Hexadecimal Calculator | Hex Math & Conversion
Calculate hexadecimal math instantly. Free online hex calculator for addition, subtraction, multiplication, and hex-to-decimal conversions.
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Introduction to the Hexadecimal Calculator
The Hexadecimal (Hex) Calculator performs arithmetic and conversions in base-16, one of the most important number systems in computer science. Unlike binary (base-2) which can make long strings of 1s and 0s hard to read, hexadecimal is compact—a single hex digit represents exactly four binary digits (a "nibble"), making it the perfect human-readable shorthand for binary data.
This free hex calculator handles addition, subtraction, multiplication, and division of hexadecimal numbers, with optional conversion to and from binary and decimal formats.
When to Use This Calculator
- Web Development: HTML color codes are written in hex (e.g., #FF5733 represents a shade of orange-red). Manipulating and mixing colors requires hex arithmetic.
- Memory Addressing: Memory addresses in computer debugging tools (debuggers, disassemblers) are displayed in hex format.
- Networking: MAC addresses (e.g., 2C:54:91:88:C9:E3) and IPv6 addresses are written in hexadecimal.
- Assembly Language: Machine code instructions, opcodes, and register values are routinely written in hex.
- Cryptography: Cryptographic keys, hashes (like SHA-256), and encrypted data are conventionally displayed as hex strings.
Hexadecimal Formula & Number System
Hex is base-16. Each digit has 16 possible values, using letters A–F for values 10–15:
| Hex | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Decimal | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Positional Values
Step-by-Step Hex to Decimal Conversion
Identify Each DigitWrite out the hex number and label each digit's positional value from right to left (16⁰, 16¹, 16², ...).
Convert LettersReplace A=10, B=11, C=12, D=13, E=14, F=15.
Multiply by PowersMultiply each digit value by its corresponding power of 16.
Sum All ProductsAdd all the results together to get the decimal value.
Worked Examples
Example 1: Hex to Decimal
Given Inputs
| Input | Value |
|---|---|
| Hex Number | 2AF₁₆ |
Calculation Steps
- Expand= 2×16² + A×16¹ + F×16⁰
- Substitute letters= 2×256 + 10×16 + 15×1
- Calculate= 512 + 160 + 15 = 687
Results
2AF₁₆ in decimal
687
Example 2: Decimal to Hex
Given Inputs
| Input | Value |
|---|---|
| Number | 255 (decimal) |
Calculation Steps
- 255 ÷ 16 = 15 r= 15 → F
- 15 ÷ 16 = 0 r= 15 → F
- Read remainders bottom to top= FF
Results
255 in hex
FF₁₆
Example 3: Hex Addition
Given Inputs
| Input | Value |
|---|---|
| Expression | A3 + 2F |
Calculation Steps
- Rightmost column= 3 + F = 3 + 15 = 18. 18 = 1×16 + 2. Write 2, carry 1.
- Left column= A + 2 + (carry 1) = 10 + 2 + 1 = 13 → D
Results
Result (hex)
D2₁₆
Verification (decimal)
163 + 47 = 210 = D2₁₆ ✓
Example 4: Hex Color Code
Given Inputs
| Input | Value |
|---|---|
| HTML Color | #FF8C00 (Dark Orange) |
Calculation Steps
- Red channel (FF)= FF₁₆ = 255₁₀
- Green channel (8C)= 8C₁₆ = 8×16 + 12 = 140₁₀
- Blue channel (00)= 00₁₆ = 0₁₀
Results
RGB Values
rgb(255, 140, 0)
Example 5: Hex to Binary
Given Inputs
| Input | Value |
|---|---|
| Hex Number | B5₁₆ |
Calculation Steps
- Convert B (=11) to binary= 1011
- Convert 5 to binary= 0101
- Concatenate= 1011 0101
Results
B5₁₆ in binary
10110101₂
Common Mistakes
Avoid these hex errors:
- Case sensitivity: Hex digits A through F can be written uppercase or lowercase (a-f), but never mix them within a single number in formal contexts. Computers treat them identically.
- Not reading remainders in reverse: Just like binary, when converting decimal to hex by repeated division, you read remainders from last to first (bottom to top).
- Forgetting carry > F: In hex addition, you carry when the column sum exceeds 15 (F). The carry is always 1 and the remainder is the column sum minus 16.
Conclusion
The Hexadecimal Calculator is an essential tool for programmers, network engineers, designers, and anyone working at the intersection of human-readable information and binary data. By mastering hex, you can read memory dumps, decode color codes, interpret MAC addresses, and understand machine code—all critical skills in modern computing. Use this free tool to perform exact hex calculations and conversions in seconds.
Frequently Asked Questions
What is hexadecimal?
Hexadecimal (hex) is a base-16 number system. It uses numbers 0-9 to represent values zero to nine, and letters A-F to represent values ten to fifteen.
Why is hex used in computer science?
Hex is widely used because it provides a human-friendly representation of binary values. One hex digit perfectly represents a 4-bit binary sequence (a nibble), making large binary numbers easier to read.
How do you add hex numbers?
You add them normally, but you carry over when the sum exceeds 15 (F) instead of 9. For example, 9 + 1 = A, and A + B = 15 (which is 15 in hex, meaning 1 * 16 + 5).
What are common uses for hex?
Hexadecimal is famously used for HTML color codes (e.g., #FFFFFF for white), MAC addresses, IPv6 addresses, and memory addresses in debugging.
How do you convert hex to decimal?
Multiply each hex digit by 16 raised to the power of its position (starting from 0 on the right) and sum the results.
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