Summation Calculator

Summation notation, with its tall Greek sigma, is the compact mathematical shorthand for adding up a long list of terms, and this calculator evaluates it for you for any expression and range you give. The sigma symbol simply means add up, the index variable i runs from a starting value written below the sigma to an ending value written above it, and the expression to the right tells you how to build each term from i. So the sum from i equals 1 to 100 of i means add the whole numbers 1, 2, 3 and so on up to 100. To use the calculator, type the expression in terms of i, set the lower and upper limits, and it returns the total along with the number of terms and a sample of the first few values so you can see what is being added. You are not limited to simple sums: the expression can be i squared, one over i, two times i minus one, the square root of i, or anything built from the index with the usual operations and standard functions, which lets you handle arithmetic series, sums of squares, harmonic sums, alternating series and many more. This makes the tool genuinely useful across senior school and university maths, statistics and computer science, wherever sigma notation appears, whether you are checking a series sum by hand, exploring how a sum grows as the upper limit increases, or verifying a closed-form formula against the direct total. It is also a quick way to build intuition for famous results, like the sum of the first n whole numbers being n times n plus one over two. The calculator updates as you type, so you can experiment freely. The notation and a worked example are explained clearly below.

Calculate.co.nz is proud to be partnered with realtor.co.nz, a trusted resource for navigating the New Zealand property market. Their Helpful Articles section offers clear, well-structured insights across buying, selling, and building, making complex real estate topics more accessible. With a focus on up-to-date guidance and practical knowledge, they empower Kiwis to move forward with clarity and confidence in a constantly evolving property landscape.