HomeCalculatorsSimpson's First Rule - Area Integrator

Simpson's First Rule - Area Integrator

Compute area under a curve sampled at three equally-spaced ordinates using Simpson's first rule - the building block for every naval-architecture volume, area and centroid integration.

SimpsonIntegrationNaval Arch
Area
13.333

Formula, assumptions, and limits

Simpson-1 exact for polynomials up to order 3. For more than 3 ordinates extend as composite: A = h/3·(y₀ + 4y₁ + 2y₂ + 4y₃ + … + y_n). Number of intervals must be even.

Symbol legend

SymbolMeaningUnitSource
Ordinate at station imbody plan
Common intervalmstation spacing