How to Calculate Hexadecimal Numbers: A Simple Guide

Hex numbers may look tricky at first glance, but they’re actually pretty straightforward once you understand the system behind them.

In this article, we’ll break down what hexadecimal numbers are, how to convert them to and from decimal, and how to perform simple calculations using hex.

We also provide a calculator to simplify things.

🙋‍♀️ What Is a Hexadecimal Number?

The hexadecimal number system (also known as hex) is a base-16 system. This means it uses 16 unique symbols to represent values:

Hex digits: 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

So, for example:

• A in hex is equal to 10 in decimal
• F in hex is equal to 15 in decimal

Hexadecimal is commonly used in computing and digital electronics because it’s more compact than binary and aligns well with byte boundaries.

Try the Hexadecimal Converter and Calculator

with support for five operations:

• Convert Only
• Add
• Subtract
• Multiply
• Divide

To use it enter two Hex numbers and select an operation.

🧮 How to Convert Hexadecimal to Decimal

To convert a hexadecimal number to a decimal, follow this simple method:

Step-by-step example: Convert 2F to decimal

Each digit in a hex number represents a power of 16, starting from the right:

2F = (2 × 16^1) + (15 × 16^0)
   = (2 × 16) + (15 × 1)
   = 32 + 15
   = 47 (decimal)

So, 2F in hex is 47 in decimal.

🧮 How to Convert Decimal to Hexadecimal

To convert from decimal to hex, divide the number by 16 repeatedly and record the remainders:

Step-by-step example: Convert 47 to hex

1. 47 ÷ 16 = 2 remainder 15 → F
2. 2 ÷ 16 = 0 remainder 2 → 2

Now reverse the remainders: 2F

So, 47 in decimal is 2F in hex.

✏️ ➕ Hexadecimal Addition Example

Let's add 1A + 2F:

Step 1: Convert to decimal
1A = 26
2F = 47
Sum = 26 + 47 = 73

Step 2: Convert result back to hex
73 ÷ 16 = 4 remainder 9 → hex is 49

Answer: 1A + 2F = 49

✏️ ➖ Hexadecimal Subtraction Example

Let’s subtract 2F - 1A:

Step 1: Convert to decimal
2F = 47
1A = 26
Difference = 47 - 26 = 21

Step 2: Convert back to hex
21 ÷ 16 = 1 remainder 5 → hex is 15

Answer: 2F - 1A = 15

✨ Quick Tips for Working with Hex

• Use a calculator or spreadsheet when working with large hex values.
• Each hex digit maps to exactly 4 binary bits.
• Common in memory addresses, color codes (e.g., #FF5733), and assembly programming.

📌 Summary

Decimal	Hex
10	A
15	F
26	1A
47	2F
255	FF

Hexadecimal math is just like decimal—only with a different base. Once you're comfortable with the conversions, calculations like addition and subtraction become second nature.

🔁 Related Posts

• How to Calculate Binary Numbers