Coordinate geometry, worked properly
The calculations a survey crew actually runs - free, and shown in full.
10 coordinate-geometry calculators that print the whole computation sheet, not just an answer. A 61-page reference library built on the public-domain BLM Manual and NGS publications. And a practice bank for anyone sitting the Fundamentals of Surveying exam.
- Calculators
- 10
- Reference pages
- 61
- Practice questions
- 330
- Solved problems
- 61
The calculators
All 10Every one runs entirely in your browser - nothing you type is uploaded, stored or logged - and every one prints the intermediate values, because a number you cannot check is a number you cannot use.
- Traverse closurePaste your courses, get closure, precision and adjusted coordinates - with the whole computation sheet visible.
- Horizontal curveAny two elements in, every element out - plus the deflection table you actually stake from.
- Vertical curveGrades and length in; the turning point, the K value and a full grade-elevation table out.
- Bearing ⇄ azimuthQuadrant bearings, azimuths, back sights and DMS arithmetic in one place.
- Area by coordinatesShoelace and DMD, side by side - because when they disagree, your vertex order is wrong.
- Inverse & forwardThe two operations every COGO session is made of, plus the intersections.
- Latitude & departureCourse by course, with the signs made explicit and the totals kept for you.
- Stationing12+34.56 arithmetic that does not go wrong when the alignment is metric.
- Scale factor & unitsGround to grid, grid to ground - and the 2-ppm foot problem, made visible.
- DMS ⇄ decimalEvery DMS notation parsed, every equivalent shown, and no 59′60″ rounding bug.
The reference library
All 61 pagesThe Bureau of Land Management's Manual of Surveying Instructions and the National Geodetic Survey's publications are works of the United States government and therefore public domain. This library explains them, cites them on every page, and is free to read forever.
- Public Land Survey SystemTownships, ranges, sections and aliquot parts as the BLM Manual of Surveying Instructions describes them - how the rectangular system was laid out, how corners were monumented, and how a retracement follows it.
- Datums & heightsHorizontal and vertical datums, the ellipsoid and the geoid, NAD 83 and NAVD 88, and the modernized reference frames that replace them.
- Coordinate systems & projectionsState Plane, UTM, low-distortion projections, and the grid-versus-ground arithmetic that decides whether a measured distance matches a published one.
- Survey types & practiceWhat an ALTA/NSPS survey is and is not, boundary versus topographic versus construction work, and the vocabulary a client, an attorney and a field crew each use for the same thing.
- FS exam guideHow the NCEES Fundamentals of Surveying exam is structured, what each subject area covers, and how to build a study plan around it.
Guides
All 12- How to pass the Fundamentals of Surveying examA realistic eight-week study plan for the FS exam: what to master first, how to drill computation under time pressure, and what the final week should look like.
- COGO basics every survey tech needsCoordinates, azimuths, inverse and forward, latitudes and departures, closure, area and intersections, with worked numbers and the sign conventions.
- US survey foot vs international footTwo feet differ by exactly two parts per million. Where they came from, why State Plane feet are usually survey feet, and how to tell which one a dataset uses.
- Traverse closure explainedAngular closure, latitudes and departures, misclosure and the 1:X ratio, compass rule against transit rule - worked end to end on one five-sided traverse.
- PLSS for beginnersTownships, ranges, sections and aliquot parts: how the rectangular system was laid out, how to read a description, and why sections are rarely 640 acres.
- An error theory primerBlunders, systematic and random error; standard deviation and standard error; propagation in quadrature; weighted means and level-loop closure.
- Compass rule vs transit ruleTwo ways to spread a traverse misclosure, and one assumption behind each. When the compass (Bowditch) rule is right, and when the transit rule is.
- Bearings and azimuths without losing a quadrantThe four conversion rules, why every computation runs on azimuths, and the quadrant errors that turn a good traverse into a wrong one.
- Horizontal curve components, worked end to endR, Δ, T, L, C, M and E on a simple circular curve, plus stationing and a deflection table - one curve carried from the plan sheet to the stakes.
- Vertical curves: finding the high and low pointEqual-tangent parabolic curves worked in full: grade change, K value, external offset, and the turning point that decides where water goes.
- Area by coordinates: the shoelace method and DMDTwo ways to compute the area of a closed figure from coordinates, why they always agree, and what a disagreement is actually telling you.
- State plane coordinates explainedZones, false origins, grid scale factor, elevation factor and the combined factor - what a state plane coordinate is and how to get back to the ground.
Preparing for the exam
330 practice questions and 61 fully worked problems
Original questions across all 7 subject areas of the Fundamentals of Surveying exam, each with a worked solution, and a library of 61 long-form problems taken end to end - givens, every step of the arithmetic, the answer, and an independent check.
A fresh round of 8 questions is free every day, and 8 solved problems stay free to read. Every calculator, the whole reference library and all the guides are free to use forever - the practice bank, the full problem library and the printable job paperwork are the paid upgrade.