How to Convert Hex to Decimal
A step-by-step guide to converting hexadecimal to decimal by hand, with worked examples from single digits to multi-digit values.
The Place-Value Method
Every hex digit is worth a power of 16 based on its position, counting from 0 on the right — the same logic decimal uses with powers of 10, just with a different base. To convert a hex value to decimal: multiply each digit by its place value, then add the results together.
The rightmost digit is worth 16⁰ (which is 1), the next is worth 16¹ (16), the next 16² (256), and so on. Remember that the letter digits A-F stand for the decimal values 10-15 before you multiply.
Worked Example: Single-Digit Hex
Hex F = Decimal 15
F = 15
F × 16⁰ = F × 1 = 15
| Step | Description | Result |
|---|---|---|
| Identify F's decimal value | F stands for 15 | 15 |
| Multiply by the place value | 15 × 16⁰ = 15 × 1 | 15 |
A single hex digit converts directly to its decimal value — no multiplication needed beyond ×1, since 16⁰ is always 1.
Worked Example: Multi-Digit Hex
Hex 1F = Decimal 31
1F = (1 × 16¹) + (F × 16⁰) = 31
1 F 16¹ 16⁰ (1 × 16) + (15 × 1) = 16 + 15 = 31
| Step | Description | Result |
|---|---|---|
| Assign place values | 1 is in the 16¹ position, F is in the 16⁰ position | 16 and 1 |
| Multiply each digit by its place value | 1 × 16 = 16, and F(15) × 1 = 15 | 16 and 15 |
| Add the results | 16 + 15 | 31 |
This same process extends to any number of digits — a 3-digit hex value adds a 16² (256) term, a 4-digit value adds 16³ (4,096), and so on.
| Hex | Calculation | Decimal |
|---|---|---|
| 2F | (2 × 16) + (15 × 1) | 47 |
| A0 | (10 × 16) + (0 × 1) | 160 |
| FF | (15 × 16) + (15 × 1) | 255 |
| 100 | (1 × 256) + (0 × 16) + (0 × 1) | 256 |
A Faster Mental Shortcut for Bytes
For any 2-digit hex value (a single byte), you can skip writing out the place-value table: take the first digit, multiply by 16, and add the second digit's value directly. 3B becomes 3 × 16 = 48, plus B (11), giving 59 — one multiplication and one addition, done in your head once it's familiar.
Common Mistakes to Avoid
- Multiplying by powers of 10 out of habit instead of powers of 16.
- Misremembering a letter's value — B is 11, not 12; this throws off every digit after it.
- Forgetting a place value entirely on a 3+ digit conversion, especially the 16² (256) term.
- Mixing up which digit goes with which power — the rightmost digit is always 16⁰, not the leftmost.
Further reading: Radix (number base) — Wikipedia
Frequently Asked Questions
What's the fastest way to convert hex to decimal without a calculator?
For a single byte (2 hex digits), multiply the first digit by 16 and add the second digit's value directly — that's the entire calculation, since 16¹ = 16 and 16⁰ = 1.
Do I need to know binary to convert hex to decimal?
No — the place-value method works directly from hex to decimal without going through binary at all. Binary is only needed if you're specifically converting hex to binary instead.
How do I handle a hex value with a letter digit like A-F?
Substitute its decimal value first (A=10, B=11, C=12, D=13, E=14, F=15), then run the same place-value calculation — the letters aren't special, they're just single digits worth more than 9.
Is there a limit to how large a hex value I can convert this way?
No — the same method extends to any number of digits, just with more place values (16², 16³, and so on) to multiply and add. It gets tedious by hand past 3-4 digits, which is where a calculator becomes worth using.