Trapezoidal Rule Calculator
Numeric integration from a table of function values.
Enter your values
Enter the lower limit a you are working with.
Enter the upper limit b you are working with.
Enter the function values y₀ … yₙ you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Numeric integration from a table of function values. |
|---|---|
| Category | Math |
| Inputs needed | Lower limit a, Upper limit b, Function values y₀ … yₙ |
| Main output | Trapezoidal estimate |
| Formula | ∫ ≈ Δx/2 (y₀ + 2y₁ + … + yₙ) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Lower limit a
- Enter the lower limit a you are working with.
- Upper limit b
- Enter the upper limit b you are working with.
- Function values y₀ … yₙ
- Enter the function values y₀ … yₙ you are working with.
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.
What do I need to enter into the Trapezoidal Rule Calculator?
Just 3 values: lower limit a, upper limit b, function values y₀ … yₙ. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Trapezoidal Rule Calculator work out the answer?
The trapezoidal rule approximates an integral as Δx/2 × (y₀ + 2y₁ + … + 2yₙ₋₁ + yₙ), treating each strip as a trapezoid. It applies the formula ∫ ≈ Δx/2 (y₀ + 2y₁ + … + yₙ) and shows the working so you can check each step by hand.
Is the Trapezoidal Rule Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.