How to Calculate Ductility

••• vvvita/iStock/GettyImages

Ductility is a mechanical property of materials that refers to the degree of plastic deformation a material can sustain prior to fracture. If little or no plastic deformation can occur, the material is brittle. You can express ductility in terms of either a percent elongation or a percent reduction in an area. However, the values for percent elongation and percent reduction in area are not necessarily the same for the same material.

Calculating Percent Elongation

  1. Measure Gauge Length

  2. Measure the original gauge length (Lo) of the material around the point of intended fracture. This value is commonly 2 inches or 50 millimeters.

  3. Apply Tensile Force

  4. Apply a tensile force to the material slowly until fracture occurs.

  5. Measure Fracture Length

  6. Fit the broken parts back together and measure the fracture length (Lf), using the same endpoints on the material as the initially measured gauge length.

  7. Work out Elongation

  8. Calculate the percent elongation using the equation 100 x (Lf-Lo) ÷ Lo.

Calculating Percent Reduction in an Area

  1. Measure Diameter

  2. Measure the diameter of the solid cylindrical material to be tested (d).

  3. Find Area

  4. Calculate the original cross-sectional area (Ao) of the rod by inserting the diameter into the equation pi x (d ÷ 2)^2.

  5. Apply Tensile Force

  6. Apply a tensile force to the material slowly until fracture occurs.

  7. Find Area at Point of Fracture

  8. Measure the diameter of the cylinder at the point of fracture (df) then calculate the cross-sectional area at the point of fracture (Af), using the same equation.

  9. Apply Equation

  10. Calculate the percent reduction in area using the equation 100 x (Ao-Af) ÷ Ao.


    • The magnitude of percent elongation depends on specimen gauge length and therefore it is customary to specify the initial gauge length when reporting the percent elongation.


    • Metals tend to become more brittle in lower temperatures and more ductile in higher temperatures.


About the Author

Dylin Tweedie holds a Bachelor of Science in chemical engineering from the University of Connecticut and a Master of Science in mechanical engineering from Rensaleer Polytechnic Institute. Tweedie has worked in the field of power generation utilizing both conventional and renewable power sources, the environmental analytical chemistry field, water filtration devices field and food services industry. In her spare time, Tweedie is an avid enthusiast of both travel and outdoor sports and is the founder of the website