Hex/Decimal Converter: Convert Between Hexadecimal and Decimal Numbers

Hexadecimal is everywhere in programming — memory addresses, color codes, character encodings, MAC addresses, and error codes. Converting between hex and decimal by hand works for small values but becomes impractical for anything larger than two digits. Our converter handles both directions instantly and shows the binary and octal representations as well.

Number Systems Explained

Decimal (Base 10)

The system you use every day. Ten digits (0-9), and each position represents a power of 10.

255 = 2*100 + 5*10 + 5*1
    = 2*10^2 + 5*10^1 + 5*10^0

Hexadecimal (Base 16)

Uses sixteen digits: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15). Each position represents a power of 16.

FF = F*16 + F*1
   = 15*16 + 15*1
   = 240 + 15
   = 255

Hex is compact. A single hex digit represents exactly 4 bits, so two hex digits represent one byte (0-255). This direct mapping to binary makes hex the preferred human-readable format for binary data.

Binary (Base 2)

Two digits (0 and 1). Each position represents a power of 2. This is the native language of computers.

11111111 = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255

Octal (Base 8)

Eight digits (0-7). Each position represents a power of 8. Less common than hex but still used in Unix file permissions and some legacy systems.

377 = 3*64 + 7*8 + 7*1 = 192 + 56 + 7 = 255

Why Hexadecimal Matters

Compact Binary Representation

One hex digit maps to exactly 4 binary digits (a nibble). This makes hex a natural shorthand for binary data:

Binary:  1010 1111 0011 1100
Hex:     A    F    3    C

Binary:  11111111
Hex:     FF
Decimal: 255

Reading AF3C is far easier than reading 1010111100111100, and the conversion between them is mechanical.

Common Hex Values to Know

Hex	Decimal	Significance
0x00	0	Null byte
0x0A	10	Line feed (newline)
0x0D	13	Carriage return
0x20	32	Space character
0x41	65	Letter ‘A’ in ASCII
0x7F	127	Max signed 8-bit value
0xFF	255	Max unsigned 8-bit value
0xFFFF	65535	Max unsigned 16-bit value
0xFFFFFFFF	4294967295	Max unsigned 32-bit value

Where You Encounter Hex

CSS and Web Colors

Web colors are hex-encoded RGB values. Each pair of hex digits represents one color channel:

#FF5733
 ││││││
 RR GG BB
 255 87 51

Memory Addresses and Debugging

Debuggers, crash logs, and stack traces show memory addresses in hex:

Segfault at 0x7FFE4A3B2C10
Stack pointer: 0x00007FFE4A3B2BF0

MAC Addresses and Network Data

Network hardware identifiers use hex with colon or dash separators:

00:1A:2B:3C:4D:5E

Character Encoding

Unicode code points are expressed in hex. The emoji for a thumbs up is U+1F44D (decimal 128077). URL-encoded characters use percent-hex notation: %20 for space (hex 20 = decimal 32).

File Formats and Hex Editors

File signatures (magic numbers) that identify file types are hex values:

PDF:  25 50 44 46  (%PDF)
PNG:  89 50 4E 47  (.PNG)
ZIP:  50 4B 03 04  (PK..)

Unix File Permissions

While permissions are technically octal, they often appear alongside hex in system programming. The chmod value 755 is octal, and understanding base conversions helps when working across these contexts.

How to Convert Manually

Hex to Decimal

Multiply each digit by its positional power of 16 and sum:

1A3 (hex) to decimal:
  1 * 16^2 = 1 * 256 = 256
  A * 16^1 = 10 * 16 = 160
  3 * 16^0 = 3 * 1   = 3
  Total = 256 + 160 + 3 = 419

Decimal to Hex

Repeatedly divide by 16 and collect the remainders:

419 (decimal) to hex:
  419 / 16 = 26 remainder 3   -> 3
  26  / 16 = 1  remainder 10  -> A
  1   / 16 = 0  remainder 1   -> 1
  Read remainders bottom to top: 1A3

For anything beyond two or three digits, this process is slow enough that a converter tool saves real time.

How to Use Our Hex/Decimal Converter

Enter a number in either hexadecimal or decimal format
View the conversion along with binary and octal equivalents
Toggle direction to convert in whichever direction you need
Copy any output with one click

Tips

Hex input accepts both uppercase and lowercase letters (ff, FF, and Ff all work)
Prefix hex values with 0x or enter the digits directly — the tool handles both
Use the binary output for bit-level analysis and the octal output for Unix permissions
All conversions happen locally in your browser — nothing is sent to a server

Quick Conversion Table

Decimal	Hex	Binary	Octal
0	0	0	0
10	A	1010	12
16	10	10000	20
100	64	1100100	144
255	FF	11111111	377
256	100	100000000	400
1024	400	10000000000	2000
65535	FFFF	1111111111111111	177777

Frequently Asked Questions

Why do programmers use hexadecimal instead of decimal? Because hex maps cleanly to binary. One hex digit equals exactly 4 bits, so a byte (8 bits) is always two hex digits. This makes it far easier to read and reason about binary data compared to decimal, where the relationship to bits is not as direct.

What does the 0x prefix mean? The 0x prefix is a convention in programming languages (C, JavaScript, Python, Java, and others) to indicate that the following digits are hexadecimal. Without the prefix, 10 could mean decimal ten or hex sixteen.

How do I convert hex to binary quickly? Replace each hex digit with its 4-bit binary equivalent: 0=0000, 1=0001, …, 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111. Concatenate them and you have the full binary value.

Can hexadecimal represent negative numbers? Not directly, but signed integer representation uses two’s complement in binary, which is then displayed as hex. For example, -1 as a 32-bit signed integer is 0xFFFFFFFF.

What is the largest hex number this tool supports? The tool handles numbers within the safe integer range of JavaScript (up to 2^53 - 1, or 9007199254740991 in decimal, which is 0x1FFFFFFFFFFFFF in hex). This is more than sufficient for virtually all practical conversion needs.

Try our free Hex/Decimal Converter to convert between hexadecimal and decimal with binary and octal output instantly.