Spring Constant Calculator
Calculate spring constant (spring rate) two ways: (1) from Hooke's Law using measured force and deflection, or (2) from the helical coil spring design formula using wire diameter, coil diameter, number of active coils, and shear modulus. Both methods are used in spring design and verification per SAE and ASME standards.
Spring constant formulas
Hooke's Law: k = F / delta (N/mm)
Helical coil spring (SAE/ASME):
k = (G x d^4) / (8 x D^3 x Na) (N/mm)
Spring index C = D / d
Where F = force (N), delta = deflection (mm), G = shear modulus (N/mm^2), d = wire diameter (mm), D = mean coil diameter (mm), Na = number of active coils. Formula from SAE Spring Design Manual HS-795.
Spring design guidelines
- Spring index C should be 4-12 for ease of manufacture and manageable stress levels.
- For compression springs with closed and ground ends, active coils = total coils minus 2.
- Maximum shear stress at the inner coil surface should not exceed 40-50% of the wire's ultimate tensile strength under full load.
- Free length / coil diameter ratio should be less than 4 to avoid buckling; add a guide if ratio is higher.
Spring constant: frequently asked questions
What is the spring constant (spring rate)?
The spring constant k is the force required per unit deflection, measured in N/mm or lb/in. From Hooke's Law: F = k x delta, where F = applied force (N) and delta = deflection (mm). A stiffer spring has a higher k value.
What is the formula for a helical coil spring rate?
For a close-coiled helical spring: k = (G x d^4) / (8 x D^3 x Na), where G = shear modulus of the wire material (N/mm^2), d = wire diameter (mm), D = mean coil diameter (mm), and Na = number of active coils. This formula is from ASME AM-4 and SAE spring design standards.
What is the shear modulus G for common spring materials?
Hard-drawn spring steel wire: G = 79,300 N/mm^2 (79.3 GPa). Stainless steel 302: G = 68,900 N/mm^2. Chrome-vanadium steel: G = 79,300 N/mm^2. Phosphor bronze: G = 41,400 N/mm^2. Values per SAE Spring Design Manual and ASTM spring wire specifications.
What is the difference between active coils and total coils?
Active coils (Na) are the coils that deflect under load. Total coils = Na + inactive (dead) coils. For a compression spring with closed and ground ends, there are typically 2 dead coils (1 at each end). For open ends, there are 0 dead coils. Use only active coils in the spring rate formula.
What is the spring index and why does it matter?
Spring index C = D/d (mean coil diameter / wire diameter). A low C (3-4) means a tightly coiled spring with higher stress concentration. A high C (10-12) means a loosely coiled spring. The ideal range is C = 4-12 for most applications. Very low C ratios are difficult to manufacture and have high stress concentrations; very high C ratios tend to buckle.
Official sources
- SAE International: SAE Spring Design Manual (HS-795).
- ASME: ASME AM-4 Mechanical Spring Design Standards.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.