Radius of Curvature Method is the most famous method for directional survey calculation. You can calculate North, East and TVD between directional surveys based on the Radius of Curvature Method as per formula below:
Where;
MD = measured depth between surveys in ft
I1 = inclination (angle) at upper survey in degrees
I2 = inclination (angle) at lower in degrees
Az1= Azimuth direction at upper survey
Az2 = Azimuth direction at lower survey
Calculation example for Radius of Curvature Method
Survey 1
Depth = 7500 ft
Inclination = 45 degree (I1)
Azimuth = 130degree (A1)
Survey 2
Depth = 7595 ft
Inclination = 52 degree (I2)
Azimuth = 139 degree (A2)
MD = 7595 – 7500 = 95 ft
As per the calculation above,
North = -49.97 ft
East = 50.66 ft
TVD = 62.91 ft
Please find the Excel sheet used for directional survey calculation with Radius of Curvature Method.
Ref book: 
Formulas and Calculations for Drilling, Production and Workover, Second Edition
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September 15th, 2009 at 4:13 pm
[...] Dogleg severity (DLS) is a normalized estimation, normally described in degrees per 100 feet or degree per 30 meters, of the overall well bore curvature between two consecutive directional surveys. Regarding a planned well path, dogleg severity may be synonymous about build and/or turn. The following formula provides dogleg severity in degrees/100 ft based on the Radius of Curvature Method. [...]
February 18th, 2010 at 8:49 am
You have a mistake in you TVD calculation equation for the radius of curvature method – you need to multiply nb 180/pi instead of (180/pi)^2
February 18th, 2010 at 10:13 am
Hi Harris,
Thanks very much for checking me. It is my mistake when I typed in up. However, the calculation sheet in this post is correct. I already double check it. I correct my post as well.
Cheers,
Rachain J.