Surveying & GIS Reference
Datums, grids and field mathematics for engineering surveyors — what WGS 84 and UTM actually define, why grid distance is not ground distance, how a traverse is adjusted, and what happens to your coordinates when they pass through CSV, KML or KMZ.
Datums & coordinate systems
Every coordinate is meaningless without the frame it was measured in. Two numbers that look like a position are only a position once you know the datum and the projection.
Geographic vs projected coordinates
Geographic coordinates — latitude and longitude — are angles on an ellipsoid. They cover the whole earth without a break, but you cannot subtract two of them to get a distance, because a degree of longitude shrinks from about 111 km at the equator to nothing at the poles.
Projected coordinates — eastings and northings — are metres on a flat grid. You can subtract them, compute areas from them and set out with them, but only inside the zone they belong to, and every projection distorts something.
Engineering survey lives in projected coordinates; GNSS and mapping data arrive in geographic ones. Most coordinate confusion on site is a conversion that was skipped or done in the wrong zone.
WGS 84
WGS 84 is the datum GPS broadcasts in, and the default for almost all global mapping data. It defines an ellipsoid — a slightly flattened sphere — that the earth's surface is measured against.
| Item | Value | Note |
|---|---|---|
| Semi-major axis a | 6 378 137 m | Equatorial radius, exact by definition |
| Inverse flattening 1/f | 298.257 223 563 | Defining constant |
| Semi-minor axis b | ≈ 6 356 752.314 m | Derived: b = a(1 − f) |
| EPSG code | EPSG:4326 | WGS 84 geographic, latitude/longitude in degrees |
- Assuming a national grid shares the WGS 84 datum. Many national systems use a local datum, and the shift between them can be tens or even hundreds of metres.
- Treating ellipsoidal height from GNSS as a level. It is measured from the ellipsoid, not from mean sea level — the difference (the geoid separation) is typically tens of metres and varies across a site.
- Mixing WGS 84 with a local site grid without a documented transformation.
UTM zones
Universal Transverse Mercator cuts the world into 60 north–south strips and projects each one separately, so distortion stays small inside any single zone.
How the grid is defined
| Property | Value |
|---|---|
| Number of zones | 60, each 6° of longitude wide |
| Zone 1 | 180° W to 174° W |
| Zone number from longitude | zone = floor((longitude + 180) ÷ 6) + 1 |
| Central meridian of a zone | CM = (zone − 1) × 6 − 180 + 3 |
| Scale factor on the central meridian | 0.9996 |
| False easting | 500 000 m — so the central meridian is 500 000 E and eastings never go negative |
| False northing | 0 m in the northern hemisphere, 10 000 000 m in the southern |
| Latitude limits | 80° S to 84° N — outside this band UTM is undefined and UPS is used instead |
| EPSG codes (WGS 84) | 326zz north, 327zz south — zone 43 N is EPSG:32643 |
floor((67 + 180) / 6) + 1 = floor(41.17) + 1 = 42. Zone 42, central meridian (42−1)×6 − 180 + 3 = +69°, EPSG:32642 in the northern hemisphere.
- Comparing or subtracting coordinates from two different zones. The numbers are valid but the frames are not the same, so the answer is meaningless.
- Dropping the hemisphere. Easting 500 000, northing 3 700 000 exists in both hemispheres and describes two places thousands of kilometres apart.
- Recording a UTM coordinate without its zone — the most common way survey data becomes unusable later.
The zone exceptions
Two regions break the regular 6° pattern, and software that ignores them puts points in the wrong grid.
| Region | Rule |
|---|---|
| South-west Norway | Between 56° N and 64° N, longitudes 3° E to 12° E all fall in zone 32, which is widened at the expense of zone 31 |
| Svalbard | North of 72° N between 0° and 42° E, only the odd zones exist: 31 below 9° E, 33 below 21° E, 35 below 33° E, and 37 beyond |
Unless you work in Scandinavia these never arise — but a conversion library that handles them is a sign it implements the grid properly rather than just the formula.
Grid convergence & scale factor
The two corrections that separate a grid from the ground. Ignoring them is the most common source of setting-out error that survives every arithmetic check.
Grid convergence — grid north is not true north
| Symbol | Meaning | Unit |
|---|---|---|
| γ | Grid convergence — the angle from grid north to true north, positive when the point lies east of the central meridian | degrees |
| Δλ | Longitude difference from the zone's central meridian | degrees |
| φ | Latitude of the point | degrees |
γ = atan(tan 2.5° × sin 33.6°) = 1.384°, about 1° 23′.An astronomic bearing of 45° 00′ becomes a grid bearing of
45° 00′ − 1° 23′ = 43° 37′. Over a 500 m line that is a lateral difference of roughly 12 m.
- Confusing grid convergence with magnetic declination. They are unrelated — one is a projection property, the other a property of the earth's magnetic field.
- Applying convergence with the wrong sign. West of the central meridian γ is negative and the correction reverses.
- Assuming convergence is negligible. It is zero only on the central meridian and grows with both latitude and distance from it.
Scale factor — grid distance is not ground distance
UTM shrinks distance on the central meridian by 0.04% so that it can stretch it near the zone edges, keeping the worst-case distortion small. The consequence on site: a distance computed from grid coordinates is not the distance you will measure with a tape or EDM.
| Distance from central meridian | Point scale factor k | Ground minus grid, per km |
|---|---|---|
| 0 km (on the CM) | 0.999600 | +400 mm |
| 100 km | 0.999723 | +277 mm |
| 150 km | 0.999877 | +123 mm |
| 200 km | 1.000093 | −93 mm |
| 250 km | 1.000370 | −369 mm |
| 300 km | 1.000708 | −708 mm |
| 334 km (zone edge at the equator) | 1.000974 | −973 mm |
Note the sign change near 180 km: inside that band the ground is longer than the grid, outside it the ground is shorter. On the central meridian itself — where many people assume there is no correction at all — the difference is already 400 mm per kilometre.
- Setting out a grid distance with a tape or EDM. Convert to ground distance first, or the point lands short or long by the amounts above.
- Forgetting the height correction. Distance must also be reduced to the ellipsoid; the combined factor is the scale factor multiplied by the height factor, and on a high site the height term can exceed the projection term.
- Applying one site-wide scale factor across a large project without checking how far the easting varies.
The first-order formula above is the one implemented in Survey GeoLink, where it is accurate to roughly one part per million across a zone. Values in the table were computed from it with R = 6 371 000 m.
Bearings & angles
Whole circle, quadrantal and back bearings
| Form | Range | Example |
|---|---|---|
| Whole circle bearing (WCB) | 0° to 360°, clockwise from north | 142° 30′ |
| Quadrantal / reduced bearing | 0° to 90° from north or south, toward east or west | S 37° 30′ E |
| Back bearing | WCB ± 180° | 142° 30′ → 322° 30′ |
142° 30′ 00″ = 142 + 30/60 = 142.5°. In quadrantal form that is 180° − 142.5° = 37.5° measured from south towards east, written S 37° 30′ E. The back bearing is 142.5 + 180 = 322.5°.
- Typing 142° 30′ into a calculator as 142.30. Thirty minutes is 0.5 of a degree, not 0.30 — an error of 0.2°, or 3.5 m over a kilometre.
- Adding 180° without wrapping back below 360°.
- Mixing bearings referenced to grid north with bearings referenced to true or magnetic north in the same computation.
Traversing
Carrying coordinates from a known point around a series of stations, then proving the loop closes. Full formulas and worked examples are on the formula reference.
The sequence
| Step | What you compute |
|---|---|
| 1. Field work | Angles at each station and horizontal distances between them |
| 2. Bearings | Carry a known bearing through the measured angles around the traverse |
| 3. Latitudes & departures | Lat = L cos θ, Dep = L sin θ for every line |
| 4. Misclosure | e = √(ΣLat² + ΣDep²) — zero for a perfect closed loop |
| 5. Relative precision | 1 : (perimeter ÷ e), compared against the accuracy required |
| 6. Adjustment | Bowditch when angles and distances are of comparable quality; Transit when angles are appreciably better |
| 7. Coordinates & area | Accumulate adjusted latitudes and departures, then area by the shoelace formula |
- Adjusting before checking. A misclosure that fails the required precision contains a gross error — a transposed digit, a missed station, a wrong bearing — and distributing it hides the mistake instead of finding it.
- Computing area before adjustment.
- Quoting relative precision upside down. Perimeter divided by error, so 1:23 000 is far better than 1:2 300.
Levelling
Two methods, one answer
The height of instrument method computes the level of the line of sight once per setup and subtracts each reading from it. The rise and fall method differences consecutive readings instead. Both must produce identical reduced levels — running them together is how the arithmetic is proved.
- Believing the arithmetic check validates the survey. It proves only that the reductions are self-consistent; a misread staff booked exactly as read passes every check. Only closing back onto a known benchmark tests the field work.
- Booking an intersight as a foresight. A foresight is the last reading before the instrument moves — nothing else.
- Forgetting that a larger staff reading means lower ground.
GNSS in practice
The constellations
GNSS is the general term; GPS is one system within it. A modern receiver usually tracks several at once, which improves availability in built-up areas and under canopy far more than it improves absolute accuracy.
| System | Operator | Coverage |
|---|---|---|
| GPS | United States | Global |
| GLONASS | Russia | Global |
| Galileo | European Union | Global |
| BeiDou | China | Global |
| QZSS | Japan | Regional — Asia-Pacific |
| NavIC | India | Regional — India and surrounds |
What accuracy to expect
These are typical field figures under open sky, not guarantees. Actual accuracy depends on satellite geometry, multipath, atmospheric conditions and how long the receiver has been observing.
| Method | Typical horizontal accuracy | Suitable for |
|---|---|---|
| Standalone smartphone or handheld GNSS | 3–5 m | Navigation, asset location, reconnaissance, marking approximate positions |
| SBAS-corrected (WAAS, EGNOS and similar) | 1–2 m | Mapping, GIS data capture |
| RTK with a base or network correction | 10–20 mm | Setting out, control, cadastral and engineering survey |
- Using standalone GNSS positions as survey control. A 3 m position cannot set out a building line, no matter how many decimal places the display shows.
- Reading displayed precision as accuracy. Six decimal places of latitude is about 0.1 m of resolution and says nothing about correctness.
- Treating GNSS height as a level — see the geoid separation note under WGS 84 above.
Field data formats
How survey points move between a receiver, a spreadsheet, CAD and a map — and where coordinates get silently mangled on the way.
CSV, KML and KMZ compared
| Format | What it is | Coordinate system | Watch out for |
|---|---|---|---|
| CSV | Plain text, one point per row. The universal exchange format for point data | Whatever you put in it — the file itself records nothing | Carries no datum or zone. Always ship a header row and state the CRS separately |
| KML | XML for geographic features, readable by Google Earth and most GIS | Always WGS 84 geographic (EPSG:4326) | Coordinates are written longitude,latitude,altitude — longitude first, the reverse of how surveyors usually say it |
| KMZ | A zipped KML, optionally with images and icons bundled in | As KML | Rename to .zip to inspect the contents; the KML inside is usually doc.kml |
- Writing
latitude,longitudeinto a KML. The file will parse and the points will appear — in the wrong place, often in a different country or the sea. - Exporting UTM eastings and northings into a KML. KML is defined in geographic coordinates only; project first.
- Sending a CSV of eastings and northings without the zone and datum. The recipient cannot recover them from the numbers.
- Letting a spreadsheet reformat coordinates — long numbers turn into scientific notation and leading zeros vanish.
Survey GeoLink
QSCivilCalc's free Android app applies the material on this page in the field: live GNSS position shown in both geographic and UTM coordinates with the zone stated, saved point lists, points and bearings, a triangle solver, and CSV, KML and KMZ import and export. It works offline, which is the condition most survey work actually happens in.
The scale factor and grid convergence formulas above are the ones the app implements, so a distance it reports as grid can be converted to ground with the table in the section above.
About Survey GeoLink →