🔢 Hex Calculator - Convert Hexadecimal, Binary, Decimal & Octal

Free online hexadecimal calculator to convert between hex, binary, decimal, and octal. Perform hex arithmetic operations with step-by-step solutions.

Last Updated: February 13, 2026•Reviewed by: CalcFinex Editorial Team

Hexadecimal Calculator

First Number

Operation

Convert To

Number Systems

Hexadecimal (Base 16)

Uses: 0-9, A-F

Example: 1A = 26₁₀

Binary (Base 2)

Uses: 0, 1

Example: 11010 = 26₁₀

Decimal (Base 10)

Uses: 0-9

Example: 26 = 26₁₀

Octal (Base 8)

Uses: 0-7

Example: 32 = 26₁₀

Hex Reference

Hex	Dec	Bin
0	0	0000
1	1	0001
2	2	0010
3	3	0011
4	4	0100
5	5	0101
6	6	0110
7	7	0111
8	8	1000
9	9	1001
A	10	1010
B	11	1011
C	12	1100
D	13	1101
E	14	1110
F	15	1111

Common Hex Values

FF:255 (max byte)

100:256

3FF:1023

FFF:4095

How to Use the Hex Calculator

For Conversion:

1Enter your number in the first input field
2Select the input number system (Hex, Binary, Decimal, or Octal)
3Select "Convert" operation (arrow icon)
4Choose the output number system
5Click "Calculate" to see the result with steps

For Arithmetic Operations:

1Enter the first number and select its number system
2Choose the operation (+, -, ×, ÷)
3Enter the second number (same base as first)
4Select the output number system for the result
5Click "Calculate" to see the result with detailed steps

Understanding Hexadecimal Numbers

What is Hexadecimal?

Hexadecimal (often shortened to "hex") is a base-16 number system that uses 16 distinct symbols. It uses the digits 0-9 to represent values zero through nine, and the letters A-F to represent values ten through fifteen. Hex is extensively used in computing and programming because it provides a human-friendly representation of binary-coded values. Each hex digit represents exactly four binary digits (bits), making conversions between hex and binary straightforward.

Why Use Hexadecimal?

Hexadecimal is preferred in computing for several important reasons:

Compact representation: 2 hex digits can represent a full byte (8 bits) instead of 8 binary digits
Easy conversion: Each hex digit maps directly to 4 binary digits
Human-readable: Easier to read and remember than long binary strings
Memory addresses: Computer memory addresses are typically displayed in hex
Color codes: Web colors use hex format (#RRGGBB)
Debugging: Machine code and memory dumps are shown in hex

Hex Place Values

In hexadecimal, each digit position represents a power of 16, starting from 16⁰ on the right. Here's how the hex number 2A3 breaks down:

16²
256

16¹
16

16⁰
1

= (2×256) + (10×16) + (3×1) = 512 + 160 + 3 = 675 in decimal

Hex Digit Values

Numeric Digits (0-9)

Same as decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Letter Digits (A-F)

A=10, B=11, C=12, D=13, E=14, F=15

Hexadecimal Conversions

Hex to Decimal

Multiply each digit by 16 raised to its position and sum the results.

Example: 1A3₁₆ to decimal

= (1 × 16²) + (A × 16¹) + (3 × 16⁰)

= (1 × 256) + (10 × 16) + (3 × 1)

= 256 + 160 + 3

= 419₁₀

Decimal to Hex

Repeatedly divide by 16 and record remainders, then read backwards.

Example: 419₁₀ to hex

419 ÷ 16 = 26 remainder 3

26 ÷ 16 = 1 remainder 10 (A)

1 ÷ 16 = 0 remainder 1

Reading backwards: 1A3₁₆

Hex to Binary

Convert each hex digit to 4 binary digits.

Example: 2F₁₆ to binary

2₁₆ = 0010₂

F₁₆ = 1111₂

= 00101111₂

Binary to Hex

Group binary digits in sets of 4 (from right), convert each group to hex.

Example: 11010110₂ to hex

Group: 1101 0110

1101₂ = D₁₆

0110₂ = 6₁₆

= D6₁₆

Hexadecimal Arithmetic Operations

Hex Addition

Rules:

Add like decimal, carry at 16

A + 7 = 17₁₀ = 11₁₆ (carry 1)

F + 1 = 16₁₀ = 10₁₆ (carry 1)

Example:

+ 2F

A+F=25₁₀=19₁₆, 1+2+1=4

Hex Subtraction

Rules:

Subtract like decimal

Borrow 16 when needed

10₁₆ - 1 = F (borrowed 16)

Example:

- 1A

F-A=5, 2-1=1

Hex Multiplication

Process:

Multiply each digit

Carry when product ≥ 16

2 × 8 = 16₁₀ = 10₁₆

Example:

A × 3 = 30₁₀ = 1E₁₆

(10 × 3 = 30 in decimal)

Hex Division

Process:

Similar to long division

Divide step by step

Work in base 16

Example:

20₁₆ ÷ 4 = 8

(32 ÷ 4 = 8 in decimal)

Real-World Applications of Hexadecimal

🎨

Web Design Colors

Hex color codes (#RRGGBB) are the standard for web design. Each pair represents red, green, and blue values from 00 to FF, creating 16.7 million possible colors.

💾

Memory Addresses

Computer memory addresses are displayed in hex format. Programmers use hex to reference specific memory locations when debugging or working with low-level code.

🌐

MAC Addresses

Network device MAC addresses use hex format (e.g., 00:1A:2B:3C:4D:5E). Each pair represents one byte of the 6-byte hardware identifier.

🔐

Cryptography

Cryptographic hashes (SHA-256, MD5) and encryption keys are represented in hex. This compact format makes it easier to display and verify long binary values.

📝

Character Encoding

Unicode code points are often written in hex (e.g., U+1F600 for 😀). This standard format helps identify characters across different systems and languages.

⚙️

Assembly Programming

Assembly language and machine code use hex to represent instructions and data. It's more readable than binary while maintaining direct hardware correspondence.

Related Math Calculators

💻

Binary Calculator

Convert binary numbers

🔬

Scientific Calculator

Advanced math operations

Percentage Calculator

Calculate percentages easily

➗

Fraction Calculator

Add, subtract fractions

Frequently Asked Questions (FAQs)

Learn More About Hexadecimal

Educational Resources

📚
Khan Academy - Computer Science
Free courses on hexadecimal and number systems
📖
Math is Fun - Hexadecimal
Interactive tutorials on hex numbers
🎓
Coursera - Digital Systems
University-level courses on number systems

Technical References

🔧
MDN - Hex Color Values
Web development hex color documentation
💡
GeeksforGeeks - Hexadecimal System
Comprehensive programming tutorials on hex
📝
Wikipedia - Hexadecimal
Detailed encyclopedia article on hexadecimal

About This Calculator

✓Accuracy & Reliability

Our hexadecimal calculator uses industry-standard algorithms for number system conversions and arithmetic operations. All calculations are verified against established mathematical principles and tested extensively to ensure 100% accuracy. The step-by-step solutions are designed to help users understand the conversion process while maintaining computational precision.

📚Educational Foundation

The content on this page is developed based on computer science fundamentals and mathematical principles taught in universities worldwide. Our explanations reference authoritative sources including academic institutions, technical documentation from Mozilla Developer Network (MDN), and established educational platforms like Khan Academy to ensure accuracy and educational value.

🔄Regular Updates & Maintenance

This calculator is regularly reviewed and updated by our editorial team to ensure it remains accurate, functional, and aligned with current web standards. We continuously improve the user interface, add new features based on user feedback, and update educational content to reflect best practices in programming and computer science education.

🎯Purpose & Use Cases

This tool is designed for students learning number systems, programmers working with low-level code, web developers dealing with color codes, and anyone needing quick and accurate hexadecimal conversions. It serves both educational purposes (with detailed explanations) and practical applications (with fast, reliable calculations). The calculator is used by thousands of users monthly for academic, professional, and personal projects.

Why Our Hex Calculator is Better

✓

Multiple Number Systems

Convert between Hexadecimal, Binary, Decimal, and Octal - all in one place. Most calculators only support 2-3 systems.

✓

Step-by-Step Solutions

See exactly how conversions and calculations are performed. Perfect for learning and verification - not just final answers.

✓

Arithmetic Operations

Perform addition, subtraction, multiplication, and division in any number system - not just conversions like other calculators.

✓

Educational Content

Comprehensive guides, real-world examples, and 12 detailed FAQs to help you understand hexadecimal concepts thoroughly.

✓

Quick Reference Tables

Built-in hex-to-decimal-to-binary conversion tables and common hex values for instant reference while working.

✓

Fully Responsive Design

Works perfectly on all devices - desktop, tablet, and mobile. Calculate hex values on the go with touch-optimized interface!

✓

Clean Interface

No annoying ads, popups, or distractions. Just a clean, professional interface focused on your calculations.

✓

100% Free Forever

No premium features, no subscriptions, no hidden costs. Everything is completely free with unlimited calculations.

🔢 Hex Calculator - Convert Hexadecimal, Binary, Decimal & Octal

Free online hexadecimal calculator to convert between hex, binary, decimal, and octal. Perform hex arithmetic operations with step-by-step solutions.

Last Updated: February 13, 2026•Reviewed by: CalcFinex Editorial Team

Hexadecimal Calculator

First Number

Operation

Convert To

Number Systems

Hexadecimal (Base 16)

Uses: 0-9, A-F

Example: 1A = 26₁₀

Binary (Base 2)

Uses: 0, 1

Example: 11010 = 26₁₀

Decimal (Base 10)

Uses: 0-9

Example: 26 = 26₁₀

Octal (Base 8)

Uses: 0-7

Example: 32 = 26₁₀

Hex Reference

Hex	Dec	Bin
0	0	0000
1	1	0001
2	2	0010
3	3	0011
4	4	0100
5	5	0101
6	6	0110
7	7	0111
8	8	1000
9	9	1001
A	10	1010
B	11	1011
C	12	1100
D	13	1101
E	14	1110
F	15	1111

Common Hex Values

FF:255 (max byte)

100:256

3FF:1023

FFF:4095

How to Use the Hex Calculator

For Conversion:

1Enter your number in the first input field
2Select the input number system (Hex, Binary, Decimal, or Octal)
3Select "Convert" operation (arrow icon)
4Choose the output number system
5Click "Calculate" to see the result with steps

For Arithmetic Operations:

1Enter the first number and select its number system
2Choose the operation (+, -, ×, ÷)
3Enter the second number (same base as first)
4Select the output number system for the result
5Click "Calculate" to see the result with detailed steps

Understanding Hexadecimal Numbers

What is Hexadecimal?

Why Use Hexadecimal?

Hexadecimal is preferred in computing for several important reasons:

Compact representation: 2 hex digits can represent a full byte (8 bits) instead of 8 binary digits
Easy conversion: Each hex digit maps directly to 4 binary digits
Human-readable: Easier to read and remember than long binary strings
Memory addresses: Computer memory addresses are typically displayed in hex
Color codes: Web colors use hex format (#RRGGBB)
Debugging: Machine code and memory dumps are shown in hex

Hex Place Values

In hexadecimal, each digit position represents a power of 16, starting from 16⁰ on the right. Here's how the hex number 2A3 breaks down:

16²
256

16¹
16

16⁰
1

= (2×256) + (10×16) + (3×1) = 512 + 160 + 3 = 675 in decimal

Hex Digit Values

Numeric Digits (0-9)

Same as decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Letter Digits (A-F)

A=10, B=11, C=12, D=13, E=14, F=15

Hexadecimal Conversions

Hex to Decimal

Multiply each digit by 16 raised to its position and sum the results.

Example: 1A3₁₆ to decimal

= (1 × 16²) + (A × 16¹) + (3 × 16⁰)

= (1 × 256) + (10 × 16) + (3 × 1)

= 256 + 160 + 3

= 419₁₀

Decimal to Hex

Repeatedly divide by 16 and record remainders, then read backwards.

Example: 419₁₀ to hex

419 ÷ 16 = 26 remainder 3

26 ÷ 16 = 1 remainder 10 (A)

1 ÷ 16 = 0 remainder 1

Reading backwards: 1A3₁₆

Hex to Binary

Convert each hex digit to 4 binary digits.

Example: 2F₁₆ to binary

2₁₆ = 0010₂

F₁₆ = 1111₂

= 00101111₂

Binary to Hex

Group binary digits in sets of 4 (from right), convert each group to hex.

Example: 11010110₂ to hex

Group: 1101 0110

1101₂ = D₁₆

0110₂ = 6₁₆

= D6₁₆

Hexadecimal Arithmetic Operations

Hex Addition

Rules:

Add like decimal, carry at 16

A + 7 = 17₁₀ = 11₁₆ (carry 1)

F + 1 = 16₁₀ = 10₁₆ (carry 1)

Example:

+ 2F

A+F=25₁₀=19₁₆, 1+2+1=4

Hex Subtraction

Rules:

Subtract like decimal

Borrow 16 when needed

10₁₆ - 1 = F (borrowed 16)

Example:

- 1A

F-A=5, 2-1=1

Hex Multiplication

Process:

Multiply each digit

Carry when product ≥ 16

2 × 8 = 16₁₀ = 10₁₆

Example:

A × 3 = 30₁₀ = 1E₁₆

(10 × 3 = 30 in decimal)

Hex Division

Process:

Similar to long division

Divide step by step

Work in base 16

Example:

20₁₆ ÷ 4 = 8

(32 ÷ 4 = 8 in decimal)

Real-World Applications of Hexadecimal

🎨

Web Design Colors

Hex color codes (#RRGGBB) are the standard for web design. Each pair represents red, green, and blue values from 00 to FF, creating 16.7 million possible colors.

💾

Memory Addresses

Computer memory addresses are displayed in hex format. Programmers use hex to reference specific memory locations when debugging or working with low-level code.

🌐

MAC Addresses

Network device MAC addresses use hex format (e.g., 00:1A:2B:3C:4D:5E). Each pair represents one byte of the 6-byte hardware identifier.

🔐

Cryptography

Cryptographic hashes (SHA-256, MD5) and encryption keys are represented in hex. This compact format makes it easier to display and verify long binary values.

📝

Character Encoding

Unicode code points are often written in hex (e.g., U+1F600 for 😀). This standard format helps identify characters across different systems and languages.

⚙️

Assembly Programming

Assembly language and machine code use hex to represent instructions and data. It's more readable than binary while maintaining direct hardware correspondence.

Related Math Calculators

💻

Binary Calculator

Convert binary numbers

🔬

Scientific Calculator

Advanced math operations

Percentage Calculator

Calculate percentages easily

➗

Fraction Calculator

Add, subtract fractions

Frequently Asked Questions (FAQs)

Learn More About Hexadecimal

Educational Resources

📚
Khan Academy - Computer Science
Free courses on hexadecimal and number systems
📖
Math is Fun - Hexadecimal
Interactive tutorials on hex numbers
🎓
Coursera - Digital Systems
University-level courses on number systems

Technical References

🔧
MDN - Hex Color Values
Web development hex color documentation
💡
GeeksforGeeks - Hexadecimal System
Comprehensive programming tutorials on hex
📝
Wikipedia - Hexadecimal
Detailed encyclopedia article on hexadecimal

About This Calculator

✓Accuracy & Reliability

📚Educational Foundation

🔄Regular Updates & Maintenance

🎯Purpose & Use Cases

Why Our Hex Calculator is Better

✓

Multiple Number Systems

Convert between Hexadecimal, Binary, Decimal, and Octal - all in one place. Most calculators only support 2-3 systems.

✓

Step-by-Step Solutions

See exactly how conversions and calculations are performed. Perfect for learning and verification - not just final answers.

✓

Arithmetic Operations

Perform addition, subtraction, multiplication, and division in any number system - not just conversions like other calculators.

✓

Educational Content

Comprehensive guides, real-world examples, and 12 detailed FAQs to help you understand hexadecimal concepts thoroughly.

✓

Quick Reference Tables

Built-in hex-to-decimal-to-binary conversion tables and common hex values for instant reference while working.

✓

Fully Responsive Design

Works perfectly on all devices - desktop, tablet, and mobile. Calculate hex values on the go with touch-optimized interface!

✓

Clean Interface

No annoying ads, popups, or distractions. Just a clean, professional interface focused on your calculations.

✓

100% Free Forever

No premium features, no subscriptions, no hidden costs. Everything is completely free with unlimited calculations.