Binary to Decimal
Type or paste any binary number and see its decimal value instantly, with a full place-value breakdown. Free, private and fast — the conversion happens right in your browser.
Digits 0 and 1 only. An optional 0b prefix, a leading minus sign, and spaces or underscores between digits are all accepted.
Place-value breakdown
| Position n | Bit | Place value 2n | Bit × 2n |
|---|
How to use the Binary to Decimal converter
- Enter a binary number. Type or paste any string of 0s and 1s — prefixes like 0b and spaces between groups of bits are fine.
- Read the decimal value. The result appears instantly as you type, together with the hexadecimal and octal equivalents.
- Check the breakdown or copy. The place-value table shows exactly how each bit contributes to the total; one click copies the decimal result.
About this tool
Binary (base 2) is the number system computers use internally: each bit represents a power of two, so the binary number 101101 equals 1×32 + 0×16 + 1×8 + 1×4 + 0×2 + 1×1 = 45. This binary to decimal converter does that arithmetic for you and shows the full working, which makes it handy for computer science homework, networking subnet math, debugging bitmasks and flags, or simply learning how base-2 numbers work. Because it uses arbitrary-precision arithmetic, it converts values far beyond the 64-bit range without rounding errors.
Everything runs locally in your browser — the numbers you type are never uploaded, logged or stored. Need the opposite direction? Use the Decimal to Binary converter, or the Number Base Converter for any base from 2 to 36.
Frequently asked questions
How do you convert binary to decimal by hand?
Number the bits from right to left starting at 0. Each bit set to 1 contributes 2 raised to its position. Add those powers of two together: for 1101 that is 8 + 4 + 1 = 13. The breakdown table on this page shows these exact steps for your number.
How large a binary number can this tool handle?
Up to 10,000 bits — roughly a 3,000-digit decimal number. The converter uses exact big-integer arithmetic, so even huge values are converted without any loss of precision, unlike calculators limited to 32 or 64 bits.
Can I convert negative binary numbers?
Yes, by writing a minus sign in front (e.g. -1011 = -11). Note that this is sign-magnitude notation; the tool does not interpret input as two's complement, which is how CPUs store negative integers internally.
Is my input sent to a server?
No. The conversion is performed entirely by JavaScript running in your browser. Nothing you type leaves your device, and the tool keeps working even if you go offline after the page loads.