Survey tools
Survey Calculators
Inverse
Azimuth and distance between two points.
Polar / COGO point
New point from a start point, azimuth and horizontal distance.
Area
Polygon area, perimeter and centroid from coordinates (shoelace formula).
Intersection
Bearing–bearing, distance–distance or angle–angle (forward) intersection from two known points.
Resection
Three-point resection (Tienstra) from horizontal circle readings to known points.
Least squares
Least-squares adjustment of a traverse or network: angles, directions, distances and azimuths, with standard deviations, error ellipses, residuals and statistical tests.
Free station
Resection from directions (and optionally distances) to two or more known points, adjusted by least squares. Two points need distances; three or more work with directions alone.
Curve
Horizontal circular curve elements and setting-out table (arc definition, deflection angles and chords from the PC).
Station & offset
Chainage and perpendicular offset of points from a polyline alignment (offset positive to the right), or the coordinates of a chainage and offset.
Parcel
Parcel closure from a start point and bearing/distance legs: misclosure, precision ratio, Bowditch-closed coordinates, area and perimeter.
Profile
Longitudinal profile: ground and design grades between chainages, and cut (+) or fill (−) depth at each point.
Cross-section
Cut and fill areas of a cross-section from ground and design lines (offset, level). Crossing points are found exactly.
Bearing ↔ azimuth
Convert quadrant bearings to whole-circle azimuths and back.
Slope reduction
Horizontal and vertical distance from slope distance and zenith angle.
Scale factor
Point scale factor, grid convergence, elevation factor and combined scale factor for a projected CRS.
Level book
Height-of-instrument reduction with arithmetic check and distance-weighted misclosure adjustment.
Volume
Earthwork volume from cross-section areas: average end area and prismoidal (Simpson) rule.
Formulas used
Projection scale factor k and grid convergence γ are computed numerically from the selected CRS definition using PROJ-compatible formulas, the same engine used by the Coordinate Transformation tool.
FAQ
Which angle formats can I enter?
Decimal degrees (45.5), packed D.MMSS (45.3000 = 45°30′00″) when that option is selected, or symbols such as 45°30′00″, 45 30 00 and 45d30m00s.
Are the results grid or ground values?
All COGO calculations use the coordinates you enter, so they are in whatever system those coordinates are in. Use the Scale factor calculator to convert between ground and grid distances.
How is the resection computed?
With Tienstra’s method from three known points and three horizontal circle readings. It fails near the “danger circle” through the three known points, and the calculator warns you when that happens.
How does the least-squares adjustment work?
It is a parametric (observation-equation) adjustment iterated to convergence. Each observation is weighted by 1/σ². The report gives adjusted coordinates with standard deviations and 95 % error ellipses, residuals with redundancy numbers, Baarda w-test values (|w| > 3.29 flags a probable blunder), the a-posteriori σ₀ and the χ² global test.
How many known points does a free station need?
Two, if you also measure distances to them. With directions only you need at least three, and a fourth gives redundancy so blunders can be detected.
Which volume method should I use?
Average end area is standard for earthworks and tends to overestimate. The prismoidal (Simpson) rule is more accurate when sections are equally spaced and their number is odd.
Is my data uploaded anywhere?
No. All calculations run in your browser.
Related articles and tools
- Azimuths: grid, true and magnetic northKnowledge Center
- Quadrant bearingsKnowledge Center
- Differential levelingKnowledge Center
- Distance reduction and scale factorKnowledge Center
- Traverse adjustmentKnowledge Center
- UTM coordinate systemKnowledge Center
- Traverse AdjustmentBowditch and Transit with report
- Coordinate TransformationEPSG to EPSG conversion