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Simpson's Rule Calculator

Integrate with the 1/3 and 3/8 rules, with the weight pattern shown, the subinterval count adjusted when it must be, and the error bound.

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Open Simpson's Rule Calculator and you get an answer straight away, with no account to create. Its place is under Calculus; Trapezoidal Rule Calculator and Cramer's Rule Calculator answer the questions closest to this one.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Simpson's Rule Calculator?

Integrate with the 1/3 and 3/8 rules, with the weight pattern shown, the subinterval count adjusted when it must be, and the error bound.

When would I actually use this?

Checking a derivative or an integral you worked out by hand, finding where a function turns, and getting a numeric answer when no closed form exists.

What is the most common mistake?

Integrating across a discontinuity as if it were not there. A numeric method will happily return a finite value for an integral that diverges — check the domain before trusting the number.

How is Simpson's Rule Calculator different from Trapezoidal Rule Calculator?

They sit next to each other but answer different questions. Trapezoidal Rule Calculator: approximates an integral from a function or from raw measured points, and unevenly spaced points are supported — real data rarely arrives on a regular grid. Draws the trapezoids, gives the error bound and compares to the exact value when one is obtainable. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Cramer's Rule Calculator is the closest one after this: Solves a 2×2 or 3×3 system with exact fractions, shows every determinant expanded term by term, and when D = 0 separates the two cases most calculators merge: dependent with infinitely many solutions, or inconsistent with none.

What else is worth having open alongside it?

Descartes' Rule of Signs Calculator and Rule of three — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Symbolic results are exact; numeric ones come from adaptive quadrature or a standard step method, and the tool reports which. Where both are available, compare them — a large gap means the problem is ill-conditioned.

Further reading

All guides →
ExplainerOne Cross-Multiplication Behind Six Different Problems2 is to 5 as 8 is to 20. Map scales, unit prices, percentages, recipe scaling and drawing enlargements are the same equation wearing five different names.ExplainerThree Painters Take Twelve Days; Five Do Not Take TwentyThe rule of three turns 3 → 12 into 5 → 20, and that is right for anything that scales up together. For workers and days it is exactly backwards: the answer is 7.2.ExplainerThe Pigeonhole Principle Proves a Thing Exists Without Finding ItTen items in three containers force four into one of them. 367 people force a shared birthday. Neither statement tells you which container or which pair.ExplainerA Cone Is Exactly One Third of Its CylinderRadius 5, height 10: the cone holds 261.8 and the cylinder around it holds 785.4. The ratio is exactly a third, and it holds for any base shape at all.ExplainerOne Formula That Is Also a Rectangle and Also a TriangleParallel sides of 8 and 5 with a height of 4 give an area of 26 — the average width times the height. Make the two sides equal and it is a rectangle; shrink one to nothing and it is a triangle.ExplainerTwice as Wide Holds Four Times as Much; Twice as Tall Holds TwiceA cylinder of radius 5 and height 10 holds 785.4 units of volume. Double the radius and it holds 3,141.6; double the height instead and it holds 1,570.8.