Binary to Decimal Calculator
Convert a binary number to decimal.
Only 0s and 1s
Results update as you type.
How it works
Binary is the base-2 number system that computers use, and this calculator converts a binary number into its everyday decimal, or base-10, value. You enter a binary number made up of only 0s and 1s, and it returns the decimal equivalent. The conversion works by place value: unlike decimal, where each position is a power of ten, binary positions are powers of two, doubling from right to left as 1, 2, 4, 8, 16, and so on. Each binary digit, or bit, is either present, a 1, or absent, a 0, at its place value, and adding up the place values where a 1 appears gives the decimal number. For example, the binary 1010 has 1s in the eights and twos places, so it equals eight plus two, or ten. Binary underlies all digital computing because electronic circuits naturally represent two states, on and off, as 1 and 0. Understanding binary-to-decimal conversion is fundamental for computer science students, programmers working with bitwise operations, and anyone learning how computers store numbers, colors, and data. This calculator accepts only valid binary digits and returns an error for anything containing digits other than 0 and 1. Enter a binary number to convert it to decimal.
decimal = Σ bitᵢ × 2ⁱ
A binary number is converted to decimal by giving each digit a place value that is a power of two, doubling from right to left: 1, 2, 4, 8, and so on. Each digit is multiplied by its place value and the results are summed. So the rightmost digit is the ones place, the next the twos place, and so forth.
Source:Number systems
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter binary number.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Decimal value updates instantly as you type — no button to press.
Frequently asked questions
How do you convert binary to decimal?
Give each binary digit a place value that is a power of two, starting at 1 on the right and doubling leftward. Multiply each digit by its place value and add the results. For 1010, the 1s sit in the eights and twos places, giving eight plus two, or ten. The calculator does this automatically.
What is binary?
Binary is the base-2 number system, using only the digits 0 and 1. It is the language of computers, because electronic components easily represent two states, off and on, as 0 and 1. Every number, letter, image, and instruction in a computer is ultimately stored as a sequence of these binary digits, called bits.
Why do computers use binary?
Computers use binary because digital electronic circuits reliably distinguish just two states, such as low and high voltage, which map cleanly to 0 and 1. Two states are far more robust against noise and errors than trying to distinguish ten different voltage levels for decimal, making binary the natural and dependable basis for digital computing.
What is a bit?
A bit is a single binary digit, either 0 or 1, and it is the smallest unit of information in computing. Eight bits make a byte, which can represent 256 values. Bits are the fundamental building blocks of all digital data, from numbers and text to images, audio, and program instructions inside a computer.
What if my input has digits other than 0 and 1?
A valid binary number contains only the digits 0 and 1. If your input includes any other character, such as a 2 or a letter, it is not a binary number, and the calculator returns an error rather than a value. Check your input and ensure it uses only 0s and 1s.