Lattice Multiplication Calculator

Multiply numbers using a lattice grid structure with diagonal lines for visual multiplication.

Multiply using lattice grid with diagonal lines. Also known as Italian, Gelosia, or sieve multiplication.

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Max 99,999 per number
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help_outlineHow to Useexpand_more

Using the Lattice Method

This calculator uses lattice multiplication to multiply numbers using a visual grid structure with diagonal lines. It breaks down the multiplication into smaller, more manageable steps that are easy to follow.

How to Do Lattice Multiplication:

  1. Draw the grid: Create a grid with columns for multiplicand digits and rows for multiplier digits
  2. Draw diagonals: Draw a diagonal line through each cell from top-right to bottom-left
  3. Multiply pairs: Multiply each digit pair, place tens above the diagonal, ones below
  4. Add diagonals: Sum numbers along diagonals from bottom-right to top-left
  5. Carry over: If a diagonal sum exceeds 9, carry the tens digit to the next diagonal
  6. Read answer: Read digits from top-left corner down and around to bottom-right

Also Known As:

  • Italian multiplication
  • Gelosia multiplication
  • Sieve multiplication
  • Venetian squares
  • Hindu lattice
infoWhat is Lattice Multiplication Calculator?expand_more

Lattice multiplication (also called Italian multiplication, Gelosia multiplication, or sieve multiplication) is a visual method for multiplying multi-digit numbers using a grid with diagonal lines. It helps students break down multiplication into smaller, manageable steps.

The grid structure organizes the partial products systematically, making it easier to keep track of place values. Each cell in the grid is divided diagonally—the tens digit of each product goes above the diagonal, and the ones digit goes below.

Historical note: This method was used in ancient India and later adopted by Arab mathematicians. Fibonacci introduced it to Europe in the 13th century through his book Liber Abaci.

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Lattice Method Steps:

1. Draw grid: columns = digits in multiplicand, rows = digits in multiplier

2. Draw diagonal lines through each cell (top-right to bottom-left)

3. Write multiplicand digits across the top

4. Write multiplier digits down the right side

5. Multiply each pair: tens above diagonal, ones below

6. Add along diagonals, carrying as needed

Cell Multiplication:

For each cell at row i, column j:

Product = multiplicand[j] × multiplier[i]

Tens digit → above diagonal

Ones digit → below diagonal

Diagonal Addition:

Start from bottom-right diagonal

Sum all numbers in each diagonal

If sum ≥ 10, carry tens digit to next diagonal

Final answer reads from top-left to bottom-right

lightbulbExamplesexpand_more

Example 1: 327 × 586

Create a 3×3 grid (3 digits × 3 digits)

Write 3, 2, 7 across top; 5, 8, 6 down right side

Fill cells: 3×5=15, 3×8=24, 3×6=18, etc.

Add diagonals with carrying

Product = 191,622

Example 2: 45 × 23

Create a 2×2 grid

Cells: 4×2=08, 5×2=10, 4×3=12, 5×3=15

Diagonals: 5, 10+2+1=13(carry 1), 0+0+1=1, 1+0=1

Product = 1,035

Example 3: 99 × 99

Create a 2×2 grid

All cells: 9×9=81

Diagonals: 1, 8+1+8=17(carry 1), 8+8+1=17(carry 1), 1+8=9

Product = 9,801

Example 4: 12 × 34

Create a 2×2 grid

Cells: 1×3=03, 2×3=06, 1×4=04, 2×4=08

Diagonals: 8, 4+6=10(carry 1), 0+0+1=1, 0+0=0 → read as 408

Product = 408

quizFAQexpand_more
Why use lattice multiplication instead of long multiplication?expand_more
Lattice multiplication organizes work visually, reduces carrying errors, and helps students better understand place value. Many find it easier because each step is isolated in its own cell, making the process less error-prone.
Where did lattice multiplication originate?expand_more
Lattice multiplication originated in ancient India and was later adopted by Arab mathematicians. Fibonacci introduced it to Europe in his 1202 book Liber Abaci. It was widely used in Europe until the standard algorithm became more popular.
Can lattice multiplication work with decimals?expand_more
Yes. Count the total decimal places in both numbers, perform the lattice multiplication as if they were whole numbers, then insert the decimal point in the answer with that many places from the right.
What size grid do I need?expand_more
The grid size depends on the number of digits: columns equal the digits in the multiplicand (top number), and rows equal the digits in the multiplier (side number). For 327 × 58, you need a 3-column by 2-row grid.
Why are the cells divided diagonally?expand_more
The diagonal separates tens and ones digits of each partial product. This organization aligns digits of the same place value along diagonals, making it easy to add them together correctly.