Measured Data Integration Calculator
Integrate tabulated measurements using trapezoids or composite Simpson 1/3. Keep interval contributions, signed accumulation and the entered unit labels visible.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Add signed trapezoid areas between adjacent measurements. For an even number of equally spaced intervals, Simpson 1/3 instead combines successive pairs of intervals using quadratic interpolation.
Trapezoids=ΣΔx(yi+yi+1)/2; Simpson=h/3[y0+4y1+2y2+…+yn]
Worked example
For (0,0), (1,1), (2,4), trapezoids give 3 while Simpson gives 8/3, the exact integral of x² from 0 to 2. If x is seconds and y is watts, the product unit is watt-seconds (joules).
Assumptions and input details
Enter 2–200 rows, numeric magnitude at most 1e12, with strictly increasing x and no duplicate x. Unequal spacing works for trapezoids. Simpson requires an even interval count and uniform spacing within relative tolerance 1e−9. Area is signed; negative y subtracts from the integral. The curve between samples is a numerical model, not a recovered signal. The table always shows trapezoidal interval/cumulative values, even when the selected total uses Simpson. Unit labels are descriptive only: no automatic unit conversion, resampling, uncertainty estimate or extrapolation is performed.
References: NIST DLMF numerical quadrature
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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