Summation Calculator
Calculate the sum of all integers from a to b using the Gauss summation formula. Instant result for any range.
How to Use the Summation Calculator
- Enter the starting integer a.
- Enter the ending integer b (b ≥ a).
- Click Calculate to see the sum, count, and average.
Quick Reference
| From | To |
|---|---|
| Σ(1…10) | 55 |
| Σ(1…100) | 5,050 |
| Σ(1…1000) | 500,500 |
| Σ(50…100) | 3,825 |
| Σ(1…1,000,000) | 500,000,500,000 |
Use Cases
- •Computing the sum 1 + 2 + … + N for homework problems.
- •Verifying loop summations in programming.
- •Quick arithmetic series calculations.
Formula
Σ(i, a, b) = (b − a + 1) × (a + b) / 2. This closed-form formula gives O(1) performance for any range.
Frequently Asked Questions
What does this calculator compute?
It computes the sum of all integers from your start value to your end value: a + (a+1) + … + b.
Why is it so fast?
It uses the Gauss closed-form formula instead of iterating through every number.
Can I sum non-integers?
This calculator sums integers only. Values are rounded down to whole numbers.