Lattice Multiplication Calculator
Multiply numbers with the lattice (Gelosia) method — a grid of diagonally split cells summed along diagonals, shown step by step with the full lattice.
What is lattice multiplication?
Lattice multiplication turns a multiplication into a grid of single-digit products. You build a rectangle with one column per digit of the first number and one row per digit of the second, split every cell with a diagonal, and fill in the products. Then you add along the diagonals to read the answer.
The steps
- Draw a grid: one column per digit of the first number (across the top), one row per digit of the second (down the right).
- In each cell write the product of its two digits — tens above the diagonal, units below.
- Add along each diagonal, starting bottom-right, carrying into the next diagonal.
- Read the result down the left edge, then across the bottom.
Worked example: 327 × 586
The top row of cells (times 5) holds 15, 10, 35 — written as tens-and-units in each split cell. After filling the whole grid and adding along each diagonal with carries, the diagonals give 1, 9, 1, 6, 2, 2. Read down the left and across the bottom: 327 × 586 = 191,622.
Smaller example: 27 × 34
A 2 by 2 lattice gives the diagonal sums that read out as 918.
Same answer, different bookkeeping
Lattice multiplication produces the exact same product as long multiplication. The difference is that every single-digit product gets its own cell, so multiplying and carrying never happen at the same moment — the adding is all done at the end along the diagonals, which relies on the same place-value idea as long addition.
Common mistakes
- Swapping tens and units inside a cell.
- Adding across rows instead of along diagonals.
- Forgetting to carry from one diagonal to the next.
Frequently asked questions
- What is lattice multiplication?
- Lattice (or Gelosia) multiplication is a grid method for multiplying two numbers. You draw a rectangle of cells, one per pair of digits, split each cell with a diagonal, write each single-digit product with its tens above the diagonal and units below, then add along the diagonals to read off the answer.
- How do you read the answer in the lattice method?
- After adding along each diagonal and carrying, read the digits down the left edge of the grid and then across the bottom edge. Those digits, in that order, form the product. For 327 times 586 you read 191622.
- Where do the tens and units go in each cell?
- Each cell holds one single-digit product. The tens digit goes in the upper-left triangle above the diagonal, and the units digit goes in the lower-right triangle below it. A product like 5 times 3 equals 15 is written as 1 above and 5 below.
- Why add along the diagonals?
- Each diagonal collects digits of the same place value. Adding along a diagonal is the same as adding a column in long multiplication, and a carry passes to the next diagonal up, exactly like carrying to the next column.
- Is lattice multiplication the same as long multiplication?
- They always give the same product. Lattice multiplication separates every single-digit product into its own cell and does all the adding at the end along diagonals, which many learners find easier because multiplying and carrying do not happen at the same time.
- Does lattice multiplication work for large numbers?
- Yes. The grid simply grows to one column per digit of the first number and one row per digit of the second. This calculator handles up to 12 digits in each number.
- Who invented lattice multiplication?
- The method spread through medieval Europe from Arabic and Indian mathematics and appears in Fibonacci's Liber Abaci. It is also called Gelosia multiplication after the lattice-like window grilles it resembles.