All Categories

Surveying & Geomatics

Measuring the land: slope and grade, coordinate areas, stadia, traverse latitudes and map scale

Slope / Grade Percentage

NEWBasic
G=riserun×100G = \frac{rise}{run} \times 100

Steepness of ground or a road as a percentage.

View details

Area by Coordinates (Shoelace)

NEWIntermediate
A=12(xiyi+1xi+1yi)A = \frac{1}{2}\left| \sum (x_i y_{i+1} - x_{i+1} y_i) \right|

Area of a polygon from the coordinates of its corners.

View details

Horizontal Distance

NEWBasic
H=LcosθH = L \cos\theta

Level distance from a slope distance and its inclination angle.

View details

Vertical Distance

NEWBasic
V=LsinθV = L \sin\theta

Elevation change from a slope distance and angle.

View details

Traverse Latitude

NEWIntermediate
Lat=Lcos(α)Lat = L \cos(\alpha)

North-south component of a traverse line from its length and bearing.

View details

Traverse Departure

NEWIntermediate
Dep=Lsin(α)Dep = L \sin(\alpha)

East-west component of a traverse line.

View details

Traverse Closure Error

NEWAdvanced
E=(Lat)2+(Dep)2E = \sqrt{(\sum Lat)^2 + (\sum Dep)^2}

Straight-line gap between the start and computed end of a closed traverse.

View details

Relative Precision

NEWIntermediate
RP=EPRP = \frac{E}{P}

Closure error expressed as a fraction of the traverse perimeter.

View details

Stadia Distance

NEWAdvanced
D=100scos2θD = 100 \, s \cos^2\theta

Horizontal distance from stadia hair readings on a level rod.

View details

Map Scale (RF)

NEWBasic
RF=dmapdgroundRF = \frac{d_{map}}{d_{ground}}

Representative fraction linking map distance to real-world distance.

View details

Earth Curvature Correction

NEWAdvanced
C=0.0675K2C = 0.0675 \, K^2

Drop due to Earth's curvature over a sight distance (metres, K in km).

View details

Radius from Degree of Curve

NEWAdvanced
R=5729.58DR = \frac{5729.58}{D}

Radius of a circular road or rail curve from its degree of curve.

View details

Area by Simpson's Rule

NEWAdvanced
A=h3(y0+4Σodd+2Σeven+yn)A = \frac{h}{3}(y_0 + 4\Sigma_{odd} + 2\Sigma_{even} + y_n)

Area under an irregular boundary using parabolic strips.

View details

Area by Trapezoidal Rule

NEWIntermediate
A=h(y0+yn2+Σyi)A = h\left(\frac{y_0 + y_n}{2} + \Sigma y_i\right)

Area under a boundary by summing trapezoidal strips.

View details

Bearing from Coordinates

NEWIntermediate
α=arctanΔEΔN\alpha = \arctan\frac{\Delta E}{\Delta N}

Direction of a line from the change in easting and northing.

View details

Slope Between Contours

NEWBasic
S=CId×100S = \frac{CI}{d} \times 100

Ground slope from the contour interval and horizontal spacing on a map.

View details