Line Method Multiplication Calculator (Crossing Lines)

Multiply by drawing lines for each digit and counting where they cross. This calculator recreates the line method (crossing technique) with a diagram, per place intersection counts, and the product.

Input

Draw lines for each digit, cross them, and read the answer from the number of intersections with the line method (crossing technique).

First number

Second number

Enter a positive integer with one or two digits (1 to 99). Smaller digits make the diagram easier to read.

Result

Product of 21 times 13

273

Lines and intersections

Vertical lines are the first number and horizontal lines are the second. Intersection colors are grouped by place (band).

Number of places (bands)

Total intersections

How to do it

Draw lines for each digit

Draw that many parallel lines for each digit of 21 and 13. Use one direction for one number and the other direction for the second.

Cross them and count intersections

Cross the two groups of lines and count where they meet. The intersections separate into diagonal bands from left to right.

Total each band

Counting the intersections in each band from the highest place gives 2, 7, 3.

Carry over to get the product

Add the band values by place and carry over to obtain the product 273.

Intersections per place

Place (band)	Intersections
Place weight 100	2
Place weight 10	7
Place weight 1	3
Product	273

The line method represents each digit product as a number of intersections and adds them up by place. With larger digits the intersections become harder to count.

How it works

Split each number into digits and draw that many parallel lines for each digit. Cross the lines of one number with the lines of the other and count the intersections.
Intersections fall into diagonal bands from left to right. The total of the intersections in each band gives the value for that place.
For two two-digit numbers, the left band is the hundreds place, the middle band is the tens place, and the right band is the ones place. Add the bands and carry over to get the product.
For example, 21 times 13 gives a left band of 2, a middle band of 7, and a right band of 3, which combine to 273.
This tool accepts two positive integers with one or two digits and also shows the ordinary product as a check.

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