drilling · directional
Dogleg Severity
β = arccos[cosI₁cosI₂ + sinI₁sinI₂cos(A₂−A₁)]; DLS = β × (100/ΔMD)
click formula to derive ↑
Inputs
°
°
°
°
ft
ft
Description
Computes the rate of wellbore curvature (dogleg severity) between two adjacent survey stations from their inclination and azimuth. DLS is the primary QC metric for directional surveys and governs casing wear, drillstring fatigue, and logging-tool passage risk.
Variables
| Symbol | Unit | Description |
|---|---|---|
| DLS | °/100ft | Dogleg Severity |
| I₁ | ° | Inclination at the upper (shallower) survey station. |
| A₁ | ° | Azimuth at the upper survey station, measured clockwise from north. |
| I₂ | ° | Inclination at the lower (deeper) survey station. |
| A₂ | ° | Azimuth at the lower survey station, measured clockwise from north. |
| MD₁ | ft | Measured depth of the upper survey station. |
| MD₂ | ft | Measured depth of the lower survey station. Must exceed MD₁. |
Assumptions
- Survey stations are accurate (verified gyro or properly corrected MWD survey)
- The wellbore curves smoothly (as a circular arc) between the two stations — no unsurveyed direction reversal in between
- Station spacing is short enough that the constant-curvature assumption is reasonable (typically ≤100 ft / 30 m)
Limitations
- DLS between widely spaced stations can mask real curvature if the wellbore direction reverses between surveys
- Does not by itself indicate which plane (build, turn, or both) the curvature occurs in — see min_curvature_survey for the 3D position
- Magnetic interference or poor gyro calibration can produce spurious azimuth changes that inflate apparent DLS
Use Cases
- → Real-time directional QC: Screen each new MWD survey against the planned curve to catch overbuild, key-seating risk, or tool-face control issues while drilling.
- → Casing and liner running risk: Identify high-DLS intervals before running casing or a liner to assess drag, buckling, and connection bending-stress risk.
- → Logging tool and ESP passage: Confirm planned curvature stays within the rated DLS limit for rigid logging tools, ESPs, or other equipment that must pass through the curve.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Bone Spring laterals typically build at 8-12°/100ft through the curve section, then hold DLS below 1-2°/100ft through the lateral to minimize casing wear over long horizontal runs.
Bakken
Build sections commonly target 10-12°/100ft to reach lateral inclination within a tight kick-off window dictated by Three Forks/Middle Bakken stacking.
Eagle Ford
High build rates (up to 15°/100ft) are used in short-radius curve designs to reach target laterals from constrained surface pad spacing.
Global
A DLS of 3°/100ft is a widely used conservative screening threshold for conventional 5-1/2" to 7" casing strings; liners and ESP-equipped wells often require tighter limits.
References
Primary source
Need geoscience support? BauerCalc is just one of the tools we build. If you're looking for independent expertise in well planning, geosteering, reservoir characterization, or opportunity evaluation, visit BauerSubsurface.com.