Binary to Decimal Calculator
Convert any base-2 binary number into its decimal (base-10) equivalent instantly. Free, accurate, and includes a full step-by-step breakdown of the calculation.
Convert Binary to Decimal
Enter a binary number below using only 0s and 1s. Your decimal equivalent updates instantly, along with a full positional breakdown showing exactly how each digit contributes to the final value.
Enter Your Binary Number
Only digits 0 and 1 are valid
Conversion Result
Your binary number in decimal form
How Binary to Decimal Conversion Works
Every binary digit, or “bit,” represents a power of 2 based on its position, counting from the right starting at zero. Here is the three-step process behind every calculation this tool performs.
Assign Place Values
Starting from the rightmost digit, assign each bit a power of 2: 2⁰, 2¹, 2², and so on, moving left.
Multiply Each Digit
Multiply every bit (0 or 1) by its corresponding power of 2. A 0 contributes nothing; a 1 contributes the full value of that position.
Sum the Results
Add together every non-zero product from step two. The total is the decimal equivalent of your binary number.
Common Binary to Decimal Values
Standard binary-to-decimal equivalents for the numbers 0 through 15, useful for quickly checking your own calculations.
| Binary | Decimal |
|---|---|
| 0000 | 0 |
| 0001 | 1 |
| 0010 | 2 |
| 0011 | 3 |
| 0100 | 4 |
| 0101 | 5 |
| 0110 | 6 |
| 0111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
| 1101 | 13 |
| 1110 | 14 |
| 1111 | 15 |
Binary to Decimal FAQ
Everything you need to know about converting binary numbers to decimal.
Multiply each binary digit by 2 raised to the power of its position, counting from 0 on the right, then add the results together. For example, binary 101 is (1×2²) + (0×2¹) + (1×2⁰) = 4 + 0 + 1 = 5.
Binary 1010 equals decimal 10. It is calculated as (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10.
Binary is a base-2 numeral system, so it only has two possible digits: 0 and 1. Computers use it because digital circuits naturally represent two states, such as off and on or low and high voltage.
This calculator safely handles binary numbers up to 53 bits long, which covers virtually all everyday, academic, and programming use cases without losing precision.