Instrument Seconds and the Decimal Degrees Software Wants
Survey work is booked in seconds of arc because that is the resolution a total station reads to. Angular accuracy classes are quoted in seconds, closure tolerances are written in seconds, and a horizontal angle comes out of the instrument as degrees, minutes and seconds. Everything downstream — a CAD drawing, a GIS layer, a coordinate geometry routine, a machine-control model — wants one decimal number instead. That single translation sits between the field book and every deliverable.
Where Seconds Are the Working Unit
Instrument specifications
Traverse closure
Geodetic coordinates
Setting out and monitoring
Reducing a Booked Angle Ready for the Office
Handle the seconds separately from the minutes; that keeps the field book legible and makes a transcription mistake obvious rather than hidden inside one long decimal.
Enter the seconds from the booking sheet
Type just the seconds — 36, 5.5, 12.8 — into the left field. The decimal degree equivalent appears immediately, and a comma is accepted as the decimal mark for crews working with European notation.
Add the minutes and whole degrees
Divide the minutes by 60 and add both parts to the degrees. Keep at least six decimal places while you are still adding things up; four decimals only step in units of about a third of a second, which is coarse for control work.
Reverse it to check a tolerance
Press the swap button (↔) when the number arrives as a decimal instead — a misclosure of 0.0042° from an adjustment report becomes 15.1″, which is the form the specification is written in.
Switch the target to gon for a European job
Both dropdowns are searchable and carry every angle unit in the app, so the same seconds figure reads as gon for a continental client and as decimal degrees for the local drawing without a second entry.
Instrument Classes and What a Second Costs on the Ground
The gon column is there for jobs specified in the continental European system, where the right angle is 100 gon and a full circle 400. The last column is the practical one: how far sideways an angular error carries a sight at a hundred metres, which is a typical urban traverse leg.
| Angle (″) | Decimal degrees | Gon | Offset at 100 m | Typical context |
|---|---|---|---|---|
| 1″ | 0.000278° | 0.000309 | 0.48 mm | Precision instrument class; deformation monitoring |
| 2″ | 0.000556° | 0.000617 | 0.97 mm | Control and cadastral work |
| 5″ | 0.001389° | 0.001543 | 2.42 mm | General engineering survey |
| 10″ | 0.002778° | 0.003086 | 4.85 mm | Construction-grade setting out |
| 20″ | 0.005556° | 0.006173 | 9.70 mm | Topographic detail pickup |
| 30″ | 0.008333° | 0.009259 | 14.54 mm | Half a minute — a coarse booking increment |
| 60″ | 0.016667° | 0.018519 | 29.09 mm | One full minute of arc |
A useful field check falls out of the first row: one second subtends roughly half a millimetre at a hundred metres, so about a millimetre at two hundred. If a sight is 200 m away and the target moved a millimetre, the instrument sees a second.
What Speeds Up the Reduction
A whole page of bookings in one pass
Values recompute on each keystroke, so a column of seconds from the field book can be worked straight through by overtyping the field rather than resetting anything.
Gon and degrees from the same entry
The unit lists are complete on both sides, so a job specified in gon and a drawing dimensioned in degrees can be served without converting twice.
Check a decimal misclosure against the spec
Swapping the direction turns an adjustment report's decimal degrees back into the seconds that the tolerance clause is written in.
Clean values for the coordinate file
Copy returns the digits alone, so nothing has to be stripped before the number goes into a coordinate geometry field or an import sheet.
Questions from the Survey Crew
What does a two-second total station actually promise?
It is a standard deviation for a horizontal direction measured on both faces, determined under a laboratory test standard — not a worst case for a single pointing in the field. Two seconds is 0.000556°, or about a millimetre of lateral offset at a hundred metres. Real results also depend on centring over the mark, the target's own accuracy, refraction and how steady the tripod is, and on a short sight the centring error usually dominates the instrument entirely.
Why does GIS software reject a bearing typed 47° 12′ 36″?
Because that is three numbers in one string, and most coordinate fields expect a single value. The sexagesimal notation also has no agreed encoding — the prime and double prime are sometimes typed as apostrophes, sometimes as quotation marks, sometimes omitted — so parsers give up. Reducing to 47.21 before the value crosses that boundary sidesteps the whole problem, and it is worth keeping enough decimals that the seconds survive: four places resolve to about a third of a second, six to better than a hundredth.
Why do continental European crews book in gon instead of seconds?
The gon, also written grad or gradian, splits the right angle into 100 parts and the full circle into 400, which makes it decimal all the way down. There is no sixty-to-one carry to mishandle: a milligon is simply three decimal places, and quadrant arithmetic becomes adding hundreds. It came out of the metric reforms in France and stuck in surveying and civil engineering across much of Europe, where instruments are sold with a gon display option. In this app gradian and gon are the same magnitude, 0.9° each.
How much ground does one second of latitude cover?
About 30.9 metres along a meridian, since a minute of latitude is a nautical mile of 1852 m and a second is a sixtieth of that. Longitude shrinks with the cosine of the latitude, so a second of longitude is roughly 30.9 m at the equator, 21.8 m at 45° and 15.4 m at 60°. That scale explains why control sheets publish latitudes to four or five decimal places of a second — a thousandth of a second is about 31 millimetres, which is the order of accuracy geodetic control is expected to hold.
What angular misclosure is acceptable around a closed traverse?
Specifications usually set the allowance as a constant times the square root of the number of angles turned, because independent errors accumulate that way rather than linearly. With a 5″ criterion and eight stations the allowance is 5 × √8, roughly 14″; a tighter 2″ class over the same loop gives about 6″. Once the loop closes inside that figure, the misclosure is distributed across the angles before coordinates are computed. Interior angles of a closed polygon should sum to 180° × (n − 2), and the difference from that sum is what you are testing.
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