Digital Math

Hexadecimal Math Calculator

Perform addition, subtraction, multiplication, and division on base-16 numbers easily.

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Enter your hexadecimal values using digits 0-9 and letters A-F, select your arithmetic operation, and calculate the result.

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A Guide to Base-16 Hexadecimal Calculations

The hexadecimal system (often called hex) is a base-16 numbering system. While decimal uses ten digits and binary uses two, hexadecimal uses sixteen distinct symbols: the numbers 0 through 9 followed by the letters A, B, C, D, E, and F (which represent values 10 through 15). Hexadecimal is heavily used in computing because it represents binary byte values in a much more compact, human-readable format.

Why Hex is Used in Computing

Binary strings of 0s and 1s can become extremely long and difficult to read. One byte of data consists of eight bits, which can be represented by exactly two hexadecimal characters (ranging from 00 to FF). This 4-to-1 compression ratio makes it easy for programmers to analyze data dumps, memory addresses, and file contents without getting lost in binary sequences.

To see the raw binary states behind your hex calculations, you can use our base two binary numbers tool. If you are comparing digital codes to standard arithmetic, check out our standard base ten math tool. For full formula support, you can also view our advanced scientific solver.

Everyday Digital Applications

Web Page Styling (HTML/CSS): Web colors are defined using 6-digit hex codes (like #FF5733) representing red, green, and blue intensities. You can check color ratios using our calculating percentage shares tool.
Computer Hardware Addresses: Every network card has a unique MAC address expressed as six pairs of hex numbers separated by colons.
Memory Debugging: Operating systems display memory error locations (pointers) using hex codes to help developers isolate bugs.
Digital File Signatures: File formats like PDFs or JPEGs contain header signatures written in hex that tell the system how to read the contents. You can round up file sizes using our rounding math figures tool.

How Hex Arithmetic Works

Hex arithmetic follows standard place-value rules, but you carry and borrow groups of sixteen rather than groups of ten. For example, in hex addition, adding 9 and 1 equals A (value 10). Adding F and 1 causes a carry, resulting in 10 (which represents value 16 in decimal).

Because hex letters are case-insensitive, you can write them as capital letters or lowercase. The calculator will automatically align the values and output the step-by-step arithmetic in clean hexadecimal values.

Example of Hex Addition

Suppose we want to add the hex numbers B (decimal 11) and 5 (decimal 5) together.

Aligning them: B + 5. Starting from B, we count up 5 units: C (1), D (2), E (3), F (4), and then 10 (5). The sum of B and 5 is exactly 10 in hexadecimal. Converting hex 10 back to decimal reveals 1 × 16 + 0 = 16, which matches our standard math (11 + 5 = 16). This illustrates how base-16 calculations match decimal values.