Summation Calculator
Evaluate sigma sums and pi products of any expression.
About this tool
Type an expression in n (or k, i or x), choose the start and end values and whether to sum or multiply. The tool gives the total and a table of the first and last terms with running totals.
Sigma notation
Sigma notation writes a long sum compactly: Σ from n = 1 to 10 of n² means 1 + 4 + 9 + … + 100, which is 385. The capital pi Π does the same for products. Enter any expression with standard operators (+ − × ÷ ^), brackets, factorials (n!), implicit multiplication (2n), the constants π and e, and functions such as sqrt, sin, cos, ln, log and exp. It's parsed safely, not run as code. Some useful checks: Σ n from 1 to 100 is 5,050 (Gauss's sum); Σ (1/2)^k from 0 to 20 approaches 2; Π (1 + 1/n) from 1 to 9 telescopes to exactly 10. The running-sum column shows convergence: Σ 1/n² to 1,000 is 1.64393, creeping towards π²/6 = 1.64493 (the Basel problem). Honest limits: terms are added one at a time in floating point, up to a million terms, so the tool can't give exact values of infinite series, rounding builds up in long or alternating sums, and factorials above 170! overflow to infinity. The number sequence calculator and the factorial calculator are related.
Frequently asked questions
What does Σ mean in maths?
The capital Greek letter sigma means 'add up': Σ from n = 1 to N of f(n) is f(1) + f(2) + … + f(N).
What is the sum of the first 100 numbers?
5,050, from n(n + 1) ÷ 2.
What is the sum of n squared from 1 to 10?
385, from n(n + 1)(2n + 1) ÷ 6.
Can it calculate infinite series?
Not exactly. It adds a finite number of terms, so use a large end value to see where the partial sums converge.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.