Directional Survey Dogleg Severity Calculator (Minimum Curvature Method)

Dogleg severity, DLS, measures how sharply a wellbore curves between two directional survey stations, expressed in degrees per 100 feet (or per 30 meters in metric practice). It combines the change in inclination and the change in azimuth over the measured depth between stations into a single bend angle. This calculator uses the minimum curvature method, the industry standard for computing dogleg severity and for building a wellbore trajectory from raw survey readings.

Why dogleg severity matters

Every bend in a wellbore bends the drill string and casing with it. High dogleg severity increases bending stress and fatigue on drill pipe and tool joints, raises torque and drag, accelerates casing wear at contact points, and can prevent logging tools, completion equipment, or even the casing itself from passing through. Directional drillers track DLS at every survey station to keep the build, turn, or drop rate within limits the string and casing can tolerate.

Minimum curvature method

Between two survey stations with inclination I1, I2 and azimuth Az1, Az2, the dogleg angle beta is found from:

cos(beta) = cos(I2 - I1) - sin(I1) x sin(I2) x (1 - cos(Az2 - Az1))

Dogleg severity is then the bend angle scaled to a standard course length:

DLS = beta / (MD2 - MD1) x 100, in degrees per 100 feet

The same minimum curvature method also gives the true vertical depth, north, and east coordinates of each station using a ratio factor RF = (2/beta) x tan(beta/2), applied to the average of the inclination and azimuth terms at the two stations. This calculator reports both the dogleg severity between each pair of stations and the resulting cumulative TVD, north, and east position, so a full station-by-station survey can be checked in one pass.

Worked example

Starting vertical at surface, then a station at 1,000 ft MD with 5 degrees inclination and 45 degrees azimuth, then a station at 1,100 ft MD with 10 degrees inclination and 50 degrees azimuth, the first interval has a dogleg severity of about 0.5 deg/100ft, gentle enough for a simple build. The second, shorter interval has a dogleg angle of about 5.0 degrees over only 100 ft of course length, giving a dogleg severity of about 5.0 deg/100ft, a noticeably tighter curve that would be worth flagging for torque and drag and casing wear review.

Directional Survey Dogleg Severity Calculator

Related Calculator and Reference

To check torque and hookload along the same trajectory, see the Torque and Drag (Soft String Model) Calculator. Formula reference: minimum curvature method, directional drilling survey calculations.