Young's Modulus Strain Calculator
Young's modulus measures how stiff a material is when stretched or compressed. Enter the applied force, the cross-sectional area, the original length, and the extension to compute the tensile stress, the strain, and the resulting Young's modulus. The calculator divides force by area to get stress, divides extension by original length to get strain, and divides stress by strain to get the modulus. These relationships hold only in the elastic region, below the material's yield point.
Young's modulus formula
Stress sigma = F / A
Strain epsilon = dL / L0
Young's modulus E = sigma / epsilon = (F * L0) / (A * dL)
Stress is force per unit area in pascals. Strain is the fractional change in length and has no units. Young's modulus is the ratio of the two and applies only in the elastic region, below yield.
Worked example
A 10,000 N force acts on a rod of area 0.0001 m2 and original length 2 m, stretching it by 0.001 m. Stress = 10,000 / 0.0001 = 100,000,000 Pa. Strain = 0.001 / 2 = 0.0005. Young's modulus = 100,000,000 / 0.0005 = 200,000,000,000 Pa = 200.00 GPa, close to structural steel.
Young's modulus: frequently asked questions
What is Young's modulus?
Young's modulus (E) is a material's stiffness in tension or compression. It is the ratio of stress to strain in the elastic region: E = stress / strain. A higher modulus means a stiffer material that deforms less under the same stress.
How are stress and strain defined?
Stress is force divided by cross-sectional area (sigma = F / A), measured in pascals. Strain is the change in length divided by the original length (epsilon = dL / L0), and is dimensionless.
What units does this calculator use?
Force in newtons, area in square metres, and lengths in metres. Stress and Young's modulus are returned in pascals (Pa). To convert to megapascals divide by 1,000,000, and to gigapascals divide by 1,000,000,000.
Is this valid beyond the elastic limit?
No. Young's modulus and the linear stress-strain relationship only hold within the elastic region, below the material's yield point. Past yield the material deforms plastically and E no longer applies.
Sources
- NIST: SI units (pascal, newton, metre).
- The stress-strain relation and Young's modulus are standard results of classical elasticity theory.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.