Hooke's Law Calculator (Restoring Force)
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
Hooke's law gives a spring's restoring force with F = k × x, where k is the spring's stiffness (in N/m) and x its elongation (in m). For a spring with a stiffness of 200 N/m stretched by 5 cm, the restoring force is 10 N.
Explanation
Hooke's law describes the elastic behavior of a spring: within its elastic range (before any permanent deformation), the restoring force it exerts is directly proportional to how far it's stretched or compressed from its resting position. The proportionality constant, k, is called the spring's stiffness (or spring constant), expressed in newtons per meter (N/m): the higher k is, the "stiffer" the spring and the more it resists being moved. This calculator converts the elongation entered in centimeters (the most practical unit for a typical spring) into meters before applying the formula, the SI unit consistent with the newton per meter of stiffness. This law only holds within the spring's elastic range: beyond a certain elongation (the elastic limit, specific to each spring), the relationship stops being linear and the spring can deform permanently. For the stress exerted on a section of material rather than the force of a spring, see our mechanical stress calculator.
Example: a spring with stiffness 200 N/m, stretched by 5 cm
Inputs
Stiffness: 200 N/m. Elongation: 5 cm.
Calculation
Force = stiffness × elongation = 200 × (5 ÷ 100) = 200 × 0.05 = 10.
Result
This spring's restoring force is 10 N.
Frequently asked questions
What does the stiffness k physically represent?
Stiffness k measures the spring's resistance to deformation: a spring with high stiffness needs a greater force to achieve the same elongation as a spring with lower stiffness. It depends on the material, wire diameter, and the spring's geometry — it's a characteristic specific to each spring, generally provided by the manufacturer or measured experimentally (by plotting force against elongation).
Does this formula apply to any elongation?
No, only within the spring's elastic range, where the deformation stays reversible (the spring returns to its original shape once the force is removed). Beyond the elastic limit, specific to each spring, the relationship stops being linear and permanent deformation can occur — this calculator assumes the elongation entered stays within that elastic range.
Does Hooke's law also work under compression?
Yes, the same formula F = k × x applies whether a spring is stretched (positive elongation) or compressed (shortened from its resting position), as long as the deformation stays within the spring's elastic range. This calculator treats elongation and compression the same way, as an absolute value.