Hex to Decimal Converter: Convert Hexadecimal to Decimal
A hexadecimal to decimal converter transforms hexadecimal numbers (base-16 numbers using digits 0-9 and letters A-F representing values 0-15) into decimal numbers (base-10 numbers using digits 0-9) by calculating the sum of each hex digit multiplied by its corresponding power of 16, using the conversion formula: Decimal = Σ(digit_value × 16^position), where position starts at 0 from the rightmost digit. This essential conversion process is fundamental for computer programming, web development, color code interpretation, memory address calculations, data analysis, debugging, and understanding how computers represent numerical data in hexadecimal format, enabling translation from compact hex notation used in programming, digital electronics, and system administration into human-readable decimal format for calculations, analysis, and comprehension of hexadecimal values in software development, hardware engineering, and computer science education.
🔢 Hex to Decimal Converter
Enter a hexadecimal number to convert to decimal
Maximum 16 hex digits (64-bit)
Understanding Hex to Decimal Conversion
Hexadecimal (hex) is a base-16 number system widely used in computing. It uses 16 distinct symbols: digits 0-9 represent values 0-9, and letters A-F represent values 10-15. Each position in a hex number represents a power of 16, starting from 16⁰ (equals 1) on the rightmost side. To convert hex to decimal, multiply each hex digit by its positional value and sum all results.
Hex to Decimal Formula
Conversion Formula:
\[ \text{Decimal} = \sum_{i=0}^{n-1} d_i \times 16^i \]
Where:
\( d_i \) = decimal value of hex digit at position \( i \)
\( i \) = position (0 from right, increases left)
\( n \) = total number of hex digits
Hex Digit Values:
0-9 = 0-9, A=10, B=11, C=12, D=13, E=14, F=15
Step-by-Step Conversion Method
Positional Notation Method
- Write the hex number and identify each digit
- Convert letters to values: A=10, B=11, C=12, D=13, E=14, F=15
- Assign powers of 16 to each position (right to left, starting at 16⁰)
- Multiply each digit value by its power of 16
- Add all products together to get the decimal result
Detailed Conversion Examples
Example 1: Simple 2-Digit Hex
Problem: Convert hex 2F to decimal
Step 1: Identify hex digit values
2 = 2 (decimal)
F = 15 (decimal)
Step 2: Assign position values
Hex: 2 F
Position: 1 0
Power: 16¹ 16⁰
Value: 16 1
Step 3: Calculate
Position 1: 2 × 16¹ = 2 × 16 = 32
Position 0: 15 × 16⁰ = 15 × 1 = 15
Step 4: Sum the values
32 + 15 = 47
Answer: 2F₁₆ = 47₁₀
Example 2: 3-Digit Hex Number
Problem: Convert hex 1A3 to decimal
Step 1: Convert hex digits to decimal values
1 = 1
A = 10
3 = 3
Step 2: Apply positional notation
Hex: 1 A 3
Power: 16² 16¹ 16⁰
Value: 256 16 1
Step 3: Calculate each position
1 × 256 = 256
10 × 16 = 160
3 × 1 = 3
Step 4: Sum
256 + 160 + 3 = 419
Answer: 1A3₁₆ = 419₁₀
Example 3: Common Hex Value (FF)
Problem: Convert hex FF to decimal
Quick method: FF is a common value (max 8-bit byte)
Calculation:
F = 15, F = 15
Position 1: 15 × 16 = 240
Position 0: 15 × 1 = 15
Total: 240 + 15 = 255
Answer: FF₁₆ = 255₁₀
💡 Fact: FF is the maximum value for one byte (8 bits)
Hex to Decimal Conversion Table
| Hexadecimal | Calculation | Decimal |
|---|---|---|
0 | 0 | 0 |
1 | 1 | 1 |
A | 10 | 10 |
F | 15 | 15 |
10 | 1×16 + 0×1 | 16 |
1F | 1×16 + 15×1 | 31 |
20 | 2×16 + 0×1 | 32 |
64 | 6×16 + 4×1 | 100 |
FF | 15×16 + 15×1 | 255 |
100 | 1×256 + 0×16 + 0×1 | 256 |
1A4 | 1×256 + 10×16 + 4×1 | 420 |
FFF | 15×256 + 15×16 + 15×1 | 4095 |
Hex Digit Values Reference
| Hex Digit | Decimal Value | Binary |
|---|---|---|
0 | 0 | 0000 |
1 | 1 | 0001 |
2-9 | 2-9 | 0010-1001 |
A | 10 | 1010 |
B | 11 | 1011 |
C | 12 | 1100 |
D | 13 | 1101 |
E | 14 | 1110 |
F | 15 | 1111 |
Powers of 16 Reference Chart
| Position | Power | Decimal Value | Hex Example |
|---|---|---|---|
| 0 | 16⁰ | 1 | 1 |
| 1 | 16¹ | 16 | 10 |
| 2 | 16² | 256 | 100 |
| 3 | 16³ | 4,096 | 1000 |
| 4 | 16⁴ | 65,536 | 10000 |
| 5 | 16⁵ | 1,048,576 | 100000 |
Real-World Applications
Web Development & Design
- Color codes: #FF5733 represents RGB values in hex
- CSS styling: Converting hex colors to RGB decimal
- Image processing: Pixel color values
- Alpha transparency: #FF5733CC (last two digits = alpha)
Programming & Software
- Memory addresses: 0x7FFF in code = 32767 decimal
- Error codes: HTTP status, system errors
- Unicode characters: U+0041 = 65 (letter 'A')
- Bit masks: Flag operations in programming
- Debugging: Interpreting hex dumps
Networking
- MAC addresses: 00:1A:2B:3C:4D:5E format
- IPv6 addresses: 2001:0db8::1 notation
- Port numbers: Converting hex port values
Common Hex Values
Frequently Used Hex-Decimal Pairs:
Web Colors:
#000000 = 0 (Black)
#FFFFFF = 16,777,215 (White)
#FF0000 = 16,711,680 (Red)
#00FF00 = 65,280 (Green)
#0000FF = 255 (Blue)
System Values:
0xFF = 255 (Max byte)
0x100 = 256 (One page)
0xFFFF = 65,535 (Max 16-bit)
Tips for Quick Conversion
Mental Math Shortcuts:
- Memorize A-F values: A=10, B=11, C=12, D=13, E=14, F=15
- Powers of 16: 1, 16, 256, 4096, 65536
- Single digits: 0-9 stay same, A-F add 10-15
- Two hex digits: First digit × 16 + second digit
- FF pattern: Two same digits = digit × 17 (AA = 10×17 = 170)
- Verify with calculator: For complex values
Common Mistakes to Avoid
⚠️ Conversion Errors
- Forgetting letter values: Must convert A-F to 10-15
- Wrong position counting: Always start at 0 from right
- Mixing up O and 0: Letter O vs zero (0) - only 0 is valid
- Case sensitivity confusion: A-F same as a-f (both valid)
- Invalid hex digits: G-Z are not valid hex characters
- Missing 0x prefix: Indicates hex in programming contexts
- Wrong base calculation: Use 16, not 10 or 2
RGB Color Code Example
Convert color #FF5733 to RGB decimal:
Break into components:
Red (RR): FF = 255
Green (GG): 57 = (5×16) + 7 = 80 + 7 = 87
Blue (BB): 33 = (3×16) + 3 = 48 + 3 = 51
Result: RGB(255, 87, 51)
CSS: rgb(255, 87, 51)
Frequently Asked Questions
How do you convert hex to decimal by hand?
Convert each hex digit to decimal (0-9 stay same, A=10 through F=15), multiply each by its position value (powers of 16 from right: 1, 16, 256...), then sum all products. Example: A5 = (10×16) + (5×1) = 160+5 = 165. Start from rightmost digit (position 0). Each position left multiplies by 16. Practice with small values first, memorize A-F = 10-15 for speed.
What does 0x mean before hex numbers?
0x is prefix indicating hexadecimal in programming languages (C, C++, Java, Python, JavaScript). Example: 0xFF means hexadecimal FF (decimal 255). Prevents confusion with decimal or variable names. Alternative notations: # for web colors (#FF5733), h suffix in assembly (FFh), $ in some systems. Always use 0x in code for clarity. Helps compiler/interpreter recognize number base. Convention standard across most programming languages.
How do you convert hex color codes to decimal?
Break 6-digit hex color into three 2-digit pairs (RR GG BB). Convert each pair to decimal: #FF5733 → FF=255, 57=87, 33=51 → RGB(255,87,51). Each pair represents 0-255 intensity. First two = red, middle two = green, last two = blue. Can also include alpha: #FF5733CC (CC = transparency). Many online tools and color pickers show both formats. Essential for CSS, graphics programming, image processing.
What is the decimal value of hex FFFF?
FFFF₁₆ = 65,535₁₀. Calculation: (F×16³)+(F×16²)+(F×16¹)+(F×16⁰) = (15×4096)+(15×256)+(15×16)+(15×1) = 61440+3840+240+15 = 65,535. This is maximum value for 16-bit unsigned integer (2¹⁶-1). Common in networking (port numbers), programming (unsigned short), memory addressing. Four hex digits can represent 0-65,535 range. Used extensively in system programming, embedded systems.
Why is hex used instead of decimal in programming?
Hex is compact representation of binary. One hex digit = exactly 4 binary bits (nibble). Byte (8 bits) = 2 hex digits (00-FF). Easier to read/write than long binary strings. Example: binary 11111111 = hex FF = decimal 255. Memory addresses, color codes, bit patterns more readable in hex. Direct mapping to binary makes bitwise operations intuitive. Standard in assembly language, hardware programming, debugging. Two characters represent full byte range (0-255).
Can hex numbers have decimals?
Yes! Hex can represent fractional values using hexadecimal point. Example: A.8₁₆ = 10.5₁₀. After point, positions are 16⁻¹=0.0625, 16⁻²=0.00390625, etc. Less common than decimal fractions. Used in IEEE 754 floating-point representation, some scientific computing. Most programmers work with integer hex values. Floating-point usually shown in decimal or scientific notation. Understanding hex fractions useful for low-level data format analysis, debugging binary file formats.
Key Takeaways
Converting hexadecimal to decimal is a fundamental skill in computer science, programming, and digital electronics. Understanding hex-to-decimal conversion enables you to interpret color codes, memory addresses, error codes, and other hexadecimal values commonly encountered in software development and system administration.
Essential principles to remember:
- Hex uses base-16: digits 0-9 and letters A-F (values 10-15)
- Each position represents 16^n (right to left, starting at n=0)
- Conversion formula: sum of (digit_value × 16^position)
- Memorize A=10, B=11, C=12, D=13, E=14, F=15
- Powers of 16: 1, 16, 256, 4096, 65536
- Two hex digits = one byte (00-FF = 0-255)
- 0x prefix indicates hex in programming
- Case insensitive: FF = ff
- Each hex digit represents exactly 4 binary bits
- Verify results by converting back to hex
Getting Started: Use the interactive converter at the top of this page to convert any hexadecimal number to decimal instantly. Enter your hex value (0-9, A-F), click convert, and receive the decimal result with complete step-by-step breakdown showing position values, powers of 16, and the detailed calculation process. Perfect for web development, programming, color code conversions, or learning hexadecimal number systems.
