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
Directional Drilling Books
