When a tensile load is applied into a drillstring, it results in elongation of the drillstring.
The formula to determine pipe elongation is listed below;
Oilfield unit
e = (L x T) ÷ (735,000 x W)
Where;
e = elongation, inch
L = length of drill string, ft
T = tensile load, lb
W = drill string weight, lb/ft
Metric (SI) unit
e = (L x T) ÷ (26.7 x W)
Where;
e = elongation, mm
L = length of drill string, metres
T = tensile load, kN
W = drill string weight, kg/m
Note: The equations are taken from API RP 7G 16th Edition, August 1998.
Determine the pipe elongation from the following data (this example will use “oilfield unit” for calculation.
5” DP, S-135, 4-1/2” IF Connection. The pipe specification is listed below.
W = 23.52 ppf
Length = 8,500 ft
Pick up weight = 300 Klb
Block weight without drill string = 70 Klb
Tensile load applied into the drill string is equal to pick up weight minus block weight.
T = 300 – 70 = 230 Klb
e = (8,500 x 230,00) ÷ (735,000 x 23.52)
e = 113.1 inch
Ref books: 
Drilling engineering books