CADGISHow to use the traverse calculator
- Enter the starting point name and its X (Easting) and Y (Northing).
- For each leg, enter the point it goes to and choose Bearing (N/S, angle 0°–90°, E/W) or Azimuth (0° to <360° clockwise from North). Then enter the distance. Use + Add leg and × to add or remove legs.
- Press Calculate traverse. After that, results update as you edit.
- Tick Check closure for a closed traverse, or press Calculate closing leg to find the line back to the start.
- Press Copy results to paste a text report into your notes or report.
This is a plane (2D) calculation on grid coordinates. Distances must be horizontal and in the same unit as the coordinates, for example meters. The tool doesn't apply a traverse adjustment such as Bowditch or Transit. It reports the misclosure so you can decide what to do.
Traverse formulas
Bearing to azimuth
| Quadrant bearing | Azimuth | Example |
|---|---|---|
| N θ E | θ | N 45° E = 45° |
| S θ E | 180° − θ | S 30° E = 150° |
| S θ W | 180° + θ | S 60° W = 240° |
| N θ W | 360° − θ | N 20° W = 340° |
Coordinates of the next point
ΔX = Distance × sin(Azimuth)
ΔY = Distance × cos(Azimuth)
X₂ = X₁ + ΔX
Y₂ = Y₁ + ΔY
Surveying azimuths run clockwise from North (the Y axis). That's why ΔX (Easting) uses sine and ΔY (Northing) uses cosine, the opposite of the usual math-class convention measured from the X axis.
Closure and relative precision
Closure error e = √((ΣΔX)² + (ΣΔY)²)
Relative precision = 1 : (Traverse length ÷ e)
For a traverse that closes on another known point, the misclosure is the computed end point minus that point's known coordinates. All closure values come from the unrounded coordinate changes, so display rounding never affects them.
Worked examples
Example 1: a single leg
Start at X = 500000, Y = 2800000. Leg N 45° E, 100 m. The azimuth is 45°, so ΔX = 100 × sin 45° = 70.711 and ΔY = 100 × cos 45° = 70.711. The new point is X = 500070.711, Y = 2800070.711.
Example 2: a closed loop with a small misclosure
| Leg | Azimuth | Distance | ΔX | ΔY | X | Y |
|---|---|---|---|---|---|---|
| Start A | — | — | — | — | 1000.000 | 1000.000 |
| A → B | 0° | 100.000 | 0.000 | 100.000 | 1000.000 | 1100.000 |
| B → C | 90° | 100.010 | 100.010 | 0.000 | 1100.010 | 1100.000 |
| C → D | 180° | 100.000 | 0.000 | −100.000 | 1100.010 | 1000.000 |
| D → A' | 270° | 100.000 | −100.000 | 0.000 | 1000.010 | 1000.000 |
ΣΔX = 0.010 and ΣΔY = 0.000, so the closure error is 0.010. The traverse length is 400.010, giving a relative precision of 1:40,001. The closing leg from A' back to A is 0.010 at azimuth 270° (due West).
Frequently asked questions
What is a traverse in surveying?
A traverse is a series of connected survey lines. Each line's direction and length is measured, and the coordinates of each station follow from the previous one. It's the standard way to set up control points along a route or around a site.
What is the difference between an open and a closed traverse?
A closed traverse returns to its starting point, or ends on another known point, so you can check its accuracy through the misclosure. An open traverse ends on an unknown point and can't be checked that way.
What does relative precision 1:10,000 mean?
The closure error is one ten-thousandth of the total traverse length, for example 0.1 m over 1,000 m. Required values depend on the survey class and local regulations, so this tool doesn't judge pass or fail.
Can I enter bearings in degrees, minutes and seconds?
Yes. Type 45 30 15 or 45°30'15", or use decimal degrees such as 45.504167.
Does the calculator adjust the traverse?
No. It computes coordinates, closure and the closing leg from your data exactly as entered. Adjustments such as the Bowditch (compass) rule are not applied.