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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.

Related tools

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Simpson's Rule CalculatorIntegrate 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.Cramer's Rule CalculatorSolves 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.Descartes' Rule of Signs CalculatorSign changes in f(x) and f(−x) marked one by one, then every possible (positive, negative, complex) combination that adds up to the degree.Rule of threeSolve a proportion: if A gives B, what does C give?Antilog Calculator (inverse logarithm)The antilogarithm undoes the logarithm: antilog_b(y) = bʸ, so log_b(bʸ) = y. Pick base 10, e, 2 or your own, enter the exponent, and the result comes back with the inverse relationship spelled out and the round trip checked. Bases of zero or less, and base 1, are rejected with the reason.Bernoulli ODE SolverSolves y′ + P(x)y = Q(x)yⁿ by showing the substitution v = y^(1−n) that turns it into a linear equation, then integrating. The two degenerate cases are handled explicitly: n = 0 is already linear, n = 1 is separable.Convolution CalculatorLinear and circular discrete convolution with the sliding-and-summing steps shown term by term, plus a symbolic continuous convolution solved exactly through the Laplace convolution theorem.Derivative CalculatorCompute single, partial, implicit and directional derivatives symbolically.

Trapezoidal Rule Calculator works straight from this page — free, instant, nothing to install. It sits under Calculus in our catalogue, alongside Simpson's Rule Calculator and Cramer's Rule Calculator.

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 does Trapezoidal Rule Calculator do?

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.

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 Trapezoidal Rule Calculator different from Simpson's Rule Calculator?

They sit next to each other but answer different questions. 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. 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 →
ExplainerThe Expected Value Is a Number That Never HappensOutcomes of 10, 20 and −5 with probabilities 0.5, 0.3 and 0.2 give an expected value of 10. Shift the probabilities slightly and it becomes 10.5 — a result none of the three outcomes can produce.ExplainerAn Error Bar That Shrinks Is Not the Standard DeviationFor 10, 12, 15, 11, 13, 14 the standard deviation is 1.87 and the standard error is 0.76. They answer different questions, and only one of them gets smaller as you collect more data.ExplainerAn r of 0.85 That Proves NothingFive points give r = 0.853, which sounds strong. The threshold for significance at five points is 0.878, so this one falls short — and a perfect parabola scores exactly zero.ExplainerQuadruple the Sample to Halve the IntervalA mean of 100 with a standard deviation of 15 over 30 observations gives 100 ± 5.37 at 95 %. Going to 120 observations gives ± 2.68 — exactly half, because the sample size enters under a square root.ExplainerThe Same Three Temperatures Give Three Different Coefficients of VariationFor 2, 4, 4, 4, 5, 5, 7, 9 the coefficient of variation is 42.76 %. It is the right tool for comparing spread across different scales — and completely wrong for any scale whose zero was chosen by convention.ExplainerThree Dice Cluster, and One Die Does Not3d6 and 1d20 have almost the same average and nothing else in common. Against a target of 12 the three dice are better, against 18 they are five times worse — and the calculator gives the exact figures rather than a simulation.