Hex Addition Calculator
Add two hexadecimal numbers instantly and see the full carry-by-carry breakdown, plus decimal, binary, and octal results for every calculation.
How to Add Hexadecimal Numbers
Hex addition works exactly like decimal addition, column by column from the right — the only thing that changes is where a column carries. In decimal, a column carries once it reaches 10. In hex, a column carries once it reaches 16, since hex is base 16.
That means A through F behave as ordinary digits worth 10 through 15 — B + 4 is just 11 + 4 = 15, which is F, no carry needed. A column only carries once the sum of its digits (plus anything carried in) reaches 16 or higher.
Hex Addition Example, Step by Step
4B7 + 2E9 = 7A0
4B7 + 2E9 = 7A0
1 1
4 B 7
+ 2 E 9
-------
7 A 0| Step | Description | Result |
|---|---|---|
| Ones place (16^0) | 7 + 9 = 16 decimal = 0x10 | write 0, carry 1 |
| 16s place (16^1) | B(11) + E(14) + carry 1 = 26 decimal = 0x1A | write A, carry 1 |
| 256s place (16^2) | 4 + 2 + carry 1 = 7 decimal = 0x7 | write 7, no carry |
A column can never carry more than 1, even in the worst case: the largest possible column total is F + F plus a carried-in 1 — 15 + 15 + 1 = 31 decimal, which is still less than 32 (two carries' worth).
Single-Digit Hex Addition Reference
The boundary to watch for: any two single hex digits sum to at most 1E (F + F). Here's where that boundary sits.
| Digits | Sum | Carries? |
|---|---|---|
| 7 + 8 | F | No — largest sum that stays a single digit |
| 8 + 8 | 10 | Yes — smallest sum that carries |
| A + A | 14 | Yes |
| C + D | 19 | Yes |
| F + F | 1E | Yes — largest possible sum of two digits |
Common Mistakes When Adding Hex Numbers
- Carrying at 10 out of habit instead of 16 — the single most common slip.
- Misremembering a letter's value — B is 11, not 12; mixing this up throws off every column after it.
- Treating hex digits as text characters instead of numeric values when adding by hand.
- Dropping the 0x prefix when copying a result into code, so it gets read as decimal.
Frequently Asked Questions
How do you add two hexadecimal numbers?
Line the numbers up by place value and add column by column from the right, just like decimal addition. The only difference is the carry threshold: any column that totals 16 or more carries exactly 1 into the next column.
What happens when a hex addition carries?
The column's total gets converted to hex, the last digit of that value is written in place, and a 1 moves to the next column — the same mechanic as decimal addition carrying at 10, just at 16 instead.
Can I add more than two hex numbers at once?
This calculator adds two values at a time. To add three or more, add the first two, then add that result to the next number, and repeat — the same way you'd chain decimal addition by hand.
Is hex addition the same as binary addition?
They follow the same logic — carry once a column's total reaches the base — but hex carries at 16 instead of 2. Since one hex digit represents exactly 4 binary bits, hex addition is a faster shorthand for the same underlying binary math.
Do I need to convert to decimal to add hex numbers?
No — you can add directly in hex once you know each letter's value (A=10 through F=15). Converting to decimal first is often easier while you're still learning, until the digit sums become familiar.
In a carry column, why does B + E (plus a carry) equal 1A?
B is 11 and E is 14. With a 1 carried in from the previous column, that's 11 + 14 + 1 = 26 in decimal, and 26 in hex is 1A — so you'd write A in that column and carry the 1 onward.