QuickCalculators multiplies whole numbers on a lattice grid, filling each cell with a two-digit partial product and summing diagonals with carries only at the end. Enter multiplicand and multiplier to see the completed lattice and the product read from the outer diagonal totals.
Multiply using the lattice grid
Lattice multiplication, also called gelosia or Italian multiplication, draws a rectangle of cells with diagonals, one cell per digit pair. Each cell holds the product of its row and column digits, tens above the diagonal and ones below. Lattice Multiplication Calculator fills that grid automatically for the entered factors.
Worked case: 327 × 586. The grid is 3 by 3 because each factor has three digits. Cell products such as 3 × 5 = 15, 2 × 8 = 16, and 7 × 6 = 42 occupy their squares with the tens digit above the slash and the ones digit below. No carrying happens inside a cell.
Read the diagonals to get the answer
After every cell is filled, add along each diagonal from right to left, writing the ones digit of each diagonal sum and carrying tens into the next diagonal. The sequence of outer digits is the product. QuickCalculators labels those diagonal sums so the final number can be read without guessing direction.
For 327 × 586 the product is 191,622. Reading the diagonals from the lower right toward the upper left builds that six-digit result. A carry out of the leftmost diagonal becomes the leading digit when needed.
Avoid this common mistake
The lattice is not a different multiplication. It is the same partial products as the standard algorithm, arranged so no carrying is required until the diagonal stage. Treating lattice as a rival operation confuses students who already know place-value multiplication. Both layouts compute identical cell products.
Standard multiplication also forms 300 × 500, 20 × 80, and so on; the lattice just parks each single-digit product in a square first. The final diagonal addition is where regrouping appears, matching ordinary carrying at the end.
Build a lattice by hand
To build a lattice by hand, draw an m-by-n grid for an m-digit times n-digit problem, draw a diagonal in each cell, write one factor across the top and the other down the side, fill products, then add diagonals. Practice on a smaller pair such as 23 × 45 before larger homework.
Steps for 23 × 45: four cells; products 8, 12, 12, and 15; diagonal sums produce 1,035. Checking 23 × 45 by another method should match. The calculator's grid is a reference for those hand-drawn cells.
Frequently asked questions
What is lattice multiplication?
Lattice multiplication is a grid method that places each single-digit partial product in a cell split by a diagonal, then adds along diagonals to form the final product. It is also known as gelosia or Italian multiplication. QuickCalculators draws the completed lattice for the inputs.
How do you do lattice multiplication?
To do lattice multiplication, build a cell for every digit pair, write each two-digit product with tens above and ones below the diagonal, then sum the diagonals with carries from right to left. The outer digits spell the answer.
What is 327 × 586 by the lattice method?
Three hundred twenty-seven times 586 by the lattice method equals 191,622. The 3×3 grid holds the nine single-digit products, and the diagonal sums assemble that total. Enter the same factors on this page to replay the grid.
Why is it called lattice multiplication?
It is called lattice multiplication because the drawn grid resembles a lattice or window trellis, historically linked to gelosia screens. The diagonals create the characteristic crossed look. The name describes the layout, not a change in the arithmetic.
What do the diagonal lines do?
The diagonal lines separate the tens digit from the ones digit inside each cell and create the channels used when summing place values. Adding along those diagonals gathers like place values together. Carries move from one diagonal to the next.
Is lattice multiplication faster than the standard method?
Lattice multiplication is not automatically faster than the standard method; speed depends on practice and digit length. Some learners prefer the delayed carrying. Both methods produce the same product when completed carefully.
Summary
Lattice Multiplication Calculator fills a gelosia grid for whole-number products and reads the answer from diagonal sums. The example 327 × 586 equals 191,622. Lattice cells hold the same partial products as the standard algorithm, with carrying postponed until the diagonals. Hand construction follows draw, fill, then add along the diagonals.