Sum of Even Numbers Calculator

About this calculator

The sum of every even number from 2 up to n follows a closed-form formula: if m is the count of even numbers up to n (m = n / 2, rounded down), the sum equals m × (m + 1), a direct consequence of the classic arithmetic-series result Gauss is famously said to have discovered as a schoolboy for summing consecutive integers.

This calculator is used in math education to demonstrate how a closed-form formula replaces manual addition or a loop-based sum, and it is a common early exercise in programming courses that teaches students to derive an O(1) formula instead of writing an O(n) loop to add up numbers one at a time.

Enter an upper limit n, and this calculator returns both the count of even numbers up to that limit and their total sum.