Hex Calculator

Perform hexadecimal arithmetic and convert between decimal and hex instantly.

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Calculation Examples

Calculation Case Result
Hex addition: 1A3 + 2F 1D2 (decimal 466)
Hex to decimal: FF 255
Decimal to hex: 1000 3E8
Hex subtraction: 20 minus 1 1F (decimal 31)
Mihail Doncenco
Mihail Doncenco Site Creator & Calculator Expert

Founder and developer of CalcMate. Builds and maintains every calculator on this site, focusing on formula accuracy and clear, practical results.

How to Use the Hex Calculator

Enter your first value using hexadecimal digits (0-9 and A-F) or decimal digits, depending on your input format. Select the operation: addition, subtraction, multiplication, or division. Enter the second value and click Calculate.

To use the tool as a pure converter, enter a single value in hex or decimal and leave the second field empty. The result appears in both number systems at once. This helps with memory addresses, HTML color codes, and any case where you move between base-16 and base-10. Intermediate carry and borrow steps are shown so you can follow the arithmetic.

How Hexadecimal Arithmetic and Conversions Work

Hexadecimal is a base-16 positional system with sixteen symbols: 0-9 for zero through nine, and A-F for ten through fifteen. The decimal value of a hex number is \[N = \sum_{i=0}^{n} d_i \times 16^i\] where \(d_i\) is the digit at position \(i\), counting from 0 at the rightmost digit.

In addition, digits are summed column by column. When a column total exceeds 15, the excess carries to the next position. For example, \(F_{16} + 2_{16} = 11_{16}\), because \(15 + 2 = 17 = 1 \times 16 + 1\). In subtraction, if a digit is smaller than the one being subtracted, you borrow 16 from the next column, the same logic as decimal borrowing but in base-16.

To convert decimal to hex, divide repeatedly by 16 and record the remainders, writing 10-15 as A-F. Read the remainders from last to first. To convert hex to decimal, multiply each digit by its power of 16 and add the results.

Hex addition example showing base-16 carry rules and decimal conversion steps

Useful Tips 💡

  • Use uppercase A-F to follow standard programming and documentation conventions.
  • Leave the second input field empty to use the tool purely as a hex-to-decimal or decimal-to-hex converter.

📋Steps to Calculate

  1. Enter the first number in hexadecimal or decimal format.

  2. Select the arithmetic operation, or leave the second field empty for conversion only.

  3. Click Calculate to see results in both hex and decimal with step-by-step carry or borrow details.

Mistakes to Avoid ⚠️

  1. Using letters outside A-F, such as G or H, which are not valid hexadecimal digits.
  2. Carrying at 10 instead of 16 during manual addition, a base-10 habit that gives wrong results in hex.
  3. Reading decimal-to-hex remainders in the wrong order: read them from last to first, not first to last.
  4. Ignoring two's complement when subtracting signed values, which changes how you should read the result.

Practical Applications📊

  1. Calculate memory offsets and pointer arithmetic in low-level and systems programming.

  2. Convert RGB values to hex color codes for CSS: RGB(255, 87, 51) becomes #FF5733.

  3. Read and verify register values and data encodings in embedded systems and firmware debugging.

Questions and Answers

Can this tool perform bitwise operations like AND, OR, and XOR?

The calculator covers hex addition, subtraction, multiplication, division, and conversion, while bitwise AND, OR, and XOR are a separate family of operations. To do them by hand, convert each hex digit to 4 bits, apply the logic gate bit by bit, and convert back. For example, \(0xF0\ \text{AND}\ 0x0F = 0x00\) because no bit positions overlap, and \(0xA0\ \text{OR}\ 0x0B = 0xAB\) because the bits combine. They are essential for subnet masks, register flags, and packed data fields.

How do signed hex values and two's complement work?

In two's complement, the highest bit gives the sign, and a value with that bit set is negative. For an 8-bit value, 0xFF is 255 unsigned but -1 signed, and 0x80 is -128. To read a signed result, subtract \(2^{n}\) from the unsigned value when the top bit is set, where \(n\) is the bit width. For example, \(0\text{xFE} = 254 - 256 = -2\). Subtracting 0x20 from 0x10 in 8-bit arithmetic gives 0xF0, which is -16 signed. C, C++, and most CPU registers use this convention.

How do you convert a decimal number to hexadecimal?

Divide the number by 16, record the remainder (10-15 become A-F), then divide the quotient by 16 again and repeat until the quotient is zero. Read the remainders from last to first. For 255: \(255 \div 16 = 15\) remainder \(15\) (F), then \(15 \div 16 = 0\) remainder \(15\) (F), giving \(FF_{16}\). For 1000: \(1000 \div 16 = 62\) remainder 8, \(62 \div 16 = 3\) remainder 14 (E), \(3 \div 16 = 0\) remainder 3, giving \(3E8_{16}\).

How do you convert hex to a decimal integer?

Multiply each hex digit by 16 raised to its position, counting from 0 at the rightmost digit, and add the results. For \(A1_{16}\): \((10 \times 16^1) + (1 \times 16^0) = 160 + 1 = 161\). For \(FF_{16}\): \((15 \times 16^1) + (15 \times 16^0) = 240 + 15 = 255\). This is the general formula \(N = \sum_{i=0}^{n} d_i \times 16^i\) applied digit by digit.

How does hexadecimal addition work with carries?

Hex addition works like decimal addition, except digits roll over at 16 instead of 10. When two digits sum to 16 or more, write the remainder and carry 1 to the next column. For example, \(9_{16} + 8_{16} = 17_{10} = 11_{16}\): write 1 and carry 1. Take \(1A3_{16} + 2F_{16}\): in the rightmost column, \(3 + F = 18 = 12_{16}\), so write 2 and carry 1; then \(A + 2 + 1 = D\); the result is \(1D2_{16}\), which is 466 in decimal. The calculator shows each carry step.

What is a hex calculator and why is it used in computing?

A hex calculator performs arithmetic and conversions in base-16, which uses the digits 0-9 and the letters A-F. Hex is standard in computing because one hex digit represents exactly 4 bits (a nibble) and two digits represent one byte. That alignment with binary makes hex far shorter and easier to read than binary for memory addresses, machine code, color values, and network data. Most debuggers and disassemblers show addresses and register values in hex by default.

Why is hex the preferred format for web colors and memory addresses?

Hex matches the byte structure of the data. A CSS color like #FF5733 packs three 8-bit channels into six hex digits: FF is red 255, 57 is green 87, and 33 is blue 51. Each pair runs from 00 to FF, which is 0 to 255, exactly one byte. Memory addresses follow the same logic: a 32-bit address takes 8 hex digits and a 64-bit address takes 16. Reading 0x7FFF is much easier than reading the 15 ones in its binary form.
Disclaimer: This calculator is designed to provide helpful estimates for informational purposes. While we strive for accuracy, financial (or medical) results can vary based on local laws and individual circumstances. We recommend consulting with a professional advisor for critical decisions.