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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.

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How to use this calculator

Traverse legs

Known coordinate stations

To stationBearing (DD)Distance (m)

Enter the legs in order (whole-circle bearings 0–360°, clockwise from north), then press Calculate. A loop returns to the start; a link traverse closes on the known end point you enter. Everything runs in your browser.

Enter the traverse legs above, then press Calculate to see the misclose, adjustment, area and plot.

How the calculations work

Every figure on this page comes from the steps below — the same compass-rule method a surveyor works by hand. θ is a whole-circle bearing (clockwise from north), d is horizontal distance, and Σ means “sum over all legs”.

1Latitude & departure of each leg

A leg's bearing and distance resolve into a northing component (latitude, ΔNorth) and an easting component (departure, ΔEast):
ΔNorth = d × cos θ ΔEast = d × sin θ
If you enter slope distances, each is first reduced to the horizontal using the vertical angle v:
d = slope length × cos v

2Bearings from angles (Angles mode)

When you work from turned angles instead of bearings, the first line's bearing is fixed and each station's angle to the right gives the next forward bearing:
Bₖ = ( Bₖ₋₁ + 180° + angleₖ ) mod 360°
With a closing angle back to the first line, the angular misclose is spread equally across the n turned angles:
angular misclose = B₁(computed) − B₁(known) correction per angle = − angular misclose ÷ n

3Misclose

Add up the components and compare the computed end point with where it should be — the start (loop) or the known end (link). The difference is the misclose:
eE = ( E_start + ΣΔEast ) − E_end eN = ( N_start + ΣΔNorth ) − N_end linear misclose e = √( eE² + eN² ) misclose bearing = atan2( eE , eN )

4Rate of error & survey class

The closure ratio compares the perimeter with the misclose. It passes if it is tighter than your chosen standard (e.g. 1 : 8,000):
rate of error = 1 : ( perimeter ÷ e )

5Bowditch (compass-rule) correction

The Bowditch rule distributes the misclose along the legs strictly in proportion to each leg's length. The same fraction — leg length ÷ total perimeter — is applied to both the easting and the northing error, giving the ΔE adj / ΔN adj column:
ΔE adjₖ = − eE × ( dₖ ÷ Σd ) ΔN adjₖ = − eN × ( dₖ ÷ Σd )
Adding it to the raw components gives the Adj ΔEast / Adj ΔNorth (the components after adjustment):
Adj ΔEastₖ = ΔEastₖ + ΔE adjₖ Adj ΔNorthₖ = ΔNorthₖ + ΔN adjₖ

6Final coordinates

Run the adjusted components out from the start coordinate. After the last leg they close exactly on the start (loop) or the known end (link) — the Final E / Final N column:
Eₖ = Eₖ₋₁ + Adj ΔEastₖ Nₖ = Nₖ₋₁ + Adj ΔNorthₖ

7Enclosed area (closed loop)

The area inside a closed loop comes from the adjusted coordinates by the shoelace formula:
A = ½ × | Σ ( Eₖ × Nₖ₊₁ − Eₖ₊₁ × Nₖ ) |
Then hectares = A ÷ 10,000 (metres) or acres = A ÷ 43,560 (feet).

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

  1. Enter the legs in order around the closed traverse: each leg's bearing (DD, DMS or DDM) and horizontal distance.
  2. Set the start easting and northing (any local or grid value).
  3. 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.

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Cite this tool

Zerdly. (2026). Bowditch Adjustment Calculator. Retrieved from https://www.zerdly.com/tools/bowditch-adjustment-calculator/

Tip: Enter any known values to calculate the remaining results.

Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.