Young's Modulus Calculator
Enter any two of stress, strain, and Young's modulus to solve for the third. Or supply applied force, cross-sectional area, original length, and change in length to let the calculator derive everything from scratch. Switch between metric and imperial units at any time. The result panel shows the worked steps, an annotated stress-strain curve, and a material reference table so you can compare your result against common engineering materials.
Formula
Worked example
A steel rod (E = 200 GPa) with a cross-section of 500 mm2 is pulled by a force of 10,000 N. Stress = F/A = 10000 / (500 x 1e-6 m2) = 20 MPa. Strain = sigma/E = 20 MPa / 200,000 MPa = 0.0001 (0.01%). If the rod is 100 mm long, it elongates by 0.01 mm.
What is Young's Modulus?
Young's modulus (symbol E, also called the modulus of elasticity or elastic modulus) is a material property that describes how much a solid deforms under tensile or compressive stress along an axis. It is defined as the ratio of longitudinal stress (force per unit area) to longitudinal strain (fractional change in length) in the linear elastic region of the material. A high modulus means the material is stiff: it requires a large stress to produce a small strain. Steel (around 200 GPa) is roughly 3 times stiffer than aluminum (around 69 GPa) and about 4,000 times stiffer than natural rubber (around 0.05 GPa). The concept was formalized by the British physicist Thomas Young in 1807, building on earlier work by Leonhard Euler and others.
The stress-strain formula and how this calculator uses it
The three linked quantities are stress (sigma = F/A), strain (epsilon = dL/L0), and Young's modulus (E = sigma/epsilon). Given any two, you can calculate the third. This calculator offers three solve modes. In Modulus mode, you supply stress and strain and the calculator returns E. In Stress mode, you supply E and strain and the calculator returns sigma. In Strain mode, you supply E and stress and the calculator returns epsilon. You can also enable the physical inputs toggle and enter applied force (F), cross-sectional area (A), original length (L0), and change in length (dL): the calculator derives stress and strain for you, then computes E. All stress and modulus values are converted internally to SI (pascals) and the result is displayed in GPa and MPa for metric users, and in psi for imperial reference.
When does Young's modulus apply?
Young's modulus is only valid in the linear elastic region of a material's stress-strain curve, below the proportionality limit. In this region, stress and strain are proportional (Hooke's law), and the deformation is fully recoverable when the load is removed. Once stress exceeds the yield strength, the material deforms plastically: the linear relationship breaks down, and this simple formula no longer applies. For large deformations or highly nonlinear materials (rubber, biological tissue), more complex constitutive models are used instead. Temperature also affects the modulus: it typically decreases as temperature rises, which matters in high-temperature engineering applications such as turbine blades or exhaust components.
How to read the material reference table
The reference table lists approximate room-temperature modulus values for 13 common materials spanning six orders of magnitude, from rubber (0.05 GPa) to diamond (1220 GPa). These are representative bulk values. Real modulus values depend on alloy composition, grain orientation, heat treatment, porosity, and measurement method, so always consult a certified material datasheet for design work. Wood is orthotropic: its modulus along the grain is 5-20 times higher than across it. Concrete is typically used in compression only and its modulus varies with mix design. For comparative purposes, the gauge visual on this page marks your computed modulus against the steel and aluminum reference bands.
Young's Modulus of Common Engineering Materials
| Material | Young's Modulus (GPa) | Notes |
|---|---|---|
| Diamond | 1220 | Highest natural modulus |
| Tungsten | 411 | Dense, stiff metal |
| Structural steel | 200 | Common engineering standard |
| Stainless steel (304) | 193 | Corrosion resistant |
| Cast iron | 170 | Brittle, compressive strength |
| Copper | 130 | Ductile, electrical conductor |
| Titanium alloy | 114 | High strength-to-weight ratio |
| Aluminum alloy | 69 | Lightweight structural material |
| Glass | 64 | Amorphous, brittle |
| Concrete | 30 | Varies by mix, compression only |
| Oak wood (along grain) | 12 | Orthotropic, varies with grain |
| Nylon 66 | 3 | Thermoplastic polymer |
| Rubber (natural) | 0.05 | Highly elastic, nonlinear |
Approximate values at room temperature. Real values vary with alloy, heat treatment, and direction of loading.
Frequently asked questions
What is the unit of Young's modulus?
Young's modulus has units of pressure (force per area) because strain is dimensionless. The SI unit is the pascal (Pa). In practice, values are quoted in megapascals (MPa) or gigapascals (GPa) for metals and ceramics, or in pounds per square inch (psi) or kips per square inch (ksi) in US engineering. Steel is approximately 200 GPa or 29,000 ksi.
What is the Young's modulus of steel?
Structural carbon steel typically has a Young's modulus of about 200-210 GPa (29,000-30,500 ksi). This value is remarkably consistent across most carbon and low-alloy steels and is largely independent of grade or heat treatment (unlike strength). Stainless steels are slightly lower at around 193 GPa.
What is the difference between Young's modulus, shear modulus, and bulk modulus?
These are three elastic moduli that describe different modes of deformation. Young's modulus (E) describes resistance to axial stretching or compression. Shear modulus (G) describes resistance to shear (angular) deformation. Bulk modulus (K) describes resistance to uniform volumetric compression. For isotropic materials, the three are related by Poisson's ratio (nu): G = E / [2(1 + nu)] and K = E / [3(1 - 2*nu)].
Why does Young's modulus matter in engineering design?
Engineers use Young's modulus to calculate deflections, natural frequencies, and buckling loads. A beam's stiffness under a point load depends directly on E times the area moment of inertia. Choosing a higher-modulus material (steel instead of aluminum, for example) reduces deflection for the same cross-section, or allows a smaller cross-section for the same deflection limit.
Does Young's modulus change with temperature?
Yes. For most metals, Young's modulus decreases as temperature increases. Steel loses roughly 3-4% of its room-temperature modulus at 200 degrees Celsius and about 30% at 600 degrees Celsius. This reduction is critical for structural fire safety calculations and for high-temperature machinery. Ceramics tend to retain their modulus to higher temperatures than metals.
How do I measure Young's modulus experimentally?
The most common method is a tensile test: a standard specimen is pulled in a universal testing machine, and load and extension are recorded. Stress and strain are calculated from load, original cross-section, and gauge length. The slope of the stress-strain curve in the linear elastic region is Young's modulus. Non-destructive alternatives include ultrasonic pulse-echo testing and resonant frequency methods, which measure acoustic wave speed and relate it to elastic constants.