Hex Multiplication: How to Multiply Hexadecimal Numbers

Hex multiplication works like ordinary long multiplication, but hexadecimal is base 16. Digits A-F stand for decimal 10-15, and a column carries into the next one once its total reaches decimal 16 instead of decimal 10. That single difference — carrying at 16 instead of 10 — is the entire trick to multiplying hexadecimal numbers by hand.

This guide covers the hex digit values, a full hexadecimal multiplication table, the carrying rule that drives every hex multiplication, and several worked examples verified against decimal, from single digits to a multi-digit case with partial products.

What Is Hex Multiplication?

Hex multiplication is multiplication performed in base 16, where every number is written using sixteen digit symbols: 0 through 9, then A through F for the values a single 0-9 digit can't hold.

Hex digit	Decimal value
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
A	10
B	11
C	12
D	13
E	14
F	15

Each position in a hex number represents a power of 16 — 1, 16, 256, 4096, and so on — the same positional-notation idea decimal uses with powers of 10. Multiplication works one digit at a time, exactly like decimal long multiplication. The only change is what happens when a column's product runs high: it carries at 16 instead of at 10. For the full place-value breakdown behind this, see how to convert hex to decimal.

Hexadecimal Multiplication Table

Before working through the rules, it helps to have every single-digit product on hand. Here's the complete hexadecimal multiplication table — every combination of two hex digits from 0 to F, with the result written in hexadecimal rather than decimal. Find one digit in the left column and the other across the top; the cell where they meet is the hex product.

A few entries worth double-checking by hand: 2 × A = 14, A × A = 64, and F × F = E1 — all three match the table above.

How to Read the Hex Multiplication Table

Reading the table is a simple lookup, but it helps to walk through it once:

A × 3. Locate A in the left column and 3 across the top. Their intersection reads 1E. Checked in decimal: 10 × 3 = 30, and 30 decimal converts to 1E in hex (30 = 1 × 16 + 14, and 14 is E). So A × 3 = 1E₁₆.

5 × C. Locate 5 in the left column and C across the top. Their intersection reads 3C. Checked in decimal: 5 × 12 = 60, and 60 decimal is 3C in hex (60 = 3 × 16 + 12, and 12 is C). So 5 × C = 3C₁₆.

6 × 9. Locate 6 in the left column and 9 across the top. Their intersection reads 36. Checked in decimal: 6 × 9 = 54, and 54 decimal is 36 in hex (54 = 3 × 16 + 6). So 6 × 9 = 36₁₆.

Hexadecimal Multiplication Rules

The core hexadecimal multiplication rules:

1. Convert any A-F digits to their decimal values before multiplying.
2. Multiply digit by digit, the same way as decimal long multiplication.
3. If a column's product is less than decimal 16, write its hex digit directly with no carry.
4. If a column's product is 16 or greater, divide by 16: the remainder is the hex digit written, and the quotient is carried into the next column.
5. For multi-digit multiplication, multiply the top number by each digit of the bottom number separately, producing one partial product per digit.
6. Shift each partial product one place to the left for every place value of the digit it came from — exactly like shifting partial products left in decimal long multiplication.
7. Add all the partial products together in hexadecimal to get the final result.
8. Convert any digit from 10-15 back into A-F before writing it down.

That's the complete method — the same shape as decimal long multiplication, with a carry threshold of 16 instead of 10.

How Carrying Works in Hex Multiplication

This is the one idea worth understanding well, because it's where hex multiplication actually differs from decimal.

In decimal, a column carries once its product reaches 10. In hexadecimal, a column carries once its product reaches decimal 16, because each hex column is worth 16 times the one to its right.

Take 3 × A, a single-digit product from the table above. 3 × A (10) = 30 decimal. Since 30 is 16 or greater, it needs to carry:

30 decimal = 1 x 16 + 14
14 decimal = E hexadecimal

Write E in the current column, and carry 1 into the next column. That's why the table shows 3 × A = 1E₁₆ — the E is the remainder after dividing by 16, and the leading 1 is the carry that had nowhere else to go but a new column.

This is the same rollover idea as hex addition, just triggered by a product instead of a sum — see hex addition for the carrying rule applied to sums.

How to Multiply Hexadecimal Numbers Step by Step

For a number with more than one digit multiplied by a single hex digit, apply the carrying rule column by column, right to left:

1. Convert the multiplier and each digit of the top number to decimal.
2. Multiply the rightmost digit of the top number by the multiplier.
3. If the product is under 16, write its hex digit with no carry.
4. If the product is 16 or more, write (product mod 16) in hex and carry (product ÷ 16, rounded down) into the next column.
5. Move one digit left, multiply by the multiplier again, add any incoming carry, and repeat steps 3-4.
6. After the leftmost digit, if a carry remains, write it as a new leading digit.

3C₁₆ × 5₁₆

  3C
x  5
----
 12C

• Rightmost digit: C (12) × 5 = 60 decimal. 60 = 3 × 16 + 12, so write C, carry 3.
• Next digit: 3 × 5 = 15, plus the carried 3 = 18 decimal. 18 = 1 × 16 + 2, so write 2, carry 1.
• No digits remain, so the leftover carry becomes a new leading digit: 1.

Result: 12C₁₆.

Decimal check: 3C₁₆ = (3 × 16) + 12 = 60. 60 × 5 = 300. And 12C₁₆ = (1 × 256) + (2 × 16) + 12 = 256 + 32 + 12 = 300. Both totals agree: 3C₁₆ × 5₁₆ = 12C₁₆.

Single-Digit Hex Multiplication Examples

A few more single-digit products, verified against decimal and against the table above:

3 × A = 1E₁₆. Decimal check: 3 × 10 = 30, and 30 = (1 × 16) + 14, giving 1E.

5 × C = 3C₁₆. Decimal check: 5 × 12 = 60, and 60 = (3 × 16) + 12, giving 3C.

A × A = 64₁₆. Decimal check: 10 × 10 = 100, and 100 = (6 × 16) + 4, giving 64.

F × F = E1₁₆. Decimal check: 15 × 15 = 225, and 225 = (14 × 16) + 1, giving E1 — the largest possible single-digit hex product.

Multi-Digit Hex Multiplication Example

Multiplying two multi-digit hex numbers uses partial products, just like decimal long multiplication. Here's 1A₁₆ × 2F₁₆, which needs two partial products because the multiplier 2F has two digits:

   1A
 x  2F
 -----
  186   <- 1A x F
+ 340   <- 1A x 2, shifted one place left
 -----
  4C6

• Partial product 1 (1A × F): F (15) × A (10) = 150 decimal = 96 hex (write 6, carry 9). F (15) × 1 = 15, plus carry 9 = 24 decimal = 18 hex — since this is the leftmost digit, write the full 18. Reading it together: 186₁₆.
• Partial product 2 (1A × 2): 2 × A (10) = 20 decimal = 14 hex (write 4, carry 1). 2 × 1 = 2, plus carry 1 = 3. Reading it together: 34₁₆. Because this digit (2) sits in the 16s place of 2F, its partial product is shifted one place left before adding: 340₁₆.
• Adding the partial products: 186₁₆ + 340₁₆. Rightmost column: 6 + 0 = 6. Middle column: 8 + 4 = 12 decimal = C, no carry. Leftmost column: 1 + 3 = 4. Total: 4C6₁₆.

Decimal check: 1A₁₆ = (1 × 16) + 10 = 26. 2F₁₆ = (2 × 16) + 15 = 47. 26 × 47 = 1,222. And 4C6₁₆ = (4 × 256) + (12 × 16) + 6 = 1,024 + 192 + 6 = 1,222. Both totals agree: 1A₁₆ × 2F₁₆ = 4C6₁₆.

This is why the rule says to shift each partial product left by its digit's place value: the 2 in 2F is worth 2 × 16, not just 2, so its partial product has to be shifted before it can be added correctly.

Hexadecimal Multiplication Examples

A few more verified examples, from single digits to multi-digit:

Hex calculation	Decimal equivalent	Hex result
6 × 9	6 × 9 = 54	36₁₆
8 × 7	8 × 7 = 56	38₁₆
C × D	12 × 13 = 156	9C₁₆
3C × 5	60 × 5 = 300	12C₁₆
1A × 2F	26 × 47 = 1,222	4C6₁₆
2A × 1F	42 × 31 = 1,302	516₁₆

How to Check Hex Multiplication Using Decimal

The most reliable way to verify a hex multiplication is to redo it in decimal:

1. Convert the first hex operand to decimal.
2. Convert the second hex operand to decimal.
3. Multiply the two decimal values.
4. Convert the decimal product back to hexadecimal (or convert your hex result to decimal) and confirm both match.

Using the 1A × 2F example above:

1A16 = 26
2F16 = 47
26 x 47 = 1222
4C616 = 1222

Both sides equal 1,222, confirming 1A₁₆ × 2F₁₆ = 4C6₁₆. For longer numbers, the Hex to Decimal Converter and Decimal to Hex Converter make this check quick without doing the place-value math by hand.

Common Hex Multiplication Mistakes

• Carrying at 10 instead of 16. A habit carried over from decimal — a hex column carries once its product reaches decimal 16, not 10.
• Treating A-F as letters rather than numeric values. Multiplying hex digits without first converting A-F to their decimal values (10-15) produces a meaningless result.
• Forgetting to shift partial products. Each partial product needs to be shifted left according to the place value of the digit that produced it — skipping the shift misaligns every column that follows.
• Writing a decimal product directly into the answer. A column product like 150 has to be converted to its hex digit and carry (6, carry 9), never left as the number 150.
• Incorrectly adding hexadecimal partial products. Once partial products are shifted, they still need to be added using hex addition rules — carrying at 16, not 10 — not ordinary decimal addition.
• Mixing decimal and hexadecimal notation. Writing an intermediate decimal value in the same line as a hex answer makes the result ambiguous and easy to misread.
• Forgetting to convert 10-15 back to A-F. A column result of 12 needs to be written as C, not left as the number 12.

Hex Addition, Subtraction, and Multiplication

All three operations share the same base-16 place-value system; they just handle overflow differently:

	Hex Addition	Hex Subtraction	Hex Multiplication
Base	16	16	16
Digits available	0-9, A-F	0-9, A-F	0-9, A-F
Overflow direction	Carries into the next column	Borrows from the next column	Carries into the next column
Triggers at	Column total of 16 or more	Top digit smaller than bottom digit	Column product of 16 or more
Extra step	None	None	Shift and add partial products for multi-digit numbers

If addition's carrying rule or subtraction's borrowing rule isn't already familiar, hex addition and hex subtraction cover them with the same kind of verified, column-by-column examples used here.

Hex Multiplication and Number Base Converters

Working through partial products by hand is the best way to actually understand how hexadecimal multiplication carries, but for longer numbers or a quick double-check, a converter is faster than redoing the column math. Convert both operands to decimal with the Hex to Decimal Converter, multiply, and convert the answer back with the Decimal to Hex Converter — or use the Hex Converter for quick lookups between bases while you check your work.

Frequently Asked Questions

What is hex multiplication?

Hex multiplication is multiplication performed in base 16 (hexadecimal), the number system that uses sixteen digits: 0-9 and A-F, where A-F stand for decimal 10-15. It works exactly like decimal multiplication, except a column carries into the next one once its total reaches decimal 16 instead of 10.

How do you multiply hexadecimal numbers?

Convert any A-F digits to their decimal values, multiply the same way you would in decimal, and write the hexadecimal digit for each column's total, carrying 1 into the next column whenever a total reaches 16 or more. For numbers with more than one digit, multiply by each digit separately to get partial products, shift each partial product left according to its place value, then add the partial products together in hexadecimal.

How does carrying work in hexadecimal multiplication?

Whenever a column's product is 16 or greater in decimal, divide it by 16: the remainder is the hex digit written in that column, and the quotient is the amount carried into the next column. For example, 30 decimal equals 1 × 16 plus 14, so the digit written is E (14) and 1 is carried — the same rollover decimal addition does at multiples of 10, just at multiples of 16 instead.

What is a hexadecimal multiplication table?

A hexadecimal multiplication table lists the product of every pair of single hex digits (0 through F) with the result written in hexadecimal rather than decimal. It works exactly like a decimal times table, just extended to sixteen rows and sixteen columns instead of ten, and it's the fastest way to look up any single-digit hex product without recalculating it by hand.

How do you multiply A and F in hexadecimal?

A (10) times F (15) equals 150 in decimal. Converting 150 to hexadecimal: 150 = 9 × 16 + 6, so 150 decimal is 96 in hex. That means A × F = 96₁₆, which also appears directly in the hexadecimal multiplication table where the A row meets the F column.

Can hexadecimal multiplication be checked using decimal?

Yes. Convert both hex operands to decimal, multiply the decimal values, then convert your hex answer to decimal (or the decimal product back to hex) and compare. If both match, the multiplication is correct. The Hex to Decimal Converter and Decimal to Hex Converter make this quick for longer numbers.