Convert hexadecimal to decimal by summing place values – each digit is multiplied by a power of 16, with A-F standing for 10-15. Works exactly for any length.
Show calculation steps
Processed privately in your browser — nothing you paste is uploaded, logged or stored.
Sixteens, summed
Decoding hex to decimal is place-value expansion in base 16: rightmost digit times one, next times sixteen, then 256, 4096 and up. Letters contribute their values ten through fifteen. The result is the sum — computed exactly, term by term, in the steps panel for your input.
This is the direction you use when a datasheet, debugger or error dialog shows hex and your reasoning — or your calculator — wants ordinary numbers.
Worked example
Input: BEEF
B(11)×4096 = 45056
E(14)× 256 = 3584
E(14)× 16 = 224
F(15)× 1 = 15
------
48879| Power | Value |
|---|---|
| 16^0 | 1 |
| 16^1 | 16 |
| 16^2 | 256 |
| 16^3 | 4096 |
| 16^4 | 65536 |
| 16^5 | 1048576 |
Anchors that speed you up
FF = 255 (the byte ceiling), 100 = 256, FFFF = 65535, 10000 = 65536. With those four anchors, most practical hex values resolve by offset: 0x1F4 is 0x200 − 0xC = 512 − 12 = 500. The exact expansion is always available below the anchor estimate.
Field uses
Converting exit codes and HRESULTs for bug reports, translating hex file sizes and offsets into human quantities, reading Unicode code points, and cross-checking address arithmetic — all daily occurrences in systems programming, reverse engineering and firmware work.
Exactness and privacy
A 64-digit hex value expands to its exact 78-digit decimal — no precision ceiling exists. Invalid characters and mismatched prefixes produce positional, named errors. Computation never leaves your browser.
How to use the Hex to Decimal Converter
- Enter the hex number – 0x prefix and either letter case are fine.
- Click "Convert to decimal".
- The steps multiply each digit by its power of 16 and add – the exact place-value expansion of YOUR input.
- Copy the decimal result.
Frequently asked questions
How does the place-value method work in base 16?
Rightmost digit ×1, next ×16, next ×256, next ×4096… For BEEF: B(11)×4096 + E(14)×256 + E(14)×16 + F(15)×1 = 45056+3584+224+15 = 48879. The steps write this out for your value.
What do the letters stand for again?
A=10, B=11, C=12, D=13, E=14, F=15 – six extra digit symbols so base 16 has its full sixteen. Case is irrelevant on input.
Why does 0xFF equal 255?
F is 15, so FF = 15×16 + 15 = 255 – the largest single byte. That anchor is worth memorising: FF=255, FFFF=65535, and each further pair of Fs multiplies the ceiling by 256.
Can this decode a long hash or address?
Yes – a 64-digit hex value converts to its full 78-digit decimal exactly. Whether decimal form is USEFUL for a hash is another matter, but the conversion is precise.
What mistakes does validation catch?
Non-hex characters (G-Z, punctuation) with position, a mismatched 0b/0o prefix, and empty input. O-for-0 confusion is the classic – the error points at the exact character.
How is this different from hex to binary?
Different target: binary expansion is per-digit lookup (structural), decimal requires the arithmetic sum (numerical). Both preserve the value exactly; which you want depends on whether the next step is human maths or bit inspection.
Is the computation local?
Yes – place values are summed in your browser with BigInt precision. Nothing is transmitted.
