Simpson's 3/8 Rule Calculator

About this calculator

Simpson's 3/8 rule approximates a definite integral by fitting cubic curves through groups of four equally-spaced points, using the formula ∫f(x)dx ≈ (3h/8)[f₀ + 3f₁ + 3f₂ + 2f₃ + 3f₄ + 3f₅ + 2f₆ + … + fₙ], where h is the spacing between points. Unlike the standard Simpson's 1/3 rule, this variant requires the number of intervals to be a multiple of three, and it's often combined with the 1/3 rule to handle interval counts that don't divide evenly by either method alone.

Engineers and numerical analysts use Simpson's 3/8 rule to estimate integrals of functions known only at discrete sample points — such as data from sensors or experiments — and it's a standard topic in numerical methods coursework as an alternative to the more common 1/3 rule for specific interval-count situations.