Survey

Coordinate geometry: inverses, forwards, intersections, resection, offset shots, traverses, and areas.

• Angular closure of a loop traverse

  How far a loop traverse's measured angles miss their geometric sum, (n − 2) × 180° for interior angles, against an allowable K√n, with the angles balanced.

• Area by coordinates (acreage)

  The area enclosed by plane-survey coordinates by the coordinate (shoelace) method, in square units, acres, and hectares, with the perimeter.

• Coordinates from a bearing and distance

  The coordinates of a point from a known point, a bearing or azimuth, and a horizontal distance (a radial sideshot).

• Intersection (bearings and distances)

  Where two lines cross, a line meets a circle, or two circles meet: bearing–bearing, bearing–distance, and distance–distance intersections from two known points, every solution returned and labeled.

• Inverse between two coordinates

  The bearing, azimuth, and horizontal distance between two plane-survey coordinates (northing, easting).

• Least-squares network adjustment (2D)

  Adjusts a small horizontal network of distances, angles, and direction sets by weighted least squares, with adjusted coordinates, standard errors, 95% error ellipses, the reference variance, and a chi-square test.

• Total-station offset shot

  The coordinates of a point the prism cannot sit on: from a shot beside it with left, right, in, or out offsets, or from an angle offset to the center of a tree or pole.

• Three-point resection

  The coordinates of an occupied station from the angles it turned between three known points, by Tienstra's method, with a warning when the station is near the danger circle.

• Station and offset from a line

  A point's station and offset from a straight alignment, with the foot of its perpendicular, or the point at a given station and offset. Offsets are positive to the right.

• Traverse closure and adjustment

  Latitudes, departures, linear misclosure, and precision ratio for a closed loop traverse, adjusted by the compass (Bowditch), transit, or Crandall rule.

Horizontal and vertical curves.

• Horizontal circular curve

  All elements of a simple circular curve (radius, deflection, tangent, length, chord, external, middle ordinate, degree of curve) from any two, with PC and PT stations.

• Circular curve layout table

  PC and PT stations for a circular curve and a layout table at a chosen interval: station, deflection from the PC, chords, and coordinates when the PI position and back tangent are given.

• Vertical curve length for sight distance

  The shortest crest or sag vertical curve that gives a sight distance, from the standard formulas with your eye, object, or headlight heights, stating which case applies; design values come from your design manual.

• Spiral-curve-spiral transition

  The elements of a clothoid spiral-curve-spiral (spiral angle, X, Y, p, k, long and short tangents, total tangent), its TS, SC, CS, and ST stations, and deflections along the spiral.

• Unequal-tangent vertical curve

  A vertical curve with different tangent lengths each side of the PVI: PVC, PVT, and the point under the PVI, the high or low point, and the elevation at any station.

• Vertical curve

  PVC and PVT stations and elevations, the high or low point, and the K value of a symmetric parabolic vertical curve.

Volumes, truck loads, grades, and slope stakes.

• Average end area volume

  Earthwork volume between two cross-sections by the average end area method, in cubic yards and cubic feet.

• Grid (borrow-pit) volume

  Cut and fill over a grid of existing elevations against a finished grade: the net volume by corner weights and the four-point method, with the balance line where cut turns to fill.

• Side slope and grade (H:V)

  A construction side slope or grade with its ratio labeled H:V and V:H, refusing an unlabeled 3:1, with rise, run, or slope length from any two; for a plain unit conversion of a slope, use the slope converter.

• Prismoidal volume

  Earthwork volume by the prismoidal formula with a measured middle section, and its difference from the average end area method.

• Profile grade analysis

  The grade of every segment along an elevation profile, the steepest and average grade, total climb and descent, and each segment steeper than your limit flagged.

• Cross-section cut and fill areas

  Cut and fill areas between the existing ground and a design template across one station, each split where the two cross, with the grade points where they meet.

• Swell, shrink, and truck loads

  Loose and compacted volumes from a bank volume with your swell and shrink factors, and the truck loads to haul it.

• Slope stake (catch point)

  Where a road template's cut or fill slope meets existing ground on one side, its offset and the cut or fill to the shoulder, found by iteration and written in stake notation.

• Cone, frustum, and prism volumes

  The volume of a cone, frustum, or prism from its dimensions, or of a conical pile from its base and an angle of repose you enter with its source.

• Stockpile volume (TIN)

  A stockpile's volume from its base outline and surface shots: a Delaunay TIN measured above the plane fitted to the base, in cubic units and cubic yards.

GNSS field work: precision budgets, OPUS sessions, and antenna heights.

• Antenna height from a slant measurement

  The vertical height to the antenna reference point from a slant height measured to the edge of the antenna, its radius, and the mark-to-ARP offset.

• Site localization (calibration)

  Fits local site coordinates to grid coordinates through control points seen in both, by a similarity (scale, rotation, shift) or affine transform, with residuals, their root mean square, and a check for a feet-and-meters mix-up.

• OPUS session planning

  Which NGS OPUS processing a planned GNSS session gets (rapid-static or static), whether its length qualifies, and the RINEX file name for the day.

• RTK and PPK precision budget

  The precision a receiver's a mm + b ppm specification promises over your baseline, horizontal and vertical, scaled to a confidence level and compared with your target.

Deeds, legal descriptions, and old units.

• ALTA/NSPS relative positional precision

  The allowable relative positional precision between two adjacent boundary corners under the 2026 ALTA/NSPS standards, compared with the 95% error ellipse from your adjustment.

• Basis-of-bearing rotation

  Rotates deed or plat bearings to a new basis of bearing (like grid north) from one line whose bearing is known in both, and reports the rotation angle.

• Deed parser (metes and bounds)

  Turns pasted metes-and-bounds deed text into a table of calls (bearings, distances, curves, and monuments) for you to confirm and edit before anything is plotted.

• Deed plot, closure, and area

  Plots confirmed deed calls (lines and curves), then reports the misclosure, its direction, the precision ratio, and the area closed by the implied closing line. Courses are never adjusted unless you choose to.

• Legacy land units

  Converts chains and links, rods, furlongs, varas, and arpents from old deeds and plats to US survey feet, feet, and meters, with the definition used; varas and arpents need a jurisdiction.

• PLSS legal description reader

  Reads a Public Land Survey System description like NE¼ SW¼ Sec 12, T3N R4W, 6th PM into plain words, and gives the nominal aliquot area of a standard 640-acre section.

Slope, stadia, and level-run reductions, heights you cannot reach, curvature and refraction, and scale between grid and ground.

• Combined scale factor (grid and ground)

  The elevation factor and combined factor from a grid scale factor and height, and conversion of a distance between grid and ground.

• Curvature and refraction correction

  How much the earth's curve, less the bending of the line of sight, lowers a level sight over a distance, with the textbook coefficient for the refraction coefficient used.

• EDM atmospheric and prism corrections

  Corrects a measured EDM distance for the air it traveled through (in ppm, entered or worked out from temperature, pressure, and humidity) and for the prism constant, each listed.

• Height of an inaccessible object

  The height of a tower, tree, or building you cannot reach, from zenith angles to its base and top and a horizontal distance, or from two stations in line with it.

• Level run reduction and closure

  Heights of instrument and elevations from a level book, the arithmetic check, and for a loop or a run between benchmarks, the misclosure, its allowable, and the adjusted elevations.

• Slope distance to horizontal and vertical

  Horizontal distance, vertical difference, and elevation difference from a slope distance and zenith angle, with two-face means and the curvature and refraction correction for long sights.

• Stadia reduction

  Horizontal distance, vertical difference, and elevation difference from a stadia rod interval and the sight's zenith angle.