Choose a constant type; enter known values. Instantly compare SI and custom units, plus checks. Download results, view examples, and learn how it works.
| Mode | Inputs (sample) | Output (approx.) | What it suggests |
|---|---|---|---|
| Spring constant (k) | F = 120 N, Δx = 0.015 m | k ≈ 8000 N/m | Stiffer spring gives smaller deflection. |
| Young’s modulus (E) | F = 3500 N, A = 250 mm², ΔL = 0.8 mm, L₀ = 500 mm | E ≈ 8.75×10¹⁰ Pa (87.5 GPa) | Higher E means less axial stretch. |
| Shear modulus (G) | F = 900 N, A = 400 mm², Δx = 0.5 mm, L = 50 mm | G ≈ 2.25×10⁸ Pa (225 MPa) | Higher G resists shape distortion. |
| Bulk modulus (K) | ΔP = 1.6 MPa, V₀ = 2 L, ΔV = -8 cm³ | K ≈ 4.0×10⁸ Pa (0.4 GPa) | Higher K means less compressible fluid/solid. |
Elasticity constants quantify how strongly something resists deformation. A spring constant k links force to deflection, while material moduli (E, G, K) link stress to strain. Higher values typically mean greater stiffness, but the meaning depends on the loading mode.
For a spring operating in its linear range, Hooke’s law uses k = F/Δx. If a spring has k = 8000 N/m, then 80 N produces about 0.01 m deflection. Nonlinear springs exist, but k is still useful for small deflections or for an average stiffness over a chosen range.
Young’s modulus E describes axial stiffness. Many structural steels are around 200 GPa, aluminum alloys are commonly near 69–72 GPa, and titanium alloys are often near 110 GPa. Polymers vary widely, from hundreds of MPa to several GPa, and rubber-like materials can be far lower.
Shear modulus measures resistance to sliding deformation. For isotropic materials, G relates to E and Poisson’s ratio ν by G = E / (2(1+ν)). With steel (E ≈ 200 GPa, ν ≈ 0.30), G is roughly 77 GPa.
Bulk modulus describes how volume changes under pressure. Water at room conditions is commonly near 2.2 GPa, meaning it is hard to compress. Gases have much smaller effective bulk modulus at low pressures. In the formula K = -ΔP/(ΔV/V₀), compression gives negative ΔV, so the minus sign makes K positive.
Material stiffness alone does not guarantee a stiff part. In axial loading, elongation scales with L₀ and inversely with area A. Doubling the length doubles extension, while doubling the area halves extension, even if E stays constant. The calculator highlights this through stress and strain conversions.
Most errors come from mixed units: mm with m², or MPa with Pa. This tool converts to SI internally, then converts back to your chosen output. If your answer looks off by factors of 1000 or 1,000,000, re-check length and area units first, then pressure units.
Large strains, plastic deformation, temperature effects, and viscoelasticity can break the simple formulas. Metals can yield, polymers can creep, and rubbers can be strongly nonlinear. Treat the computed value as a linear estimate around the measured range, then validate with test data or standards.
No. k is a component stiffness (force per deflection). E is a material property (stress per strain). A spring’s k depends on its geometry and material.
Compression usually gives negative ΔV while ΔP is positive. The minus sign makes K positive for compression. Use “magnitude” if you prefer an always-positive result.
Use consistent units that match your measurements. Common choices are N, mm, and mm² for test rigs. The calculator converts to SI internally, so accuracy mainly depends on correct unit selection and precise inputs.
Only if you also know Poisson’s ratio ν and the material is isotropic. Then G = E/(2(1+ν)). Otherwise, measure shear response or use published data for your material.
First check mm vs m, and mm² vs m². Next check kPa/MPa/GPa vs Pa. A small unit mismatch can change results by 10³ or 10⁶, especially in modulus calculations.
No. Modulus measures stiffness, not strength. A material can be stiff but brittle, or flexible but tough. Strength relates to yielding or fracture limits, which are separate properties from E, G, or K.
You can, but treat results as an approximate linear stiffness over your chosen range. Rubber and many polymers change stiffness with strain, temperature, and time, so confirm with experimental curves or manufacturer data.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.