Area by Offsets from Baseline
Computes irregular boundary area from perpendicular baseline offsets using the trapezoidal or Simpson's rule.
Offsets along the baseline
| Distance along baseline (m) | Offset (m) | |
|---|---|---|
List the offsets in order along the baseline (distances increasing). Simpson’s rule needs equal spacing and an odd number of offsets. Runs in your browser.
Result
Trapezoidal: Σ ½(yᵢ + yᵢ₊₁)·(xᵢ₊₁ − xᵢ). Simpson’s (equal spacing h): (h/3)(y₀ + yₙ + 4·Σodd + 2·Σeven). Simpson’s is usually closer when the boundary curves smoothly.
How to use this calculator
- Enter each offset (the perpendicular distance to the boundary) at its distance along the baseline, in order.
- Add or remove rows to match your survey; keep the distances increasing.
- Read the area by the trapezoidal rule, and by Simpson's rule where the spacing is equal.
How it works
The trapezoidal rule treats the boundary between offsets as straight: area = Σ ½(yᵢ + yᵢ₊₁) × (xᵢ₊₁ − xᵢ). It works for any spacing.
Simpson's rule fits a curve through each pair of strips and is usually more accurate for a smoothly curving boundary, but it needs equal spacing and an even number of strips (an odd number of offsets): area = (h/3)(y₀ + yₙ + 4·Σodd + 2·Σeven).
Worked example
Offsets 0, 5, 8, 6, 0 at 10 m spacing. The trapezoidal rule gives 190 m² and Simpson's rule gives 200 m² — Simpson's is usually closer when the boundary curves smoothly.
Frequently asked questions
When can't I use Simpson's rule?
When the offsets aren't equally spaced, or there's an even number of them (an odd number of strips). The tool falls back to the trapezoidal rule and tells you Simpson's doesn't apply.
Which rule should I trust?
For a straight or near-straight boundary they agree closely. For a smoothly curving boundary, Simpson's rule is generally more accurate where it applies.
Is this official course material?
No. It is free study support mapped to surveying course levels — not official North Metropolitan TAFE content or advice. Always follow your lecturer and the official assessment brief, and check your own working.
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Cite this tool
Zerdly. (2026). Area by Offsets from Baseline. Retrieved from https://www.zerdly.com/tools/area-by-offsets-from-baseline/
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.