Decimal to Hex Converter

Hexadecimal is base 16. Where decimal uses ten digits (0-9) and rolls over to a new place at ten, hex uses sixteen — 0 through 9, then A, B, C, D, E and F standing in for ten through fifteen. Roll over happens at sixteen, so decimal 16 is written 10 in hex, and decimal 255 is FF.

The reason hex exists has nothing to do with humans finding it natural and everything to do with binary. Sixteen is two to the fourth power, which means one hex digit maps to exactly four binary digits — a nibble — with no remainder and no arithmetic. F is 1111, 8 is 1000, A is 1010, every time, in every context. That clean four-to-one mapping is why a 32-bit value that would take thirty-two ones and zeros collapses into eight readable hex digits, and why you can convert between hex and binary by substitution rather than by calculation.

Decimal has no such relationship with binary. Ten is not a power of two, so converting decimal to binary means actual division, and long binary strings have no tidy decimal shorthand. Hex is the compromise the computing world settled on: compact enough to read aloud, structured enough to translate to machine representation on sight.

How hex is written

Because a string like 4051 is ambiguous on its own, hex almost always carries a marker. You will see 0x4051 in C, C++, Java, Python, JavaScript and most assembly; #4051 in CSS and design tools; 4051h or $4051 in older assemblers and on some hardware datasheets; and a plain subscript 16 in maths textbooks. All four mean the same number. Our converter accepts the 0x and # forms and strips them silently, so you can paste straight from code or a stylesheet.

• 0x prefix — C, C++, Java, Python, JavaScript, Go, Rust, most assemblers
• # prefix — CSS, HTML, graphic design tools, colour pickers
• h suffix or $ prefix — legacy assembly, hardware datasheets, retro computing
• Subscript 16 — mathematics and computer science textbooks
• No prefix at all — hex dumps, MAC addresses, checksums, UUIDs

The standard method is repeated division by 16. Divide your decimal number by 16 and write down the whole-number quotient and the remainder. Divide that quotient by 16 and note the new remainder. Keep going until the quotient reaches zero. Then read the remainders from the bottom up — that string, with 10 to 15 replaced by A to F, is your hex number. The reason it runs bottom-to-top is that each division peels off the least significant digit first.

1. Divide the decimal number by 16.
2. Write down the quotient and the remainder.
3. Convert any remainder of 10-15 to its letter: 10=A, 11=B, 12=C, 13=D, 14=E, 15=F.
4. Replace the number with the quotient and repeat from step 1.
5. Stop when the quotient is 0.
6. Read the remainders bottom-to-top. That is your hex value.

Worked example: 789 in hexadecimal

789 divided by 16 is 49 with a remainder of 5. Then 49 divided by 16 is 3 with a remainder of 1. Then 3 divided by 16 is 0 with a remainder of 3, and the quotient has hit zero, so we stop. Reading the remainders bottom-to-top gives 3, 1, 5 — so 789 in decimal is 315 in hexadecimal, usually written 0x315.

Worked example: 476 in hexadecimal

476 divided by 16 is 29 with a remainder of 12, and 12 is C. Then 29 divided by 16 is 1 with a remainder of 13, which is D. Then 1 divided by 16 is 0 with a remainder of 1. Reading bottom-to-top: 1, D, C. So 476 in decimal is 1DC in hexadecimal, or 0x1DC. This example is worth working through because it contains two letter digits, which is where hand conversion usually goes wrong.

The shortcut for numbers under 256

Any decimal from 0 to 255 fits in exactly two hex digits, and there is a faster route than dividing. Split the number into how many 16s it contains and what's left over. For 200: there are twelve 16s in 200 (192), leaving 8. Twelve is C, so 200 is C8. This works because the first hex place is worth 16 and the second is worth 1, so a two-digit hex number is just (first digit x 16) + (second digit). Most everyday hex — colour channels, byte values, ASCII codes — lives entirely in this range, so the shortcut covers more ground than it sounds like it should.

Going the other way is positional expansion, and it is easier than the division method. Number the hex digits from right to left starting at zero. Multiply each digit by 16 raised to its position, then add the results. Letters convert first: A is 10, B is 11, C is 12, D is 13, E is 14, F is 15.

Take 0x315. The rightmost digit 5 sits at position 0, so it contributes 5 x 1 = 5. The middle digit 1 is at position 1, contributing 1 x 16 = 16. The leftmost digit 3 is at position 2, contributing 3 x 256 = 768. Adding those gives 768 + 16 + 5 = 789, which matches the earlier example. Take 0xBEEF: B is 11 at position 3 (11 x 4096 = 45,056), E is 14 at position 2 (14 x 256 = 3,584), E is 14 at position 1 (14 x 16 = 224), F is 15 at position 0 (15 x 1 = 15). Total: 48,879.

There is no minus sign in hex as computers use it. A negative number is represented by two's complement, which means the answer depends entirely on how many bits you are working in — and that is why no single hex value can be called 'negative five' without saying the width first. None of the eight pages currently ranking for this term handle negative input at all, which is a real gap if you are debugging a register value or reading a memory dump.

The rule is simple: to represent a negative decimal in a given bit width, add it to two raised to that width. For -5 in 8-bit: 256 + (-5) = 251, and 251 in hex is FB. For -5 in 16-bit: 65,536 + (-5) = 65,531, which is FFFB. For -5 in 32-bit: FFFFFFFB. Same number, three different hex strings, all correct in their own context. The leading F digits are the giveaway — in two's complement, a negative number always has its top bit set, so signed values that start with 8 through F are negative.

Use the Signed toggle and bit-width selector in the converter above to switch between these representations without doing the arithmetic. The working panel shows the addition step so you can check it.

CSS and colour codes

A hex colour is three bytes: #RRGGBB, where each pair is one channel from 0 to 255. #FF0000 is pure red because the red channel is maxed at 255 and the others are zero. Grey values have equal pairs — #808080 is 128 across the board, halfway up each channel. The three-digit shorthand #F00 simply doubles each digit, expanding to #FF0000. When a designer hands you 'RGB 64, 224, 208' and the stylesheet needs turquoise, you are converting three decimals to hex and concatenating: 40, E0, D0 becomes #40E0D0. Eight-digit values like #FF0000CC add a fourth alpha pair — CC is 204, roughly 80% opacity.

Memory addresses and pointers

Debuggers, stack traces and crash logs print addresses in hex because the four-bit alignment makes structure visible. An address ending in 0 or 8 is aligned; a pointer reading 0x7FFF5FBFF8C0 tells you at a glance it is high in the address space. Decimal would hide all of that. Segment boundaries land on round hex numbers too — 0x1000 is 4,096, one memory page — so when you see an address jump from 0x0FFF to 0x1000 you are watching a page boundary being crossed. Converting an address to decimal is mostly useful for arithmetic: subtracting two pointers to get a byte offset is easier in decimal, which is exactly the round trip this converter is for.

ASCII, Unicode and character encoding

Character codes are written in hex almost everywhere they appear. URL encoding uses it — %20 is a space because a space is decimal 32, which is 20 in hex. Unicode code points use the U+ prefix with hex digits, so U+1F600 is the grinning face emoji at decimal 128,512. String escapes in most languages follow the same pattern: \x41 is A, \u00E9 is an accented e. When you dump a file and see 48 65 6C 6C 6F, that is 72, 101, 108, 108, 111 in decimal — 'Hello'.

MAC addresses and network identifiers

A MAC address is six bytes written as twelve hex digits, usually grouped in pairs: 00:1A:2B:3C:4D:5E. The first three bytes identify the manufacturer and the last three identify the device. IPv6 addresses use hex groups too, which is why they look nothing like the decimal dotted quads of IPv4. Subnet masks, VLAN IDs and port numbers cross between the two — port 65535, the highest valid port, is FFFF, which is not a coincidence: it is the largest value that fits in sixteen bits.

File signatures and hex dumps

Files identify themselves in their first few bytes. A PNG starts 89 50 4E 47, a PDF starts 25 50 44 46 — which is %PDF once you convert those to ASCII. A JPEG opens FF D8 FF. Checksums, hashes and UUIDs are all rendered in hex for the same reason: it is the shortest human-readable form that maps cleanly onto the underlying bytes. If you are ever staring at a hex editor trying to work out what a file is, the first four bytes are where you start.

Software developers

Reading a register value out of a debugger, setting a bitmask, checking whether an integer overflowed, or converting a pointer offset back to decimal to do arithmetic on it. The bit-width and signed controls matter most here — a value that reads FFFFFFFB in a 32-bit register is -5, and knowing that instantly is the difference between a five-minute bug and an afternoon.

Web designers and front-end developers

Translating between the RGB values a design tool reports and the hex a stylesheet needs. The CSS colour chart above covers the named colours; the converter handles the rest one channel at a time. The copy buttons that emit # prefixed output exist specifically for this job.

Computer science students

Number-base conversion is a first-year staple and it is usually assessed by hand. The step-by-step working panel shows the division trace rather than just the answer, so you can check your own method against it rather than only your result. The cross-base chart is built for revision.

Network and systems engineers

MAC addresses, IPv6 groups, subnet arithmetic, port numbers and packet captures are all hex-native. Converting to decimal is usually about doing range maths — working out how many addresses sit between two values, or whether an ID falls inside an allocated block.

Embedded and hardware engineers

Datasheets specify register addresses and configuration values in hex, often with the older 4051h notation. Firmware constants, memory maps and I2C addresses all live in base 16, and the bit-width selector matters because an 8-bit microcontroller register behaves very differently from a 32-bit one holding the same digits.

How do I convert decimal to hex?

Divide the number by 16, note the remainder, then divide the quotient by 16 and note that remainder, repeating until the quotient is zero. Read the remainders from the bottom up, converting 10-15 to A-F. The converter at the top of this page does it instantly and shows the division steps if you want to check the method.

What is 789 in hexadecimal?

789 in decimal is 315 in hexadecimal, written 0x315. The working is three divisions: 789/16 = 49 remainder 5, then 49/16 = 3 remainder 1, then 3/16 = 0 remainder 3. Reading the remainders bottom-to-top gives 315.

What is 476 decimal to hexadecimal?

476 in decimal is 1DC in hexadecimal, or 0x1DC. Dividing gives 476/16 = 29 remainder 12 (C), then 29/16 = 1 remainder 13 (D), then 1/16 = 0 remainder 1. The two letter digits are what make this one a common source of hand-conversion errors.

How do you write "I love you" in hexadecimal?

You convert each character to its ASCII code and write those codes in hex: 49 20 6C 6F 76 65 20 79 6F 75. That is I (73), space (32), l (108), o (111), v (118), e (101), space (32), y (121), o (111), u (117). Use the text input above the ASCII table to do this for any phrase.

How do I convert a negative decimal to hex?

You need to know the bit width first, because negatives are stored as two's complement and the answer changes with width. Add the negative number to 2 raised to the bit width: -5 in 8-bit is 256 - 5 = 251 = FB, but in 16-bit it is FFFB. Turn on the Signed toggle in the converter and pick your width.

What is 255 in hex, and why does it show up everywhere?

255 is FF. It appears constantly because it is the largest value one byte can hold, which makes it the maximum for a colour channel, an 8-bit register, or any single-byte field. When you see FF in a colour code it means that channel is at full intensity.

What's the difference between hex, binary and octal?

They are bases 16, 2 and 8 respectively — three ways of writing the same value. Hex maps one digit to four binary digits, octal maps one digit to three. Hex won out in modern computing because bytes are eight bits, which divides evenly into two hex digits but not into octal. The cross-base chart above shows all four side by side.

Why do hex numbers start with 0x or #?

Because 15 could be fifteen in decimal or twenty-one in hex, so the prefix removes the ambiguity. Programming languages settled on 0x, CSS and design tools on #, and older assemblers on an h suffix or $ prefix. They all mean the same thing, and this converter accepts any of them.

How do I convert hex back to decimal?

Multiply each hex digit by 16 raised to its position counting from the right starting at zero, then add the results. For 0x315: (3 x 256) + (1 x 16) + (5 x 1) = 789. Or just type the hex value into the right-hand field of the converter — both fields are live, so it works in either direction.

What is the largest number this converter handles?

Up to 16 hex digits, which is 18,446,744,073,709,551,615 unsigned — the full 64-bit range. That is deliberately more generous than most converters on this topic, several of which cap input at 19 decimal characters or fewer.

Is hexadecimal the same as base 16?

Yes, they are two names for the same system. Hexadecimal comes from the Greek for six and the Latin for ten. You will also see it shortened to just hex, and in maths notation as a subscript 16 after the number.