Hexadecimal to Decimal Converter
Enter the hexadecimal number you want to convert to decimal.
Table of Contents
- How does hexadecimal to decimal conversion work?
- Hexadecimal to decimal conversion formula
- Conversion process
- Examples
- Hexadecimal to decimal conversion table
- Frequently Asked Questions
How does hexadecimal to decimal conversion work?
The hexadecimal system is base 16 and the decimal system is base 10. To convert a hexadecimal number to decimal, multiply each hexadecimal digit by the corresponding power of 16 (starting from the right with 160) and add the results. The digits A, B, C, D, E, and F represent the values 10 to 15 in decimal.
Hexadecimal to decimal conversion formula
For a hexadecimal number with n digits:
N = h0·160 + h1·161 + h2·162 + … + hn·16n
Where hi is each hexadecimal digit (0–9 or A–F) in position i, and each one is multiplied by 16i. The sum of all the products gives the equivalent decimal value.
Conversion process
- Write the hexadecimal number and assign powers of 16 to each digit (160 on the right).
- Convert the letters A–F to their numeric values (A=10, B=11, C=12, D=13, E=14, F=15).
- Multiply each digit by its corresponding power of 16.
- Add all the results to get the final decimal value.
Examples
1A₁₆ to decimal| Hex digit | Decimal value | Power of 16 | Product |
|---|---|---|---|
| A | 10 | 160 = 1 | 10 × 1 = 10 |
| 1 | 1 | 161 = 16 | 1 × 16 = 16 |
Total sum: 16 + 10 = 26.
Result: 1A₁₆ = 26₁₀.
2F₁₆ to decimal| Hex digit | Decimal value | Power of 16 | Product |
|---|---|---|---|
| F | 15 | 160 = 1 | 15 × 1 = 15 |
| 2 | 2 | 161 = 16 | 2 × 16 = 32 |
Total sum: 32 + 15 = 47.
Result: 2F₁₆ = 47₁₀.
Hexadecimal to decimal conversion table
Quick reference values for short hexadecimal numbers.
| Hexadecimal | Decimal |
|---|---|
0 | 0 |
1 | 1 |
2 | 2 |
3 | 3 |
4 | 4 |
5 | 5 |
6 | 6 |
7 | 7 |
8 | 8 |
9 | 9 |
A | 10 |
B | 11 |
C | 12 |
D | 13 |
E | 14 |
F | 15 |
10 | 16 |
1F | 31 |
FF | 255 |
100 | 256 |
Frequently Asked Questions
How do you convert a hexadecimal number to decimal?
To convert a hexadecimal number to decimal, multiply each digit by a power of 16 according to its position (starting from the right with 16⁰) and add the results. The letters A–F represent the values 10–15.
What value does the letter F have in the decimal system?
In the decimal system, the letter F equals 15.