Column by column
Hex Multiplication Calculator
Multiply two hexadecimal values, with column working, the shift shortcuts for powers of two, and exact results at any size.
—
—
—
—
How hex multiplication works
Long multiplication, unchanged, with one adjustment: when a column product reaches sixteen or more, divide by sixteen and carry the quotient.
- Multiply the rightmost digit of the top number by the multiplier.
- If the product is 16 or more, divide by 16. Write the remainder, carry the quotient.
- Move left one digit, multiply, then add any carry from the previous column.
- Continue until every digit is done, then write out any final carry.
Worked example
1F × 3
ones: F × 3 = 15 × 3 = 45
45 ÷ 16 = 2 remainder 13
→ write D, carry 2
16s: 1 × 3 = 3, plus carry 2 = 5
→ write 5
result → 5D (31 × 3 = 93 in decimal)
The shifts worth knowing by heart
Multiplying by a power of sixteen is not arithmetic at all — it is appending zeros, exactly as multiplying by a power of ten is in decimal.
| Multiply by | Decimal value | Do this |
|---|---|---|
| 10 | 16 | Append one 0 |
| 100 | 256 | Append two 0s |
| 1000 | 4,096 | Append three 0s |
| 10000 | 65,536 | Append four 0s |
2F × 10 = 2F0 (47 × 16 = 752) 2F × 100 = 2F00 (47 × 256 = 12,032) FF × 100 = FF00 (255 × 256 = 65,280)
Appending a zero in hex shifts the value left by four bits. That is why hex is the natural notation for bit manipulation: whole-nibble shifts are visible as digits moving, with no arithmetic at all.
Doubling
Multiplying by 2 shifts left one bit, which does not align with digit boundaries — so it does need real arithmetic. It is worth practising because doubling appears constantly in address calculations.
| Value | Doubled | Decimal |
|---|---|---|
| 01 | 02 | 1 → 2 |
| 08 | 10 | 8 → 16 |
| 0F | 1E | 15 → 30 |
| 40 | 80 | 64 → 128 |
| 80 | 100 | 128 → 256 |
| FF | 1FE | 255 → 510 |
Exact results at any size
Multiplication grows numbers quickly, and that is where floating-point calculators quietly break. Two sixteen-digit hex values multiply to something needing up to thirty-two digits, far past the point where doubles stay exact.
This calculator uses arbitrary-precision integers, so the product of two 64-bit values is correct to the last digit. Nothing is rounded and nothing overflows.
Frequently asked questions
How do I multiply hexadecimal numbers?
Use long multiplication as in decimal, but carry whenever a column product reaches sixteen. Divide the product by 16, write the remainder and carry the quotient.
What is 1F times 3 in hex?
5D. In decimal that is 31 times 3, which is 93.
What is the shortcut for multiplying by 10 in hex?
Append a zero. Hex 10 is sixteen, so this shifts the value left by four bits, exactly as multiplying by ten appends a zero in decimal.
Why does appending a zero multiply by 16?
Because 16 is the base. Every digit moves one place left, and each place is worth sixteen times the one to its right.
Can it multiply very large hex numbers?
Yes. Arbitrary-precision arithmetic means two 64-bit values multiply exactly, with no rounding at any size.
How do I double a hex number?
Multiply by 2 normally. It shifts left one bit, which does not line up with digit boundaries, so the arithmetic has to be done properly.