Sum of Products Calculator

The sum of products refers to the sum obtained by multiplying corresponding elements from two or more series or datasets and then adding up the results. It allows us to measure the combined effect of the variables or data points, providing insights into their collective impact. Whether you're analyzing sales data, studying the behavior of multiple variables, or trying to find patterns in datasets, the sum of products can be a valuable tool.

To understand the sum of products calculation, look at the following formula:

• Dataset A: [2, 4, 6, 8]
• Dataset B: [1, 3, 5, 7]

To calculate the sum of products, you need to perform the following three steps:

1. Determine the series of numbers to perform this calculation

   The first step is to determine the series of numbers you want to calculate the sum of products with. For our example, the datasets involved are:

   • Dataset A: [2, 4, 6, 8]
   • Dataset B: [1, 3, 5, 7]

2. Multiply the corresponding number

   The next step is to compute the product of the corresponding numbers, such as a1​×b1​a1​×b1​, a2​×b2​a2​×b2​, and so on and so forth.

   For our example, they are:

   • a1​×b1​=2×1=2a1​×b1​=2×1=2
   • a2​×b2​=4×3=12a2​×b2​=4×3=12
   • a3​×b3​=6×5=30a3​×b3​=6×5=30
   • a4​×b4​=8×7=56a4​×b4​=8×7=56

💡 You can use our multiplication calculator to understand more on this topic.

3. Add up results of the multiplications

   The last step is to sum everything up using the sum of products formula below. Hence, the results for our example is:

   a1​×b1​+a2​×b2​+a3​×b3​+a4​×b4​a1​×b1​+a2​×b2​+a3​×b3​+a4​×b4​
   =2×1+4×3+6×5+8×7=2×1+4×3+6×5+8×7
   =100=100

Restated in a symbol formula — if we have two series a=[a1​,...,an​]a=[a1​,...,an​] and b=[b1​,...,bn​]b=[b1​,...,bn​], then the sum of products is given by: