Hex Multiplication Calculator
Multiply two hexadecimal numbers instantly with a full partial-product breakdown, plus decimal, binary, and octal results.
How to Multiply Hexadecimal Numbers
Hex multiplication follows the same long-multiplication method taught for decimal: multiply the first number by each digit of the second number to get a row of partial products, shift each row left by one hex place for every digit position, then add the rows together.
The arithmetic inside each step still happens in base 16 — every digit-by-digit product and every carry uses the same 16-based rules covered on the addition page, just applied to bigger intermediate numbers.
Where Hex Multiplication Actually Shows Up
Computing Memory Offsets
Array indexing comes down to element size times index — when both are already in hex (a common case in low-level and embedded code), you're multiplying in hex to find the byte offset.
offset = 10 (element size) × 5 (index) = 50
Scaling Color and Pixel Values
Graphics code that scales a color channel or alpha value by a hex factor — brightening, dimming, blending — is doing hex multiplication under the hood before the result gets clamped back to a byte.
80 × 2 = 100 (clamped to FF)
Checksum and Hash Math
Simple checksum and hashing algorithms often multiply a running hex value by a small constant each step — understanding the multiplication by hand makes it easier to spot when a hand-computed check disagrees with code.
hash = (hash × 21) + byte
Hex Multiplication Example, Step by Step
2F × 1A = 4C6
2F × 1A = 4C6
2 F
× 1 A
-------
1 D 6 (2F × A)
2 F 0 (2F × 1, shifted left)
-------
4 C 6| Step | Description | Result |
|---|---|---|
| First partial product | 2F × A(10) = 470 decimal | 1D6 |
| Second partial product | 2F × 1, shifted one hex place left = 752 decimal | 2F0 |
| Add the partial products | 1D6 + 2F0 = 470 + 752 = 1222 decimal | 4C6 |
Each partial product is found the same way a single-digit multiplication is — convert both values to decimal, multiply, convert back — then the rows combine with ordinary hex addition.
Single-Digit Hex Multiplication Reference
Unlike addition, most single-digit products already need two hex digits — worth knowing before you start chaining partial products by hand.
| Digits | Product | Two digits? |
|---|---|---|
| 3 × 5 | F | No — the largest product that stays a single digit |
| 4 × 4 | 10 | Yes — smallest product needing two digits |
| 8 × 2 | 10 | Yes |
| F × F | E1 | Yes — the largest possible product of two digits |
Common Mistakes When Multiplying Hex Numbers
- Forgetting to shift each partial product left by one hex place per digit position.
- Computing a carry in decimal and writing it down without converting it to hex first.
- Assuming a single-digit product stays a single digit — most products of two digits above 3 or 4 already carry into a second digit.
- Adding the partial products in decimal instead of hex, which produces the wrong result.
Why Use This Calculator Instead of Doing It by Hand
- Shows every partial product and shift, so you can check your own long multiplication
- Runs entirely in your browser — nothing you type gets sent anywhere
- Gives decimal, binary, and octal for the result at once
- Handles multi-digit values without you tracking each shift manually
Frequently Asked Questions
How do you multiply two hexadecimal numbers?
The same way you'd do long multiplication in decimal: multiply the first number by each digit of the second number separately, shift each of those partial products one place left per digit position, then add the partial products together in hex.
What is a partial product in hex multiplication?
It's the result of multiplying the full first number by a single digit of the second number. Long multiplication produces one partial product per digit in the second number, then sums them, shifted to line up with the digit's place value.
How do carries work in hex multiplication compared to addition?
The same carry rule applies — any column total of 16 or more carries into the next column — but multiplication columns can run higher before converting, since a single-digit product can already reach E1 (225 in decimal), compared to addition's max of 1E.
What's the largest value a single hex digit multiplication can produce?
F × F = E1 (225 in decimal) — always two hex digits, since anything above F needs a second digit. That's the number to keep in mind when summing partial products.
Can I multiply more than two hex numbers at once?
This calculator multiplies two values at a time. For three or more, multiply the first two, then multiply that result by the next number, the same way you'd chain decimal multiplication.
Do I need a multiplication table to do hex multiplication by hand?
It helps while you're learning, the same way a decimal times table does — but it's not required. Any single-digit product can be found by converting both digits to decimal, multiplying, and converting the result back to hex.
Is there a shortcut for multiplying by 10 in hex?
Yes — multiplying any hex value by 10 (16 decimal) just shifts every digit one place left and appends a trailing 0, the same trick as multiplying by 10 in decimal. 2F × 10 = 2F0.
Why does F × F only need two digits, not three?
Because the largest possible single-digit product is capped at 15 × 15 = 225 decimal, which is E1 in hex — two digits is the ceiling no matter which two single digits you multiply.