Hex to Decimal Converter
Free online hex to decimal converter with step-by-step breakdown. Convert between hexadecimal, decimal, binary, and octal number systems instantly.
About This Calculator
The hex to decimal converter instantly translates numbers between four major number systems: hexadecimal (base-16), decimal (base-10), binary (base-2), and octal (base-8). Whether you are a programmer debugging memory addresses, a student learning number base conversions, a web designer working with hex color codes, or an electronics engineer analyzing digital signals, this tool provides fast, accurate bidirectional conversion with detailed step-by-step breakdowns.
For hex to decimal conversion, each hex digit is multiplied by 16 raised to the power of its position (counting from 0 at the rightmost digit). The results are summed to give the decimal equivalent. For example, hex 1A3 = 1×16² + 10×16¹ + 3×16⁰ = 256 + 160 + 3 = 419. Our conversion table shows every digit's contribution so you can verify the arithmetic.
For decimal to hex conversion, the calculator uses the repeated-division method: divide the decimal number by 16 repeatedly, recording each remainder (converting 10-15 to A-F). The hex result is read from the last quotient (most significant digit) to the first remainder (least significant digit). For example, 419 ÷ 16 = 26 remainder 3, 26 ÷ 16 = 1 remainder 10 (A), 1 ÷ 16 = 0 remainder 1, giving hex 1A3.
In addition to the primary hex-decimal pair, the calculator automatically derives the binary and octal equivalents of every input. Binary represents numbers as sequences of 0s and 1s (each hex digit maps to 4 binary bits), while octal uses digits 0-7 (each hex digit pair maps to 3 octal digits). This makes the tool a comprehensive number base converter for technical workflows.
Number base conversion is essential across many fields. Programmers use hex for memory addresses and machine code because it is more compact than binary while staying directly convertible. Web developers use hex triplets like #FF5733 for RGB color specification in CSS and HTML. Network engineers work with hexadecimal MAC addresses and IP-to-hex conversions. Mathematics and computer science students study base systems to understand how computers represent and process numerical data at the hardware level.
Frequently Asked Questions
How does the hex to decimal converter work?
The hex to decimal converter works by multiplying each hexadecimal digit by 16 raised to the power of its position (counting from 0 at the rightmost digit). For example, hex FF = 15×16¹ + 15×16⁰ = 240 + 15 = 255 in decimal.
How do you convert decimal to hex?
To convert decimal to hexadecimal, repeatedly divide the decimal number by 16 and write down the remainders. Read the remainders from bottom to top to get the hex value. For example, 255 ÷ 16 = 15 remainder 15, giving hex FF.
What is hexadecimal notation used for?
Hexadecimal (base-16) is widely used in computing for memory addresses, color codes (like #FF5733 in CSS), MAC addresses, machine code instructions, and representing binary data in a more human-readable form since each hex digit represents 4 binary bits.
What are the letters in hexadecimal?
Hexadecimal uses digits 0-9 and letters A-F, where A=10, B=11, C=12, D=13, E=14, and F=15. These six letters let a single digit represent values 10 through 15 in the base-16 system.
How do you convert hex to binary?
Each hex digit converts to a 4-bit binary number: 0=0000, 1=0001, 2=0010, 3=0011, 4=0100, 5=0101, 6=0110, 7=0111, 8=1000, 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111. Just replace each hex digit with its 4-bit binary equivalent.
What is the difference between hex, decimal, binary, and octal?
Hex is base-16 (digits 0-9 and A-F), decimal is base-10 (digits 0-9), binary is base-2 (digits 0 and 1), and octal is base-8 (digits 0-7). Every number can be represented in any base; the converter shows all four representations of the same value.
Is this hex converter free to use?
Yes, this hex to decimal converter is completely free to use with no registration or account required. You can share your calculations via the URL.