Directional Drilling Survey Calculation Methods Guide

The purpose of this article is to understand how to perform various directional drilling survey calculation methods and terminology and we will provide a simple excel spreadsheet to help in your calculations as average angle, radius of curvature & minimum curvature Directional surveying spreadsheet.

Nowadays you will find a lot of soft-wares for the directional drilling survey calculations methods. In the same time, I have found good directional survey calculations excel spreadsheet which will help you in your calculations.

Regardless of which conventional directional survey method is used (single-shot, multishot, steering tool, surface readout gyro tool, MWD), the following three pieces of information are known at the end of a successful directional survey:

  • Survey Measured Depth
  • Borehole Inclination
  • Borehole Azimuth (corrected to relevant North).

In order to be sure the latest bottom-hole position, it is necessary to perform the directional survey calculation which includes the three inputs listed above. Only then, plot the latest bottom-hole coordinates on the directional well plot (TVD vs Vertical Section on the vertical plot, N/S vs E/W rectangular coordinates on horizontal plot). Then, you can do the projections to the target, etc.

The Purpose Directional Drilling Survey Calculations

  • Orient deflection tools for navigating well paths.
  • Determine the exact bottom hole location to monitor reservoir performance.
  • Monitor the actual well path to ensure reaching the target.
  • Fulfill requirements of regulatory agencies, such as the Minerals Management Service (MMS) in the U.S.
  • Calculate the TVD of the various formations to allow geological mapping.
  • Ensure that the well does not intersect nearby wells.
  • Evaluate the Dog Leg Severity (DLS), the total angular inclination and azimuth in the wellbore, calculated over a standard length (100 ft or 30 m).

Principles of Surveying

surveying calculations

The basic principles of directional drilling surveying calculations can be illustrated by considering the two dimensional system shown below. The position (co-ordinates) of point, B relative to the reference point A can be determined if the angle α and the distance AB is known. If the position of point A is defined as 0,0 in the X, Y coordinate system the position of point B can be determined by the following equations:

YB = AB Sin α

XB = AB Cos α

Hence the displacement of point B in the X and Y direction can be determined if the angle α and the linear distance between A and B are known. The same procedure can determine the position of a further point C. The X and Y displacement of C relative to the reference point A can be determined by adding together the X and Y displacement of Point B to A and those of Point C to B.

This process of defining the position of a point relative to a specific reference point can be continued for any number of points.

Wellbore Surveying

This same principle as that above is applied to wellbore surveying. In the case of directional drilling surveying by any method however the calculations procedure must include consideration of the following:

  • The process must be applied in three dimensions
  • The trajectory between the survey points (the path of the wellbore) is not generally a straight line

The three dimensional aspect of the problem is not a significant issue since the same process as that outlined above can be applied to the vertical displacement as well as the horizontal displacement of the survey points (stations). The procedure is described below.

The fact that a straight line does not generally define the trajectory of the wellbore is accommodated by assuming that the trajectory of the wellbore follows a simplified geometrical model.

Now Let’s check the below figure & below definitions to fully understand all directional drilling survey calculations methods and terminology.

Directional Drilling Survey Calculations Excel Spreadsheet
  • “O” is the Reference Point for the Well.
  • “S” is the Surface Location Reference Point.
  • “B” is a Survey Point.
  • “a” is the Azimuth in degrees of the Vertical Section plane. It is measured in a Horizontal Plane from the North Direction (geographic), beginning at 0° and continuing through 360° (clockwise from North axis).
  • “TVD” is the projection of SB (Measured Depth, MD, along the well path) onto the vertical axis “z”. The distance is SB3.
  • “HD” is the Horizontal Displacement, measured in the Horizontal plane passing through the Survey Point. The distance is BB3 (between Survey point end “z” axis).
  • “VS” is the Vertical Section; it is the length of the Horizontal Displacement (HD) projection onto the Vertical Section plane defined by its azimuth. The distance is B3B2.
  • “A Vertical Section Plane” is defined by its Azimuth and the U.S. origin point. Usually, the Vertical Section passing through the center of the Target is used for plotting the well profile.

How To Determine The Coordinates Of Directional Survey stations

The only information that is required to perform Directional Drilling Survey Calculations by any of its methods & to determine the coordinates of all points in the well trajectory are therefore:

First, The position of the initial reference point

(generally the Rotary Table)

Second, The measured depth (AHD) of the survey station

The depth of the survey station is provided by the driller and is calculated based on the length of drill string in the wellbore and the distance between the drillbit and the survey tool.

Third, The direction (Degrees from North) at the survey station

The direction in which the drill bit is pointing when a survey is taken is expressed in degrees azimuth.

Azimuth is the angle in degrees (°) between the horizontal component of the wellbore direction at a particular point, measured in a clockwise direction from the reference (generally North). Azimuth is generally expressed as a reading on a 0 – 360° (measured from the North) scale. For directional surveying, there are three azimuth reference systems :

  • Magnetic north;
  • True (Geographic) North;
  • Grid North.

Azimuth Reference Systems

Magnetic North (MN)

This is the direction of the horizontal component of the Earth’s magnetic field lines at a particular point on the Earth’s surface. A magnetic compass will align itself to these lines with the positive pole of the compass indicating North.

True (Geographic) North (TN)

This is the direction of the geographic North Pole. This lies on the axis of rotation of the Earth. The direction is shown on maps by the meridians of longitude.

Grid North (GN)

The meridians of longitude converge towards the North Pole and South Pole and therefore do not produce a rectangular grid system. The grid lines on a map form a rectangular grid system, the Northerly direction of which is determined by one specified meridian of longitude. The direction of this meridian is called Grid North.

For example, in the often-used Universal Transverse Mercator (UTM) coordinate system, the world is divided into 60 zones of 6 degrees of latitude, in which the central meridian defines Grid North. Grid North and True North are only identified for the central meridian. Comparison of co-ordinates is only valid if they are in the same grid system.


All azimuths must be quoted in the same reference system to be meaningful. This is usually the Grid North system. Azimuths are often measured in systems other than the Grid North system.

Two conversions typically have to be applied to the measured azimuths:

  • Grid Convergence
  • Declination
Grid Convergence :

Grid convergence converts azimuth values between the Grid North and the specified True North system.

The grid convergence angle is the angle between the meridians of longitude (TN) and the North of the particular grid system (GN) at a given point. By definition, the grid convergence is positive when moving clockwise from True North to Grid North and negative when moving anti-clockwise from True North to Grid North.

The value of grid convergence depends upon location. Close to the Equator, the convergence is slight and it increases with increasing latitude.


Declination converts azimuth values between the Magnetic North and True North systems.

Declination is the angle between the horizontal component of the Earth’s magnetic field lines and the lines of longitude. By definition, the declination is positive when moving clockwise from True North to Magnetic North, and negative when moving anti-clockwise from True North to Magnetic North.

Values of declination change with time and location and that representative of the parameters at the time of drilling should be used.

Fourth, The inclination (Degrees from the vertical) of the wellbore at the survey station

The inclination of the wellbore is the angle in degrees that the wellbore deviates from the vertical.

Directional Drilling Survey Calculations Methods / Models & Terminology

Several directional drilling survey calculation methods have been used in oilfields. At the end of the article, you shall know that you can download the directional drilling Excel spreadsheet.

Only four have had widespread use:

  • Tangential calculation method.
  • Average Angle calculation method.
  • The radius of Curvature calculation method.
  • Minimum Curvature calculation method.

The Tangential Calculation Method is the oldest, least sophisticated and most inaccurate directional survey calculation method. This method should never be used.

Average Angle and Radius of Curvature Directional drilling survey calculations methods are in common field use. Average Angle method (in particular) lends itself easily to a hand-held calculator. Radius of Curvature method is more widely used. However, official directional survey reports should not use either if the above methods except when demanded by the customer.

Minimum Curvature survey calculation method should be used for all office calculations and official survey reports. Where possible, it should also be the field calculation method chosen. The directional driller is advised to have at the well-site a hand-held calculator which is programmed for both Radius of Curvature and Minimum Curvature methods of directional survey calculation Terminology.


“Most Inaccurate Directional Drilling Survey Calculation Methods & Terminology”

Tangential Survey Calculations Method

This method uses the inclination and hole direction at the lower end of the course length to calculate a straight line representing the wellbore that passes through the lower end of the course length. Because the wellbore is assumed to be a straight line throughout the course length, it is the most inaccurate of the methods discussed and should be abandoned completely.

∆ North = ∆ MD sin I2 cos A2
∆ East = ∆ MD sin I2 sin A2
∆ TVD = ∆ MD cos I2
∆ Displacement = ∆ MD sin I2

Balanced Tangential Calculations Method

Modifying the tangential directional drilling survey calculation method & Terminology by taking the direction of the top station for the first half of the course length, then that of the lower station for the second half can substantially reduce the errors in that method. This modification is known as the balanced-tangential method.

This method is very simple to program on hand-held calculators and gives accuracy comparable to the minimum curvature method, see the below spreadsheet.

∆North =1/2 x ∆MD (sin I1 cos A1 + sin I2 cos A2)
∆East = 1/2 x ∆MD (sin I1 sin A1 + sin I2 sin A2)
∆TVD = 1/2 x ∆MD (cos I1 + cos I2)
∆ Displacement = 1/2 x ∆MD (sin I1 + sin I2)

Average angle Directional Drilling Survey Calculation Method With Excel Spreadsheet

Average angle Directional survey Calculation Method

The directional survey calculation method uses the average of the inclination and hole-direction angles measured at the upper and lower ends of the course length. The average of the two sets of angles is assumed to be the course length’s inclination and direction. The well path is then calculated with simple trigonometric functions.

∆ North = ∆ MD sin A cos B
∆ East = ∆ MD sin A sin B
∆ TVD = ∆ MD cos A
∆ Displacement (CD) = ∆ MD sin A
∆ Vertical Section = CD x cos ( B – target direction)


A = (I1+I2)/2
B = (A1+A2)/2

Download The Directional Drilling Survey Calculation Excel Spreadsheet For Average angle Method & Terminology From Below.


The Radius of Curvature Directional Drilling survey Calculation Methods & Terminology, which is more widely used With Excel Spreadsheets.

Radius of Curvature method surveying spreadsheet

With the inclination and hole direction measured at the upper and lower ends of the course length, this directional survey calculation method generates a circular arc when viewed in both the vertical and horizontal planes. Curvature radius is one of the most accurate methods available.

In the below directional drilling survey calculations Excel spreadsheet, you will find that we are using this method to get these calculations.

Radius of Curvature directional drilling method surveying spreadsheet

Also There is another directional drilling calculation excel spreadsheet provided by drillingformula which is a good one to use quickly.

Radius of Curvature directional drilling method surveying spreadsheet

Minimum Curvature: Most Accurate Directional Drilling survey calculations methods and terminology With Excel Spreadsheet

minimum curvature directional surveying method spreadsheet

Brfore Downloading Minimum Curvature Method Spreadsheet, you shall know that, this method, the most accurate of all listed, uses the inclination and hole direction measured at the upper and lower ends of the course length to generate a smooth arc representing the well path.

The difference between the curvature-radius and minimum curvature directional drilling survey calculation methods and terminology is that curvature radius uses the inclination change for the course length to calculate displacement in the horizontal plane (the true vertical depth [TVD] is unaffected). In contrast, all minimum curvature method spreadsheet uses the Dogleg Severity (DLS) to calculate displacements in both planes.

Minimum curvature method in below spreadsheet is considered to be the most accurate method, but it does not lend itself easily to normal, hand-calculation procedures.

minimum curvature method spreadsheet for directional Directional Drilling survey calculation methods & Terminology
Minimum curvature method directional drilling excel spreadsheet Calculations

You Can Download This amazing Directional drilling survey calculation From Drilling-Formula For Minimum Curvature Method spreadsheet From Below

download minimum curvature directional surveying method spreadsheet

Mercury Survey Calculation Method

So-called because it was used at Mercury, Nevada at the U. S. nuclear test site. This directional survey calculation method combines the tangential and balanced tangential calculation methods and considers the length of the survey tool (STL).It treats the portion of the course over the length of the survey tool as a straight line (i.e.tangential) and the rest of the course in a balanced tangential manner.

∆ TVD = (∆MD-STL) /2 × (cos I1+cos I2)+STL × cos I2
∆ North = (∆MD-STL) /2 × (sin I1+cos A1+sin I2 cos A2)+ STL × sin I2 cos A2
∆ East = (∆MD-STL) /2 × (sin I1+sin A1+sin I2 sin A2)+ STL × sin I2 sin A2

Comparison Between Different Directional Drilling Survey Calculation Methods & Terminology

The directional survey results are compared against those from the minimum-curvature method, as shown in Below Table. Large errors are seen in the tangential method for only approximately 1,900 ft of deviation.

This demonstrates that the tangential method is inaccurate and should be abandoned altogether. The balanced-tangential and average-angle methods are more practical for field calculations and should be used when sophisticated computational equipment or expertise is unavailable. These should be noted as “Field Results Only.”

accuracy difference in directional survey calculation methods

Dogleg severity

Dogleg Severity is a measure of the amount of change of inclination and/or direction of a bore hole. It is usually expressed in degrees per 100 feet or degrees per 10 or 30 metres of course length.

Several formulae are available to compute the total effects when there is a change in both inclination and direction between survey points. In the following formulae:

Dogleg severity (DLS) = {cos-1 [(cos I1 x cos I2) + (sin I1 x sin I2) x cos (A2 – A1)]} x (100 ÷ MD)

I1 = Inclination at Survey point 1
A1 =Azimuth at Survey point 1
I2 =Inclination at Survey point 2
A2 =Azimuth at Survey point 2

The above formula is commonly used in estimating fatigue and strength criteria for tubular goods. It makes no assumptions about the well path, and is therefore independent of survey calculation methods.

Download Now Drilling Survey Calculations Excel Spreadsheet

This directional drilling calculation excel spreadsheet version made by Drill-Bite has a number of new features as:

  • Compatibility with Excel 2007 to 2013 for Windows 32 and 64 bits (WinXP, Win7, Win8)
  • Storing of multiple branches of the same well
  • Anti-collision calculation (center to center only)
  • Multiple wells drawing
  • New file storing data (no backward compatibility provided)

3 thoughts on “Directional Drilling Survey Calculation Methods Guide”

  1. Madam/ Sirs,

    Do you have a formula in SI (Metric, ie meters) for BURR (Build-Up Rate Required) for directional drilling in oil and gas well drilling?

    N.B. Your site is awesome !

    Thank you.


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