Differential leveling measures elevation differences using the formula: HI = benchmark elevation + backsight rod reading; point elevation = HI − foresight rod reading. Always close the loop back to a known benchmark and verify the closure error is within tolerance (typically ±0.05 ft for field grade work) before accepting any intermediate elevations.
Why Differential Leveling Matters
Every grade check, pipe invert verification, and as-built elevation traces back to a differential leveling loop. GPS rovers compute the same math electronically. Understanding the manual method lets you verify suspect elevations, set up without electronics when needed, and catch errors before they propagate through a day of work.
Core Formulas
Point Elevation = HI − Foresight (FS) rod reading
Closure Check: ∑BS − ∑FS = closing BM elevation − starting BM elevation
Step-by-Step Procedure
1. Shoot the Benchmark (Backsight)
Backsight reading: 4.82 ft
HI = 285.43 + 4.82 = 290.25 ft
2. Shoot Foresights to Work Points
Point elevation = 290.25 − 3.15 = 287.10 ft
Design elevation: 287.20 ft | Deviation: −0.10 ft (LOW)
3. Move the Instrument Using Turning Points
A turning point (TP) carries elevation forward when the instrument must move. Shoot a foresight at the TP with the old setup, then a backsight at the TP with the new setup.
(Move instrument) Backsight at TP-1: 5.13 ft → New HI = 287.77 + 5.13 = 292.90 ft
4. Close the Loop and Check Closure
Calculated elevation = 292.90 − 7.48 = 285.42 ft
Published elevation: 285.43 ft | Closure error: +0.01 ft ✓ (within ±0.05 ft)
Field Notes Table
| Station | BS (+) | HI | FS (−) | Elevation | Notes |
|---|---|---|---|---|---|
| BM-1 | 4.82 | 290.25 | — | 285.43 | Brass disk NW corner |
| Pad SW | — | — | 3.15 | 287.10 | Design 287.20; −0.10 |
| TP-1 | 5.13 | 292.90 | 2.48 | 287.77 | Hub in gravel |
| BM-1 close | — | — | 7.48 | 285.42 | Error: −0.01 ✓ |
Allowable Closure
| Survey Type | Allowable Closure |
|---|---|
| Field grade checks | ±0.05 ft |
| DOT third-order survey | 0.05 ft × √(miles) |
| Second-order survey | 0.017 ft × √(km) |
Common Mistakes
- Moving the instrument between BS and FS: Any movement changes the HI, invalidating all subsequent foresights from that setup.
- Unstable turning point: A TP that settles between the foresight and backsight throws the entire traverse. Use a steel pin or a concrete surface.
- Not recording immediately: Write every reading in the field book the moment it is taken. Memory fails after two or three setups.
Use the Elevation Calculator to pre-compute HI and target rod readings. See also: Reading a Grade Rod: Field Guide.