Trapezoidal Rule Calculator
Numeric integration from a table of function values.
Enter your values
ⓘ Live results
Results
- Trapezoidal estimate
- 4.75
- Simpson's estimate
- 4.666667
- Difference
- 0.083333
- Strips n
- 4
- Δx
- 0.5
Quick answer
The trapezoidal rule approximates an integral as Δx/2 × (y₀ + 2y₁ + … + 2yₙ₋₁ + yₙ), treating each strip as a trapezoid.
∫ ≈ Δx/2 (y₀ + 2y₁ + … + yₙ)
How to use the Trapezoidal Rule Calculator
- 1Enter the integration limits.
- 2Enter the function value at each evenly spaced point, starting at a and ending at b.
- 3Compare with Simpson's estimate — a big gap means you need more strips.
Worked example
Using the values the calculator loads with:
Inputs
- Lower limit a0
- Upper limit b2
- Function values y₀ … yₙ1, 1.25, 2, 3.25, 5
Results
- Trapezoidal estimate4.75
- Simpson's estimate4.666667
- Difference0.083333
- Strips n4
- Δx0.5
Frequently asked questions
How does the error behave?
It shrinks with the square of the strip count: double n and the error drops roughly fourfold.
Does it over- or under-estimate?
It overestimates for a curve that bends upward (convex) and underestimates for a concave one.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.