🔟 Octal to Decimal Converter with Steps
By Shihab Mia · Updated 2026-07-18
Spaces and an optional 0o prefix are ignored. Only the digits 0 to 7 are allowed.
| Digit | Place value | Contribution |
|---|
This octal to decimal converter turns any base 8 number into its base 10 value in one step, so 377 becomes 255 and 12 becomes 10. It shows the full positional breakdown (377 = 3x64 + 7x8 + 7x1 = 255), the number of digits, and the matching hexadecimal and binary values. Everything runs in your browser, and it stays exact for very long octal numbers, well past the values most calculators can handle.
What is the Octal to Decimal Converter?
Octal is a base 8 number system: every digit runs from 0 to 7, and each position is worth eight times the position to its right. Decimal, the numbers you use every day, is base 10, where each position is worth ten times the one to its right. An octal to decimal conversion is simply the job of asking, for each digit in the octal string, how much that position is worth, multiplying, and adding the results together. The rightmost digit is the ones place (8 to the power 0), the next is the eights place (8 to the power 1), then 64, 512, 4096 and upward.
To convert octal to decimal by hand, write the place values above the digits from right to left: 1, 8, 64, 512, 4096 and so on. Then multiply each octal digit by its place value and total the results. For the octal number 377 the places from the left are 64, 8 and 1, so the sum is 3x64 + 7x8 + 7x1, which equals 192 + 56 + 7, or 255. Unlike binary, where each digit is only 0 or 1, an octal digit can be any value from 0 to 7, so you actually multiply rather than just picking out the 1s. This is exactly what the converter above does, and it prints that breakdown line so you can check the work.
The same octal to decimal method scales to any length. Three octal digits pack neatly into common values: 377 is 255, which is also the largest value a single byte can hold, and 400 is 256. Octal has a close relationship with binary because 8 is a power of 2, so every octal digit maps to exactly three bits. That is why octal was popular on early computers and still shows up today: the Unix file permission 755, for example, is octal, and each digit expands to a three bit read, write and execute flag.
On the computing side, standard JavaScript number math is exact only up to 53 bits, so a naive parseInt starts losing precision on very long octal strings. This tool uses BigInt internally, which keeps the decimal result exact no matter how many digits you paste in, and it still reports the hexadecimal and binary forms of the same value. So whether you are checking a homework problem, decoding a Unix permission mode, or converting a long octal dump, the octal to decimal result you see is the true value, not a rounded approximation.
When to use it
- Checking a homework or exam answer when converting an octal number to decimal by hand.
- Reading a Unix or Linux file permission such as 755 or 644 and finding its decimal value.
- Teaching or learning place value in base 8 with a live positional breakdown you can watch update.
- Cross checking an octal value against its hexadecimal and binary forms while working on low level code.
How to use the Octal to Decimal Converter
- Type or paste an octal number (only the digits 0 to 7) into the input box, or tap one of the example buttons.
- Read the decimal value at the top; it updates instantly as you type.
- Check the positional breakdown line to see how each digit and place value adds up to the total.
- Use the copy buttons to grab the decimal, hexadecimal, or binary result for use elsewhere.
Formula & method
Worked examples
Convert the octal number 377 to decimal.
- Write the place values from right to left under the digits: 64, 8, 1.
- Match each digit to its place: 3 over 64, 7 over 8, 7 over 1.
- Multiply each digit by its place value: 3x64 = 192, 7x8 = 56, 7x1 = 7.
- Add the contributions: 192 + 56 + 7 = 255.
Result: 377 in octal equals 255 in decimal (hex FF, binary 11111111).
Convert the Unix permission octal 755 to decimal.
- Place values for 3 digits are 64, 8, 1.
- Match the digits: 7 over 64, 5 over 8, 5 over 1.
- Multiply each digit: 7x64 = 448, 5x8 = 40, 5x1 = 5.
- Add the contributions: 448 + 40 + 5 = 493.
Result: 755 in octal equals 493 in decimal (hex 1ED, binary 111101101).
Octal digit place values (powers of 8) used in octal to decimal conversion
| Digit position (from right) | Power of 8 | Decimal place value |
|---|---|---|
| 0 | 8 to the 0 | 1 |
| 1 | 8 to the 1 | 8 |
| 2 | 8 to the 2 | 64 |
| 3 | 8 to the 3 | 512 |
| 4 | 8 to the 4 | 4096 |
| 5 | 8 to the 5 | 32768 |
| 6 | 8 to the 6 | 262144 |
| 7 | 8 to the 7 | 2097152 |
Common octal values with their decimal, hex, and binary equivalents
| Octal | Decimal | Hex | Binary |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
| 7 | 7 | 7 | 111 |
| 10 | 8 | 8 | 1000 |
| 12 | 10 | A | 1010 |
| 17 | 15 | F | 1111 |
| 100 | 64 | 40 | 1000000 |
| 144 | 100 | 64 | 1100100 |
| 377 | 255 | FF | 11111111 |
| 755 | 493 | 1ED | 111101101 |
| 1000 | 512 | 200 | 1000000000 |
Common mistakes to avoid
- Treating octal digits like binary and only counting the nonzero ones. In binary you only add the place values under a 1, but octal digits run from 0 to 7. You must multiply each digit by its place value, so 3x64 is 192, not just 64. Do the multiplication for every digit.
- Using a digit of 8 or 9 in an octal number. Octal only has the digits 0 to 7. A value like 88 or 19 is not valid octal. If a number contains an 8 or 9 it is decimal or another base, not octal, and this tool will flag the invalid digit.
- Reading the digits in the wrong direction. Place values start at 1 on the right and multiply by 8 as you move left. If you number the positions from the left instead, the powers come out reversed. Always align the rightmost digit with the ones place.
- Assuming plain number math stays exact for long octal strings. Standard JavaScript numbers lose precision beyond 53 bits, so a long octal to decimal conversion can drift. This tool uses BigInt so the decimal result stays exact for any length you enter.
Glossary
- Octal
- A base 8 number system that uses the digits 0 to 7, where each position is worth eight times the position to its right.
- Decimal
- The everyday base 10 number system using digits 0 through 9, where each position is worth ten times the one to its right.
- Base
- The number of distinct digits a number system uses. Octal is base 8, decimal is base 10, and binary is base 2.
- Place value
- The amount a digit is worth because of its position. In octal the place values are the powers of 8: 1, 8, 64, 512 and so on.
- Most significant digit
- The leftmost digit in an octal number, which carries the largest place value and the most weight in the decimal total.
- 0o prefix
- A marker written before a number to show it is octal, used in many programming languages, for example 0o377. This converter ignores the prefix if you include it.
Frequently asked questions
How do you convert octal to decimal?
To convert octal to decimal, multiply each digit by its place value (a power of 8) and add the results. The rightmost digit is worth 1, then 8, 64, 512 and so on to the left. For 377 that is 3x64 + 7x8 + 7x1 = 255.
What is 377 in decimal?
Octal 377 equals 255 in decimal. The place values from the left are 64, 8 and 1, so the sum is 3x64 + 7x8 + 7x1, which is 192 + 56 + 7 = 255. That is also the largest value one byte can hold.
What is 755 in decimal?
The octal number 755, a common Unix file permission, equals 493 in decimal. It works out as 7x64 + 5x8 + 5x1, which is 448 + 40 + 5 = 493.
What is the formula for octal to decimal?
The formula is decimal = sum of digit x 8 to the power position, counting positions from 0 at the rightmost digit. Each digit contributes its value times its place value.
Why does octal only use the digits 0 to 7?
Octal is base 8, so it has exactly eight digits, 0 through 7, just as decimal (base 10) has ten digits, 0 through 9. There is no single symbol for 8 in octal; the value 8 is written as 10.
Can this converter handle very long octal numbers?
Yes. This octal to decimal converter uses BigInt internally, so it keeps the decimal result exact for octal strings well beyond 53 bits, unlike simple calculators that round large values.