True Vertical Depth Calculator: TVD, Displacement, and Dogleg Severity From MD and Survey

Calculate true vertical depth, horizontal displacement, and dogleg severity between directional survey stations using the minimum curvature method, build a full multi-station wellbore trajectory, or solve the measured depth interval a target dogleg severity requires. Everything updates live.

True Vertical Depth From Measured Depth and Survey

Measured depth is the actual length of pipe or wireline run into the well along the wellbore path, while true vertical depth, or TVD, is the straight down distance from surface. In a vertical well the two are equal, but as soon as a well builds angle they diverge, and converting between them correctly requires knowing the inclination and azimuth at each survey station along the way, not just the total measured depth and a single average angle.

This tool covers a quick conversion between two survey stations, a full multi-station trajectory with a plotted well path, and a reverse solve for the measured depth interval needed to hit a target dogleg severity.

The Minimum Curvature Method

The minimum curvature method is the industry standard for directional survey calculations because it treats the wellbore between two survey stations as a smooth circular arc rather than a straight line. The dogleg angle between the two directions is found from the change in inclination and azimuth, and a ratio factor spreads that curvature evenly across the interval. Delta TVD, delta north, and delta east are each computed from the average of the two station directions scaled by this ratio factor, which is more accurate than simpler tangential methods, especially across intervals with significant direction change.

Dogleg severity expresses the same dogleg angle as a rate, normalized to degrees per 100 feet of measured depth, which is the standard way the drilling industry compares how sharply different intervals of a well are turning.

Building a Full Trajectory

A complete wellbore trajectory is built by applying the minimum curvature calculation station by station, carrying the cumulative TVD, north, and east forward from one interval to the next. Plotting cumulative TVD against horizontal displacement gives the classic well path plan that shows how much a well has moved off vertical by any given depth, which is essential for anti-collision checks against nearby wellbores and for confirming a planned target will actually be reached.

Solving for Required Measured Depth

The dogleg angle between two directions depends only on the starting and ending inclination and azimuth, not on how much measured depth separates them, so it can be solved independently first. Once the dogleg angle is known, the measured depth interval needed to keep dogleg severity at or below a target value follows directly: spreading the same total turn over more feet always lowers the severity. This reverse solve is useful when planning how quickly a build section can turn without exceeding a casing or completion tool dogleg severity limit.

Common Mistakes

Using the tangential method, which averages the two station angles as straight lines rather than fitting a smooth arc, and quietly understates displacement in wells with significant turn between stations.

Forgetting that azimuth wraps around 360 degrees, so a change from 350 to 10 degrees is a 20 degree turn, not a 340 degree one, which the minimum curvature formula handles correctly through the cosine terms but a naive subtraction would not.

Applying a single average dogleg severity across a long interval instead of computing it station by station, which can hide a short, sharp turn that exceeds a tool or casing limit even though the overall average looks acceptable.

Ignoring magnetic declination or grid convergence corrections on raw azimuth readings, which shifts the entire calculated well path sideways even though the TVD is unaffected.

Who Uses This

Directional drillers and well planners converting measured depth surveys into true vertical depth and displacement.

Drilling engineers checking that build sections stay within a target dogleg severity for casing and completion tool limits.

Geologists correlating log depths and formation tops between measured depth and true vertical depth in deviated wells.

Students and early career engineers learning how the minimum curvature method converts a directional survey into a wellbore trajectory.

Try It Above

Use the quick convert tab for a single interval between two survey stations, move to the multi-station survey tab to build and plot a full wellbore trajectory, or use the solve tab when you need the measured depth interval a target dogleg severity requires.

Related Calculators and References

Continue building your workflow with the Equivalent Circulating Density Calculator. For background on the formulas used above, see PetroWiki: Calculation Methods for Directional Survey.