Convert hexadecimal (base 16) to decimal — with the positional steps shown.
Color codes like #FF5733, memory addresses like 0x7FFF, and error codes like 0x80070005 are all hexadecimal — base 16 — and each one has a plain decimal meaning. Our free Hex to Decimal Converter expands every hex digit by its power-of-16 place value, showing each term so the result is fully verifiable.
Hexadecimal won computing because one hex digit is exactly four bits: a byte is two hex digits, no fractions, no awkward splits. Programmers read hex the way musicians read notes, and converting to decimal is how you answer “but how big is that, really?”
Enter a hex number (0–9, A–F, with or without the 0x prefix) and get its decimal value with the full positional expansion plus the binary form. Developers, students, and the hex-curious get the same transparent steps.
Hexadecimal positional notation works like decimal with 16 in place of 10: FF16 = 15×16 + 15×1 = 240 + 15 = 255. The letters A–F are simply the digits for ten through fifteen — A=10, B=11, C=12, D=13, E=14, F=15 — because a base needs sixteen distinct digit symbols.
Place values run 160=1, 161=16, 162=256, 163=4096 — each column sixteen times the last. The widget writes every term (F(15) × 161), so the expansion doubles as a lesson in how all positional systems work.
Why hex, not decimal, for computers? Binary is the machine’s truth, but 32-bit addresses in binary are 32 digits of noise. Hex compresses each nibble (4 bits) to one character: 0xFF is instantly “all eight bits set,” while 255 requires a moment’s thought. Hex is binary made human-readable.
Key terms:
Strip the 0x prefix first — it marks the base, it isn’t part of the number. The widget accepts it or not.
Convert FF16 — the largest value one byte can hold.
Every “255” in computing — max color channel, broadcast address octet — is this FF.
The web color #1A4B: convert the 1A4 pair to decimal (a teal’s red channel).
Color pickers show hex; the decimal tells you the channel’s true intensity out of 255.
Priya’s designer hands her #FF5733 for a button. She needs the RGB decimals for the app theme: FF = 255, 5716 = 5×16+7 = 87, 3316 = 3×16+3 = 51 — rgb(255, 87, 51). The converter’s term-by-term expansion confirms each channel before she commits the stylesheet.
A second scenario: a crash log shows error 0x80070005. Stripping 0x and converting the significant part helps search the decimal-indexed knowledge base — the converter bridges the hex log and the decimal docs.
A third: a student learns that 0x100 = 256 = 28. The converter shows 1×256 + 0 + 0, and the “one followed by zeros” pattern clicks — powers of the base look the same in every base.
A fourth: a network engineer reads a MAC address ending in :A4. That’s 164 decimal — and the widget’s binary readout (101001002) shows exactly which bits are set in the last octet.
Colors: #RRGGBB is hex’s most visible realm — six hex digits, three bytes, 16.7 million colors. Every web designer converts channels between hex and decimal routinely.
Memory: addresses are hex because alignment is in powers of two. 0x1000 is a page boundary; 4096 in decimal hides that structure.
Networking: IPv6 addresses are eight hex groups; MAC addresses six. The colon-hex notation is networking’s native tongue.
Debugging: error codes (0x80070005), NTSTATUS values, and errno constants are hex in every debugger. Converting to decimal is step one of the search.
Unicode: code points are U+1F600 — hex by convention. The decimal 128512 is the same grinning face, but nobody writes it that way.
Cryptography: hashes are hex strings (64 hex digits = 256 bits for SHA-256). The hex is the hash’s public face; the bits are its truth.
Embedded systems: register maps, bit masks (0x0F), and fuse values are hex. Setting bit 3 means OR-ing 0x08 — decimal would obscure the bit pattern.
One pattern worth internalizing: one hex digit = one nibble = 4 bits, always. That fixed width is the entire reason hex beat octal for modern machines.Memory forensics: a hex dump’s addresses are hex; the analyst’s notes are decimal offsets. 0x1A40 = 6720 — the converter keeps the notebook consistent.
Feature flags: bitmask 0x2C enables features 2, 3, and 5 (44 = 32+8+4). Converting reveals which flags the mask sets.
Build numbers: some pipelines encode versions in hex; 0x10B = 267 decimal. Release notes translate for the humans.
Sensor calibration: ADC trim values arrive as hex (0x7F = 127, midscale). Firmware converts to apply the decimal gain formula.
Game modding: save files store stats as hex; editors show decimal. 0xFF = 255 HP is the max-potion meme made arithmetic.
Why sixteen won: hexadecimal triumphed because a byte — 8 bits, the industry’s atom — is exactly two hex digits, while it’s two-and-two-thirds octal digits. That alignment made hex the natural shorthand the moment bytes standardized, and network effects did the rest: debuggers, hex editors, color pickers, and Unicode tables all speak hex because they all handle bytes. The letters A–F were a pragmatic hack — sixteen symbols were needed and the alphabet was handy — giving us the distinctive look of 0xDEADBEEF, the engineers’ favorite magic number (decimal 3,735,928,559). Every hex value you’ll ever convert is a byte-counting exercise in disguise, which is why the widget also shows the binary: hex is binary, compressed four-to-one.
Worked scenario — the subnet detective: a network capture shows destination MAC ending in :F2:8A. The junior engineer needs the decimal for an inventory database that only accepts decimal octets. Convert F2: F=15, 2=2 → 15×16 + 2 = 242. Convert 8A: 8×16 + 10 = 138. The database gets 242 and 138; the capture’s hex stays in the ticket for the senior engineer. Later, a firewall log shows port 0x1A4 — 1×256 + 10×16 + 4 = 420 decimal — an unfamiliar high port that turns out to be the backup agent. Two conversions, two mysteries solved, zero ambiguity — because each term of the expansion is independently checkable, the engineer trusts the database entries enough to automate them.
Edge cases and pro tips: strip the 0x prefix before expanding — it labels the base, it isn’t a digit, though the widget tolerates it. Hex is case-insensitive: ff, FF, and Ff are identical, so don’t let mixed case slow you down. Watch for the classic misread — B is eleven, not eight; E is fourteen, not five; the letters continue where digits stop, they don’t restart. For long addresses, expand the significant bytes only; nobody needs all 32 hex digits of an IPv6 address expanded by hand — convert the group you’re reasoning about. And when going decimal-to-hex by hand, the remainders 10–15 become A–F after the division ladder — the letter substitution is the last step, not part of the arithmetic.
Hex to decimal: sum of digit x 16^position (A=10..F=15). FF = 255; 1A4 = 420. One hex digit = 4 bits (nibble). Source: Sigma Calculator, Hex to Decimal Converter, https://sigmacalculator.net/math-calculators/hex-to-decimal-converter/
Cite this page as: Hex to Decimal Converter, Sigma Calculator, https://sigmacalculator.net/math-calculators/hex-to-decimal-converter/
Last updated: October 12, 2026