Calculate spring constant (k), force, displacement, potential energy, and natural frequency with Hooke's Law. Supports series and parallel springs.
Enter force and displacement to calculate spring constant (stiffness)
| Spring Type | Typical Range (N/m) | Applications |
|---|---|---|
| Soft Spring | 1-100 N/m | Pens, toys, light mechanisms |
| Medium Spring | 100-10,000 N/m | Suspension, door hinges, valves |
| Stiff Spring | 10,000-100,000 N/m | Heavy machinery, industrial valves |
| Very Stiff Spring | >100,000 N/m | Vehicle suspension, presses |
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Calculate spring properties using Hooke's Law, the fundamental principle describing spring behavior. Our calculator determines spring constant, force, displacement, potential energy, and natural frequency for mechanical systems, helping engineers and students analyze spring-based mechanisms.
The spring constant (k), also called stiffness, measures how much force is needed to stretch or compress a spring by a unit distance. A higher spring constant means a stiffer spring that requires more force to deform. Hooke's Law states that the force F exerted by a spring equals the spring constant k times the displacement x from equilibrium.
Hooke's Law Formula
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In series, springs are connected end-to-end and share the same force but have different displacements. The equivalent constant is less than any individual spring. In parallel, springs share displacement but forces add up. The equivalent constant is the sum of individual constants.
The natural frequency of a spring-mass system equals (1/2pi) times the square root of k/m. A larger mass oscillates more slowly, while a stiffer spring increases frequency. The period is the inverse of frequency.
The elastic limit is the maximum deformation a spring can undergo and still return to its original shape. Beyond this limit, permanent deformation occurs and Hooke's Law no longer applies.
Elastic potential energy stored in a spring equals U = (1/2)kx², where k is the spring constant and x is displacement. This energy is recoverable when the spring returns to equilibrium.
The SI unit is newtons per meter (N/m), because k = force ÷ displacement. Imperial units are pound-force per inch (lbf/in) or per foot (lbf/ft). This calculator reports k in whatever force/length units you select.
Apply a known force and measure the resulting extension, then k = F ÷ x. With several data points, plot force against displacement — the spring constant is the slope of the straight-line (elastic) region.