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Calculators / Math / Trapezoidal integration
Trapezoidal integration calculator
Approximate area under a curve from three equally spaced values.
On this page
Approximate integral9square units
Interval width2units
Calculator controls
How to calculate
Approximate area under a curve from three equally spaced values.
integral ≈ h/2 × (y₀ + 2y₁ + y₂)
Worked example
Spacing h: 1; First function value: 1; Middle function value: 4; Last function value: 9.
Approximate integral: 9 square units; Interval width: 2 units.
Assumptions and limits
The trapezoidal rule approximates curved segments with straight lines. Accuracy depends on smoothness and spacing; more points may be required.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Approximate area under a curve from three equally spaced values. Every assumption remains visible so the result can be checked or changed.
When this tool is useful
Use the trapezoidal integration for an initial estimate, comparison, or classroom calculation.
Understanding your inputs
| Input | What to enter |
|---|---|
| Spacing h | Enter a number of at least 0.000001 and no more than 1000000000000. |
| First function value | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Middle function value | Enter a number of at least -1000000000000 and no more than 1000000000000. |
| Last function value | Enter a number of at least -1000000000000 and no more than 1000000000000. |
Frequently asked questions
What are the limits of this trapezoidal integration?
The trapezoidal rule approximates curved segments with straight lines. Accuracy depends on smoothness and spacing; more points may be required.
Can I use different units?
Use the units printed beside each field. Convert measurements first when your source uses different units.