Calculate mechanical stress, strain, and Young's modulus (modulus of elasticity) for any elastic material. Enter the applied force, cross-sectional area, original length, and final length — and get back axial stress, strain, and elastic modulus in seconds. Useful for engineering, materials science, and physics problems.
Axial Stress (σ)
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Stress (kPa)
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Strain (ε)
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Strain (%)
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Young's Modulus (E)
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Change in Length (ΔL)
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Mechanical (axial) stress is calculated as σ = F / A, where F is the applied force in Newtons and A is the cross-sectional area in square metres. The result is expressed in Pascals (Pa). Stress describes how much internal force per unit area a material experiences when an external load is applied.
Strain (ε) is calculated as ε = ΔL / L₁ = (L₂ − L₁) / L₁, where L₁ is the original length and L₂ is the final length after deformation. Strain is dimensionless — it has no units. For example, if a 2 m rod stretches to 2.004 m, the strain is (0.004) / 2 = 0.002, or 0.2%.
Young's modulus (E) is a measure of a material's stiffness. It is defined as the ratio of stress to strain: E = σ / ε. A higher Young's modulus means the material is stiffer and deforms less under the same load. Steel, for example, has a Young's modulus of about 200 GPa, while rubber can be as low as 0.01–0.1 GPa.
A high Young's modulus indicates that the material is very stiff — it requires a large amount of stress to produce even a small strain. Diamonds and steel are examples of high-modulus materials. Conversely, materials with a low Young's modulus, like rubber or foam, are much more flexible and deform easily under load.
A vertical pillar experiences compressive axial stress at any horizontal cross-section due to the weight of the material above that section. This is calculated using σ = F / A, where F is the weight force (mass × gravitational acceleration) of the segment above and A is the area of the cross-section at that point.
Yield strength is the stress at which a material begins to deform plastically — meaning it will not return to its original shape when the load is removed. Ultimate tensile strength (UTS) is the maximum stress a material can withstand before fracturing. Below the yield point, materials typically obey Hooke's Law and Young's modulus applies.
Modulus of elasticity is expressed in Pascals (Pa) in SI units, since it is the ratio of stress (Pa) to the dimensionless strain. In practice, because most engineering materials have very high moduli, gigapascals (GPa) are commonly used. 1 GPa = 1,000,000,000 Pa. In some fields, pounds per square inch (psi) or megapascals (MPa) are also used.
This calculator applies to materials that behave elastically — meaning they return to their original shape after the load is removed and stress is proportional to strain (Hooke's Law region). It is valid for metals, ceramics, and many polymers under small deformations. It does not account for plastic deformation, viscoelasticity, or non-linear material behaviour beyond the elastic limit.