Hexadecimal (hex) is a base-16 numbering system that uses the digits 0–9 and the letters A–F to represent values 0 through 15. Each hex digit represents exactly 4 binary bits (a "nibble"), making hex a compact shorthand for binary data. For example, the decimal number 255 is FF in hex (15×16 + 15 = 255) and 11111111 in binary.

How do you convert hex to decimal?

To convert hex to decimal, multiply each digit by 16 raised to its position power (starting from 0 at the rightmost digit) and sum the results. For example, 1A3 in hex: 1×16² + 10×16¹ + 3×16⁰ = 256 + 160 + 3 = 419 in decimal. The letters A–F have values 10–15 respectively.

How do you add hexadecimal numbers?

Hex addition works like decimal addition, but you carry when a column sum reaches 16 (not 10). For example, F + 1 = 10 in hex (decimal 15 + 1 = 16 = 1×16 + 0). And 9 + 8 = 11 in hex (decimal 9 + 8 = 17 = 1×16 + 1). Converting both numbers to decimal, adding, and converting back gives the same result — that is exactly what this calculator does under the hood.

What is hex used for in computing?

Hexadecimal is ubiquitous in computing because it maps cleanly to binary — every byte (8 bits) can be represented as exactly two hex digits. It is used for: memory addresses (e.g., 0x7FFF), RGB color codes (#FF5733), machine code and debugging output, file format headers (magic numbers), and network MAC addresses. Hex makes binary data human-readable without the sprawl of long binary strings.

How do you convert decimal to binary?

Divide the decimal number by 2 repeatedly, recording the remainders, then read the remainders from bottom to top. For example, 13 ÷ 2 = 6 R1; 6 ÷ 2 = 3 R0; 3 ÷ 2 = 1 R1; 1 ÷ 2 = 0 R1 → reading remainders bottom to top gives 1101. Alternatively, convert via hex: 13 = D in hex, and D = 1101 in binary (since each hex digit = 4 bits).

Why is base 16 more useful than base 8 (octal)?

Base 16 is preferred over base 8 because 16 is a power of 2 (2⁴), so each hex digit maps to exactly 4 bits. This makes byte boundaries neat: one byte = two hex digits. Octal digits (base 8 = 2³) map to 3 bits, which does not align with the 8-bit byte standard used in modern computing. Hex is also more compact: a 32-bit number needs 8 hex digits vs 11 octal digits.

Why do computers use hexadecimal instead of decimal?

Computers store data in binary (base 2), but long binary strings are unwieldy — a single byte is 8 binary digits. Hexadecimal provides a compact shorthand: each hex digit represents exactly 4 bits, so one byte = two hex digits. For example, the color red in CSS is #FF0000 — just 6 hex digits representing three bytes (R, G, B). Writing the same value in decimal would be less compact and would not align naturally with byte boundaries.

What does #FF5733 mean in CSS?

In CSS, #FF5733 is an RGB color code in hex: the first two hex digits (FF = 255 in decimal) set the red channel to maximum, the next two (57 = 87) set green to 87, and the last two (33 = 51) set blue to 51. The result is an orange-red color. Hex color codes are compact and machine-readable — #FFFFFF is white (all channels at 255), #000000 is black (all at 0), and #FF0000 is pure red.

Hexadecimal Calculator — Convert & Calculate

Converts between hex, decimal, binary, and octal, and performs arithmetic on hexadecimal numbers with results in all four bases.

How to Use the Hexadecimal Calculator

This hexadecimal calculator has two modes — switch between Base Converter and Hex Arithmetic using the toggle at the top. In converter mode, select your input base (hex, decimal, binary, or octal), type your number, and instantly see it expressed in all four bases. In arithmetic mode, enter two hex numbers and choose an operation — the result appears in all four bases simultaneously.

Hex digits are case-insensitive — you can type 1a3f or 1A3F. The calculator accepts only valid digits for the selected base, so invalid characters are filtered automatically.

The Hexadecimal Number System

Hexadecimal is a positional numbering system with base 16. The 16 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F where A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

Each position represents a power of 16. The rightmost digit is 16⁰ = 1, the next is 16¹ = 16, then 16² = 256, and so on. To convert hex to decimal: multiply each digit by its positional power and sum. For 2F in hex: 2×16 + 15×1 = 32 + 15 = 47.

Hex and Binary Equivalence

Each hex digit corresponds to exactly four binary digits (bits):

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

This means you can convert between hex and binary digit by digit without any arithmetic. For our scientific notation calculator, large numbers like memory sizes are often expressed more compactly in hex than in decimal.

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Converting Between Bases

Decimal to Hex

Divide the decimal number by 16 repeatedly, recording the remainders (in hex), then read from bottom to top. For 255: 255 ÷ 16 = 15 R15 (F); 15 ÷ 16 = 0 R15 (F) → FF. For 419: 419 ÷ 16 = 26 R3; 26 ÷ 16 = 1 R10 (A); 1 ÷ 16 = 0 R1 → 1A3.

Hex to Binary

Replace each hex digit with its 4-bit binary equivalent. For example, 3F = 0011 1111 in binary. To go back from binary to hex, group the bits into sets of 4 from right to left and convert each group.

Hex in Real-World Computing

Hexadecimal appears everywhere in computing and digital work:

Colors — HTML/CSS colors like #FF5733 encode red (FF = 255), green (57 = 87), blue (33 = 51) channels as byte pairs
Memory addresses — pointers in C and assembly are shown in hex (e.g., 0x7FFE4B20)
IP and MAC addresses — MAC addresses like 00:1A:2B:3C:4D:5E are six hex bytes
File formats — file headers (magic numbers) like FF D8 FF identify JPEG files
Unicode — code points like U+1F600 (😀) are expressed in hex

For number representation in other formats, see our decimal calculator.

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Hex Arithmetic Examples

FF + 1 = 100 (hex) — decimal 255 + 1 = 256 = 1×256 + 0×16 + 0 = 100 in hex
1A × 2 = 34 (hex) — decimal 26 × 2 = 52 = 3×16 + 4 = 34 in hex
100 − FF = 1 (hex) — decimal 256 − 255 = 1
FF ÷ F = 11 (hex) — decimal 255 ÷ 15 = 17 = 1×16 + 1 = 11 in hex

Sources & References

Hexadecimal — Wikipedia
Positional notation — Wikipedia

Hexadecimal Calculator