Binary to Decimal Converter
Binary to Decimal Converter
Type a binary number (only 0s and 1s) and read its decimal value instantly — with octal and hexadecimal alongside.
The converter is preset to base 2 (binary). You can change the From base to convert from any base 2–36 instead.
This Binary to Decimal Converter translates binary numbers — the strings of 0s and 1s that computers actually work in — into the decimal numbers humans read. Every digit in a binary number is a power of two, doubling from right to left: 1, 2, 4, 8, 16 and so on. Adding up the positions that hold a 1 gives the decimal value, so 1010 means 8 + 0 + 2 + 0 = 10. Doing that by hand for a long binary string is slow and error-prone; this converter does it instantly and exactly, and shows the octal and hexadecimal forms at the same time, because programmers constantly move between all three.
Unlike a basic calculator, this tool uses arbitrary-precision arithmetic, so very long binary values — 64-bit patterns, memory contents, coursework exercises with hundreds of digits — convert digit for digit without rounding. If you type a digit that cannot exist in binary, such as a 2, the tool says so plainly instead of silently producing a wrong answer. That makes it safe for checking homework, debugging, and verifying values from network settings, permission bits and embedded systems. The From base box is preset to 2 for binary, but you can change it to convert from any base between 2 and 36.
Binary place values — how 1010 becomes 10
| Binary digit | 1 | 0 | 1 | 0 |
|---|---|---|---|---|
| Place value | 8 | 4 | 2 | 1 |
| Counts? | Yes — add 8 | No | Yes — add 2 | No |
8 + 2 = 10. Every binary conversion works exactly like this, whatever the length of the number.
Common binary numbers in decimal
| Binary | Decimal | Binary | Decimal |
|---|---|---|---|
| 1 | 1 | 1000 | 8 |
| 10 | 2 | 1001 | 9 |
| 11 | 3 | 1010 | 10 |
| 100 | 4 | 1011 | 11 |
| 101 | 5 | 1100 | 12 |
| 110 | 6 | 1101 | 13 |
| 111 | 7 | 1110 | 14 |
| 1111 | 15 | 11111111 | 255 |
How to use
- Type or paste the binary number into the value box — only 0s and 1s.
- The From base is already set to 2 (binary); leave it there for binary input.
- Read the decimal value on the first line of the result, with binary, octal and hex below.
- For very long values, paste them whole — the conversion stays exact.
- If an error appears, look for a digit other than 0 or 1 in your input.
Frequently asked questions
How do you convert binary to decimal by hand?
Write the place values over the digits — 1, 2, 4, 8, 16, doubling right to left — then add the values wherever the digit is 1 and skip wherever it is 0. For 1101: the 1s sit on 8, 4 and 1, so the decimal value is 13.
What is 1010 in decimal?
Ten. The 1s in 1010 sit on the 8 place and the 2 place, and 8 + 2 = 10. It is the example pre-filled in the converter above, and one of the most searched binary conversions because it appears in so many beginner exercises.
Why did I get an error for my number?
Binary only allows the digits 0 and 1. If your input contains a 2 or any other character, it is not a binary number and the tool refuses rather than guessing. Check for stray spaces in the middle or letters copied along with the value.
How large a binary number can this handle?
Effectively unlimited for practical purposes. Because the conversion uses big-integer arithmetic in your browser, a binary string hundreds of digits long converts exactly, where an ordinary calculator would round everything past about sixteen decimal digits.