Bowditch Adjustment Calculator
Adjust a closed traverse by the Bowditch (compass) rule. Enter each leg's whole-circle bearing and distance and a start coordinate, and the tool returns the linear misclose, the closure ratio (rate of error, 1 : X) and the fully adjusted latitudes, departures and coordinates — all in your browser.
Traverse legs
| To station | Bearing (DD) | Distance (m) | |
|---|---|---|---|
Enter the legs in order (whole-circle bearings 0–360°, clockwise from north). A loop returns to the start; a link traverse closes on the known end point you enter. Everything runs in your browser.
Misclose & rate of error
Traverse plot
Adjusted coordinates
| Stn | Bearing | Dist | Lat | Dep | Adj Lat | Adj Dep | E | N |
|---|---|---|---|---|---|---|---|---|
| B | 45° | 150.500 | 106.420 | 106.420 | 106.449 | 106.390 | 1106.390 | 2106.449 |
| C | 135° | 120.250 | -85.030 | 85.030 | -85.006 | 85.006 | 1191.396 | 2021.443 |
| D | 225° | 150.500 | -106.420 | -106.420 | -106.390 | -106.449 | 1084.947 | 1915.053 |
| A | 315° | 120.100 | 84.924 | -84.924 | 84.947 | -84.947 | 1000.000 | 2000.000 |
The Bowditch (compass) rule spreads the misclose across the legs in proportion to their length; the transit rule spreads it by each leg's latitude / departure. The adjusted coordinates close exactly on the start point.
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Enter the legs in order around the closed traverse: each leg's bearing (DD, DMS or DDM) and horizontal distance.
- Set the start easting and northing (any local or grid value).
- Read the linear misclose and closure ratio, then use the adjusted E/N coordinates in the table.
How it works
For each leg, latitude = distance × cos(bearing) and departure = distance × sin(bearing). Summing them gives ΣLat and ΣDep, which for a perfect closed traverse would both be zero.
The linear misclose is √(ΣLat² + ΣDep²) and the closure ratio (rate of error) is perimeter ÷ misclose, written 1 : X.
The Bowditch (compass) rule distributes the misclose across the legs in proportion to their length: δLat = −ΣLat × (leg ÷ perimeter) and δDep = −ΣDep × (leg ÷ perimeter). The adjusted latitudes and departures build coordinates that close back on the start.
Worked example
Worked example. A four-leg traverse with a small misclose returns, say, a linear misclose of 0.4 m over a 541 m perimeter — a closure ratio of about 1 : 1,350. The Bowditch rule then nudges each leg's latitude and departure so the coordinates return exactly to the start point.
Common mistakes
- Entering bearings as quadrant bearings (N45°E) instead of whole-circle bearings (0–360° clockwise from north).
- Leaving out a leg or entering legs out of order — the misclose and adjustment both depend on the full closed loop.
- Treating a large closure ratio denominator as worse; 1 : 8,000 is MORE precise than 1 : 3,000.
Frequently asked questions
Is the Bowditch rule the same as the compass rule?
Yes. The Bowditch method and the compass rule are the same adjustment — the misclose is spread in proportion to each leg's length. The transit rule spreads it by each leg's latitude/departure instead.
Does this also give the misclose and rate of error?
Yes — the tool shows the linear misclose, the misclose bearing and the closure ratio (rate of error, 1 : X) alongside the full Bowditch adjustment, so you do not need a separate misclose calculator.
Related tools
- Traverse Misclose Calculator
- Traverse Closure Ratio Calculator
- Compass Rule vs Transit Rule Comparison
- Area by Coordinates Worksheet
- Bearing & Distance to Coordinates Calculator
- Coordinates to Bearing & Distance Calculator
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Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.