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.
快速参考
| 从 | 到 |
|---|---|
| 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 |
使用场景
- •Computing the sum 1 + 2 + … + N for homework problems.
- •Verifying loop summations in programming.
- •Quick arithmetic series calculations.
公式
Σ(i, a, b) = (b − a + 1) × (a + b) / 2. This closed-form formula gives O(1) performance for any range.
常见问题
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.