Simpson’s Rule Calculator

Simpson’s Rule Formula

Worked Example

y = 1/(1 + x²) at x = 0, 0.25, …, 1 (h = 0.25):

1. I = h/3 [y₀ + 4(y₁ + y₃ + …) + 2(y₂ + y₄ + …) + yₙ]
2. n = 4 intervals, h = 0.25
3. I ≈ 0.785392

Trapezoidal rule: 0.782794 · Simpson’s 1/3 rule: 0.785392 · Simpson’s 3/8 rule: needs n divisible by 3

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Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.