# Spring Rate Calculator Calculate the stiffness (spring rate) of a cylindrical helical compression/extension spring. k = G·d⁴ / (8·D³·n) in N/mm. Includes shear-modulus presets for common spring materials. > Canonical page: https://elysiatools.com/en/tools/spring-rate-calculator - **Category:** Math & Numbers - **Keywords:** spring rate, spring constant, helical spring, stiffness, compression spring, shear modulus, Hooke's law, mechanical engineering ## Overview The Spring Rate Calculator computes the stiffness (spring rate) of cylindrical helical compression and extension springs using the standard mechanical engineering formula k = G·d⁴ / (8·D³·n). By selecting from common material presets like music wire, stainless steel, or chrome vanadium—or inputting a custom shear modulus—engineers and designers can instantly determine the spring constant in N/mm and calculate the spring index. ## Inputs - **Material (preset G)** (select) - **Shear Modulus G (MPa)** (number): Shear modulus of the spring material. Auto-filled by the material preset; override freely when set to Custom. - **Wire Diameter d (mm)** (number): e.g. 2 - **Mean Coil Diameter D (mm)** (number): e.g. 16 - **Active Coils n** (number): e.g. 8 - **Decimal Places** (number) ## When to use - Designing custom compression or extension springs for mechanical assemblies and machinery. - Verifying the spring constant of an existing physical spring by measuring its physical dimensions. - Selecting the appropriate spring material and coil configuration to meet specific load and deflection requirements. ## How it works - Select a spring material preset to automatically populate the shear modulus (G) in MPa, or choose 'Custom' to enter a specific value manually. - Input the physical dimensions of the spring, including the wire diameter (d), mean coil diameter (D), and the number of active coils (n). - Specify the desired decimal precision for the output calculation. - The calculator computes the spring rate (k) in N/mm and the spring index (C) using the standard helical spring deflection formula. ## Use cases - Calculating the spring constant for automotive suspension tuning using chrome silicon steel. - Sizing miniature return springs in consumer electronics using stainless steel wire. - Prototyping industrial machinery actuators that require precise force-to-deflection ratios. ## Frequently asked questions ### What is the spring rate formula used by this calculator? It uses the formula k = G·d⁴ / (8·D³·n), where G is the shear modulus, d is the wire diameter, D is the mean coil diameter, and n is the number of active coils. ### How do I find the mean coil diameter? The mean coil diameter (D) is calculated by subtracting the wire diameter (d) from the outer diameter (OD), or adding the wire diameter to the inner diameter (ID). ### What is the spring index and why does it matter? The spring index (C = D/d) is the ratio of the mean coil diameter to the wire diameter. It indicates the ease of manufacturing; a ratio between 4 and 12 is generally preferred. ### How do I determine the number of active coils? For compression springs, active coils exclude inactive end coils (e.g., subtract 2 for squared and ground ends). For extension springs, all coils are typically active. ### Can I use custom materials not listed in the presets? 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Treat every result as preliminary, not a certified design.