Number systems
How to Convert Hexadecimal to Decimal
Convert hexadecimal to decimal by hand with place values and worked examples, understand 0x notation and verify the answer with a free converter.
Hexadecimal uses sixteen symbols: 0–9 and A–F. Each position is a power of 16, so 2F means 2 × 16 + 15, which equals 47.
The key idea
For 1A3, calculate 1 × 16² + 10 × 16 + 3 = 419. Writing the powers below the digits prevents a skipped position in longer values.
Hexadecimal place values
Hexadecimal is base 16. Its digits represent values zero through fifteen: A=10, B=11, C=12, D=13, E=14 and F=15. Moving one place left multiplies the place value by 16.
| Position | Power | Decimal value |
|---|---|---|
| Rightmost | 160 | 1 |
| Second | 161 | 16 |
| Third | 162 | 256 |
| Fourth | 163 | 4,096 |
Worked hex-to-decimal conversions
For 2F, calculate 2 × 16 + 15 = 47. For 1A3, calculate 1 × 256 + 10 × 16 + 3 = 419. For 0x1F to decimal, ignore the programming prefix: 1 × 16 + 15 = 31.
You can check 419 in reverse by repeated division. Dividing by 16 gives remainder 3; dividing quotient 26 by 16 gives remainder 10, written A; the final quotient is 1. Read upward to get 1A3.
Where hexadecimal appears
One hex digit represents four binary bits and two digits cover a byte from 00 to FF. Web colors use pairs for red, green and blue: #FF8000 has decimal channel values 255, 128 and 0. Memory addresses and byte dumps often use a 0x prefix.
Common errors
- Treating A through F as invalid.
- Using powers of 10 instead of 16.
- Starting the rightmost power at 1 instead of 0.
- Including
0xas digits. - Dropping meaningful leading zeros.
Verify values with the hex to decimal converter. For other radices use the base converter, then connect results to bits with the decimal to binary converter.
A practical workflow
The hexadecimal converter accepts common 0x notation and displays the decimal answer. Keep leading zeros when a value represents a fixed-width address, color channel or data field.
Checks and limitations
Hex appears in programming, byte values and web colors. Use the base converter for another radix and decimal-to-binary when you need to connect the result to bit patterns.
Check the result in the working tool
Open the Hex to decimal converter with the same values used in the example. Read the labels and units beside the result, then keep the source information until the output has been checked for its intended use.
Quick answers
Frequently asked questions
What is 0x1F in decimal?
0x1F is 31: 1 × 16 plus 15.
Does letter case matter in hexadecimal?
No. ff and FF both represent decimal 255. Uppercase is often used simply to make hexadecimal values easier to recognize.
What is FF in decimal?
FF is 15 × 16 + 15, which equals 255. It is the largest unsigned value that fits in one byte.
Why do programmers prefix hexadecimal values with 0x?
The prefix tells readers and software that the following digits use base 16. It is notation rather than part of the numeric value being converted.
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