems that used 12-bit, 24-bit, or 36-bit word sizes because these numbers divide cleanly by 3. Today, octal remains widely used in Unix and Linux operating systems for managing file permissions.
In Linux file systems, permission settings use three octal digits:
- Read (r) equals a value of 4.
- Write (w) equals a value of 2.
- Execute (x) equals a value of 1.
When you see a command like chmod 755, the numbers represent file rights for the owner, group, and public users. The owner gets 4 + 2 + 1 = 7 (full access), while the group and others get 4 + 1 = 5 (read and execute).
Octal Conversion Table
The chart below lists the standard conversions between octal, decimal, binary, and hexadecimal for values 0 through 15.
| Octal (Base 8) | Decimal (Base 10) | Binary (Base 2) | Hexadecimal (Base 16) |
|---|---|---|---|
| 0 | 0 | 0000 | 0 |
| 1 | 1 | 0001 | 1 |
| 2 | 2 | 0010 | 2 |
| 3 | 3 | 0011 | 3 |
| 4 | 4 | 0100 | 4 |
| 5 | 5 | 0101 | 5 |
| 6 | 6 | 0110 | 6 |
| 7 | 7 | 0111 | 7 |
| 10 | 8 | 1000 | 8 |
| 11 | 9 | 1001 | 9 |
| 12 | 10 | 1010 | A |
| 13 | 11 | 1011 | B |
| 14 | 12 | 1100 | C |
| 15 | 13 | 1101 | D |
| 16 | 14 | 1110 | E |
| 17 | 15 | 1111 | F |
Frequently Asked Questions
What digits are allowed in an octal number?
An octal number can only contain digits from 0 to 7. Digits 8 and 9 are invalid in base 8.
Why is 8 represented as 10 in octal?
Because octal only has eight single digits (0 through 7), reaching eight forces a carry over to the next position. Therefore, 8 in decimal equals 10 in octal.
How do I convert octal to binary?
Replace each octal digit with its 3-bit binary equivalent. For instance, octal 52 becomes binary 101 010.
What is octal 777 in decimal?
Octal 777 equals 511 in decimal. The math is (7 x 64) + (7 x 8) + (7 x 1) = 448 + 56 + 7 = 511.
Can octal numbers be negative?
Yes, octal numbers can be negative. In written notation, a minus sign is placed in front of the number, such as -75.
How do I write octal numbers in programming languages?
Most programming languages use a prefix to identify octal literals. In C, C++, and Python, octal values start with 0 or 0o, such as 0755 or 0o755.