Free Surveying Tool
Level Loop Closure Calculator
Enter your rod readings and get misclosure, tolerance check, and Bowditch-adjusted elevations — instantly. Single-wire and three-wire modes.
Level Mode
Benchmark ID
Known Elevation (ft)
Tolerance Standard
Level Loop Readings
BS = Backsight · FS = Foresight · HI = Height of Instrument. Distances optional — needed for tolerance check and Bowditch adjustment.
| Station | Backsight (BS) | H.I. (calc) | Foresight (FS) | Dist (ft) | Elevation (calc) | |
|---|---|---|---|---|---|---|
| — | — | |||||
| — | — | |||||
| — | — |
Level Loop Reference
Backsight (BS)
A rod reading taken on a point of known elevation. Added to the known elevation to compute the Height of Instrument (HI = Elev + BS).
Foresight (FS)
A rod reading taken on a new point to establish its elevation. Subtracted from the HI (Elev = HI − FS).
Height of Instrument (HI)
The elevation of the instrument's line of sight. Computed as HI = known elevation + backsight reading.
Turning Point (TP)
A temporary benchmark used to extend the level loop beyond one instrument setup. Both a foresight and backsight are taken on each TP.
Misclosure
The difference between the computed closing elevation and the known benchmark elevation. A perfect loop yields 0. Also equals Σ BS − Σ FS.
Bowditch Rule
Distributes the misclosure proportionally along the loop based on the cumulative distance traveled. Correction at each point = −misclosure × (cumulative dist / total dist).
Three-Wire Leveling
Taking top, middle, and bottom stadia wire readings for each rod shot. The mean of the three wires is used for elevations. Equal intervals (|T−M| ≈ |M−B|) indicate a quality reading.
Stadia Distance
Approximate horizontal distance derived from three-wire leveling: Distance = 100 × (Top − Bottom). Useful for computing section lengths for the Bowditch adjustment.
Tolerance Standards
| Order | Tolerance (ft) | Tolerance (mm) | Typical Use |
|---|---|---|---|
| First Order Class I | ±0.014√M | ±4√K | Primary geodetic control, dam monitoring |
| First Order Class II | ±0.020√M | ±5√K | Secondary geodetic, major infrastructure |
| Second Order Class I | ±0.025√M | ±6√K | State plane control, highway projects |
| Second Order Class II | ±0.035√M | ±8√K | Local control, bridge surveys |
| Third Order | ±0.050√M | ±12√K | General land surveys, topographic |
M = total loop distance in miles · K = total loop distance in kilometers
Level Loop Formulas
// Height of Instrument
HI = Elevationknown + BS
// New point elevation
Elevationnew = HI − FS
// Misclosure
e = Elevationclosing − ElevationBM = Σ BS − Σ FS
// Bowditch correction at point i
Ci = −e × (di / dtotal)
// Three-wire mean
Mean = (Top + Mid + Bot) / 3
// Three-wire balance check
|T − M| − |M − B| ≤ 0.003 ft