SettingsSettings for this calculationUS
Offsets for a wandering edge measured off a straight line; coordinates for a plot with a survey.
Offsets suit a bed or a boundary that curves: run a tape along the straight side you have — a path, a kerb, a fence — and measure square off it to the edge at every station. Coordinates suit a polygon whose corners a surveyor or a drawing has already fixed.
Trapezoidal treats the edge as straight between stations; Simpson's rule fits a curve through them.
On a smoothly curving edge Simpson's rule is closer for the same stations; on an edge with corners between stations neither rule is, and the stations should go at the corners. Simpson's rule needs an even number of intervals — an odd number of offsets — and closes a last odd strip as a trapezoid.
The fixed distance along the baseline between one offset and the next.
Closer stations follow a wandering edge better. Every metre or two (3 to 6 ft) is usual for a garden bed; a field boundary might go at ten or twenty metres (30 to 65 ft).
How many offsets you took, including the first and the last; the fields after that count are ignored.
The first and last offsets are at the two ends of the baseline and are often zero where the edge meets it.
The distance square off the baseline to the edge at station 1.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 2.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 3.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 4.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 5.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 6.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 7.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 8.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 9.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 10.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
The distance square off the baseline to the edge at station 11.
Measured at right angles to the baseline. An offset of zero is a real value, where the edge touches the line; stations beyond the count above are ignored.
Area
274.6 ft²
The trapezoidal rule joins each pair of offsets with a straight line. On an edge that bows outward it reads slightly low, which Simpson's rule, shown beside it, corrects.
- Baseline length
- 58.5 ft
- Area by the trapezoidal rule
- 274.63 ft²
- Area by Simpson's rule
- 273.54 ft²
They open the calculator with your figures already in it
Irregular Area Calculator (Offsets and Coordinates): 275 ft² — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Area by offsets from a straight baseline (Ghilani and Wolf, Elementary Surveying: An Introduction to Geomatics): trapezoidal rule A = d × (o1/2 + o2 + … + on−1 + on/2); Simpson's one-third rule A = (d/3) × (o1 + 4o2 + 2o3 + 4o4 + … + on) over an even number of intervals
- Area by coordinates, the shoelace formula: A = ½ × |Σ (xi × yi+1 − xi+1 × yi)| taken round the polygon in order (Ghilani and Wolf, Elementary Surveying)
Inputs used
- What You Measured
- Offsets square off a baseline at a fixed interval
- Rule for the Offsets
- Trapezoidal — straight lines between offsets
- Interval Between Offsets
- 6.5 ft
- Number of Offsets (2 to 11)
- 10
- Offset 1
- 2 ft
- Offset 2
- 3.5 ft
- Offset 3
- 4.5 ft
- Offset 4
- 6 ft
- Offset 5
- 8 ft
- Offset 6
- 6.5 ft
- Offset 7
- 5 ft
- Offset 8
- 3.5 ft
- Offset 9
- 3 ft
- Offset 10
- 2.5 ft
- Offset 11
- 0 ft
- Number of Corners (3 to 8)
- 4
- Corner 1 Easting (x)
- 0 ft
- Corner 1 Northing (y)
- 0 ft
- Corner 2 Easting (x)
- 330 ft
- Corner 2 Northing (y)
- 0 ft
- Corner 3 Easting (x)
- 260 ft
- Corner 3 Northing (y)
- 260 ft
- Corner 4 Easting (x)
- 66 ft
- Corner 4 Northing (y)
- 260 ft
- Corner 5 Easting (x)
- 0 ft
- Corner 5 Northing (y)
- 0 ft
- Corner 6 Easting (x)
- 0 ft
- Corner 6 Northing (y)
- 0 ft
- Corner 7 Easting (x)
- 0 ft
- Corner 7 Northing (y)
- 0 ft
- Corner 8 Easting (x)
- 0 ft
- Corner 8 Northing (y)
- 0 ft
Intermediate steps
- Baseline length
- 58.5 ft
- Area by the trapezoidal rule
- 274.63 ft²
- Area by Simpson's rule
- 273.54 ft²
Confidence note: The trapezoidal rule joins each pair of offsets with a straight line. On an edge that bows outward it reads slightly low, which Simpson's rule, shown beside it, corrects.
What this calculation does not cover
- A plane area. A plot on a slope has a larger surface than its plan area, and the plan area is the one a deed, a planning form and most prices use.
- Offsets assume the edge runs straight or smoothly between stations. A corner or a sudden change between two stations is missed; put a station at every corner.
- Coordinates from a map or a projected grid carry that grid's scale factor, which changes area slightly across a zone; a survey's own coordinates on a site grid do not.
Estimated cost — your price
This site holds no price list for this material — local prices vary too much to publish honestly. Enter your supplier's price and the result is costed with it.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-22 · v1.0.0
Regulatory standards & verification citations2
- Area by offsets from a straight baseline (Ghilani and Wolf, Elementary Surveying: An Introduction to Geomatics): trapezoidal rule A = d × (o1/2 + o2 + … + on−1 + on/2); Simpson's one-third rule A = (d/3) × (o1 + 4o2 + 2o3 + 4o4 + … + on) over an even number of intervals
- Area by coordinates, the shoelace formula: A = ½ × |Σ (xi × yi+1 − xi+1 × yi)| taken round the polygon in order (Ghilani and Wolf, Elementary Surveying)
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