Free tool · Survey calculations
Traverse Adjustment Calculator: Bowditch, Transit and Least Squares
Type the angles and distances of a closed traverse and get the misclosures, precision and adjusted coordinates — by Bowditch, Transit or least squares — and close a level run in the same place.
Free · no sign-up · works in your browser, on phone and computer
Example · A six-station closed loop, adjusted by least squares
- Control
- CP-01 228450.312 441203.845 · reference object CP-02
- Observed
- 6 angles in d.mmss and 6 distances round CP-01 → TS-01 … TS-05 → CP-01
- Angular misclosure
- +2.0″ (allowed ±13.2″)
- Linear precision
- 1 : 125,383
- TS-01 adjusted
- E 228,702.460 · N 441,012.337
What it does
Loop, link or open
A closed loop back to its start, a link between two known points, or an open traverse. A secondary traverse can hang off stations a primary one just fixed.
Three adjustments
Bowditch, Transit, or least squares with residuals, a chi-square test and error ellipses — checked against C√n and 1 : N tolerances.
Level runs too
Rise and fall or height of instrument from staff readings, or height differences, closed against C√K.
Reports to keep
A plan or profile of each run, a CSV of every point, and a printable report with the closure and final coordinates.
How to use it
- 1
Press Use the tool, or Try the example to see a worked loop, link and level run.
- 2
Type or paste the control points, then each station's angle and distance — or the staff readings under Level run.
- 3
Read the misclosures and adjusted coordinates, then download the CSV or print the report.
Who it's for
- Land and engineering surveyors closing a control traverse
- Civil engineering students checking a field-book traverse or level run
- Site engineers carrying a level or coordinates round a site
Entering a traverse
- Control first: the start station needs known coordinates, and so does the reference object you sight from it (or type its bearing instead). A link traverse also needs the closing station and its reference.
- One row per station: the angle observed there and the distance to the next station. A loop ends with the closing angle back at the start; a link ends with the angle at the closing station.
- Angles are in d.mmss by default (124.3129 is 124°31'29"); decimal degrees and gon are under the angle format. Distances are horizontal, in metres.
- From Excel: copy the columns and paste into the first cell, or use Paste rows. Enter moves to the next cell and adds a row at the end.
Primary and secondary traverses
Work out the primary traverse first. Its adjusted stations become known points, so a secondary traverse can start on one and close on another, and a level run can start or close on them. Every station ends up in one list you can download.
For many points at once, or to see the stations on Google Earth, the same Traverse adjust is in the Excel to KML app.
Questions
Which adjustment should I use?
Bowditch spreads the misclosure in proportion to the leg lengths and suits angles and distances of similar quality. Transit spreads it by the size of each easting and northing change and suits better angles than distances. Least squares weighs every angle and distance by its standard error and gives residuals and a statistical test, so it is the most rigorous.
What format do the angles take?
By default d.mmss, so 81.3127 is 81°31'27". You can switch to decimal degrees or gon. Each angle is turned clockwise from the back station to the forward station; anticlockwise angles are an option.
How is the angular misclosure allowed?
As C√n seconds, where n is the number of angles. The primary, secondary and tertiary presets set C and the linear precision required; you can change both.
Does it adjust heights?
Yes, if you type the height difference for each leg the heights are carried round and their misclosure is spread too. For proper levelling use the Level run tab.
Is my work saved?
Only in this browser, so it is there when you come back. Nothing is sent anywhere. Start again clears it.
More free tools
- Coordinates on a mapClick the map, search a place or use your location to get its latitude and longitude, degrees-minutes-seconds, UTM zone and easting/northing, with a Google Maps link.
- DMS ↔ decimal degreesConvert degrees, minutes and seconds such as 25°11'35"N to decimal degrees and back — one value or a whole list pasted from Excel.
- Lat/long ↔ UTMConvert latitude and longitude to UTM easting, northing and zone on WGS 84, or UTM back to latitude and longitude. The zone is worked out for you.
- Distance and bearingThe distance and bearing between two points from latitude and longitude on the WGS 84 ellipsoid, or from eastings and northings on a grid — plus the point at a given bearing and distance.
- Plot area from coordinatesPaste the corners of a plot as eastings and northings or latitude and longitude and get its area in m², hectares, acres, kanal and marla, with the perimeter.
- Slope and gradientWork out a slope from rise and run, or convert between percent grade, degrees and 1 in N — for roads, drains, ramps and roofs.
Got a whole sheet of points?
Open the web app in your browser, or install the Windows app to work offline. Both are free, with no point limit.