Tutorial
How to Convert Hex to Decimal by Hand
The method, the shortcut, and enough practice to stop needing either.
The converters on this site will always be faster. The point of working through it manually is that afterwards you can read a hex value without a tool at all — which is what you need when you are looking at a stack trace or a datasheet rather than a browser tab.
The method
- Write the hex number out and number the positions from the right, starting at zero.
- Work out each position's place value: 160 is 1, 161 is 16, 162 is 256, 163 is 4096.
- Convert any letter digit to its number: A is 10 through to F is 15.
- Multiply each digit by its place value.
- Add the results.
You need these two tables
| Hex | Decimal | Binary | Octal |
|---|---|---|---|
| 0 | 0 | 0000 | 0 |
| 1 | 1 | 0001 | 1 |
| 2 | 2 | 0010 | 2 |
| 3 | 3 | 0011 | 3 |
| 4 | 4 | 0100 | 4 |
| 5 | 5 | 0101 | 5 |
| 6 | 6 | 0110 | 6 |
| 7 | 7 | 0111 | 7 |
| 8 | 8 | 1000 | 10 |
| 9 | 9 | 1001 | 11 |
| A | 10 | 1010 | 12 |
| B | 11 | 1011 | 13 |
| C | 12 | 1100 | 14 |
| D | 13 | 1101 | 15 |
| E | 14 | 1110 | 16 |
| F | 15 | 1111 | 17 |
| Power | Hex | Decimal |
|---|---|---|
| 160 | 1 | 1 |
| 161 | 10 | 16 |
| 162 | 100 | 256 |
| 163 | 1000 | 4,096 |
| 164 | 10000 | 65,536 |
| 165 | 100000 | 1,048,576 |
| 166 | 1000000 | 16,777,216 |
| 167 | 10000000 | 268,435,456 |
| 168 | 100000000 | 4,294,967,296 |
Worked example: 2F
2F
position 1: 2 × 16 = 32
position 0: F × 1 = 15 (F is 15)
----
47
Worked example: 1A2B
1A2B
position 3: 1 × 4096 = 4096
position 2: A × 256 = 2560 (A is 10)
position 1: 2 × 16 = 32
position 0: B × 1 = 11 (B is 11)
------
6699
The two-digit shortcut
Any single byte — two hex digits — can be done in your head. Multiply the first digit by 16 and add the second. No table of powers needed.
C8 → 12 × 16 + 8 = 192 + 8 = 200 7F → 7 × 16 + 15 = 112 + 15 = 127 A0 → 10 × 16 + 0 = 160 + 0 = 160 3C → 3 × 16 + 12 = 48 + 12 = 60
With the sixteen digit values memorised, this becomes fast enough to do while reading a dump, which is where most of the value is.
An alternative: Horner's method
For longer numbers, this avoids large place values entirely. Start at the left, and for each new digit multiply your running total by 16 and add the digit.
1A2B, left to right start 0 digit 1: 0 × 16 + 1 = 1 digit A: 1 × 16 + 10 = 26 digit 2: 26 × 16 + 2 = 418 digit B: 418 × 16 + 11 = 6699
Same answer, smaller numbers at each step, and no need to know which power of sixteen you are on. This is also how a computer does it.
Practice problems
Work these out before checking. The answers follow.
- 1F
- A0
- FF
- 100
- 2AB
- DEAD
1. 1F → 1 × 16 + 15 = 31 2. A0 → 10 × 16 + 0 = 160 3. FF → 15 × 16 + 15 = 255 4. 100 → 1 × 256 + 0 + 0 = 256 5. 2AB → 2 × 256 + 10 × 16 + 11 = 683 6. DEAD → 13 × 4096 + 14 × 256 + 10 × 16 + 13 = 57005
Common mistakes
- Counting positions from the left. Position zero is always the rightmost digit.
- Forgetting a letter's value mid-calculation. Convert every letter to a number before you start multiplying.
- Using 10 instead of 16 as the multiplier. Easy to slip into, and the answer will look almost right.
- Dropping a zero digit. A
0still occupies a position and still shifts everything to its left.
Check your work
The hex to decimal converter gives the answer instantly and shows the nibble breakdown. Use it to check, not to skip — the practice is the point.
Frequently asked questions
How do I convert hex to decimal manually?
Multiply each digit by 16 raised to its position number, counting from zero at the right, then add the products together.
What is the fastest way to convert a two-digit hex value?
Multiply the first digit by 16 and add the second. C8 is 12 times 16 plus 8, which is 200.
What is Horner's method?
Working left to right, multiplying the running total by 16 and adding each digit. It avoids large place values and is how computers do it.
Do I need to memorise the powers of 16?
Only the first four: 1, 16, 256 and 4096. Beyond that, Horner's method avoids them entirely.
What is DEAD in decimal?
57,005. It is a valid hex number that happens to spell a word, which is why it appears as a memory marker.
Where do people usually go wrong?
Counting positions from the left instead of the right, and multiplying by 10 out of habit instead of 16.