Enter any two of the three variables — spring force (F), spring constant (k), and displacement (x) — and the Hooke's Law Calculator solves for the missing value using F = k × x. Leave the field you want to calculate blank. You'll get the unknown variable plus a visual breakdown of how the three values relate.
Calculated Result
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Spring Force (F)
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Spring Constant (k)
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Displacement (x)
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Acceleration (a = F/m)
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Hooke's Law states that the force needed to stretch or compress a spring is directly proportional to the distance it is displaced. The formula is F = kx, where F is the spring force, k is the spring constant, and x is the displacement. This linear relationship holds as long as the spring is not stretched beyond its elastic limit.
The full form of the equation is Fs = −kx, where the negative sign indicates that the spring's restoring force acts in the opposite direction to the displacement. For example, if you stretch a spring to the right, the spring force pulls back to the left. In magnitude calculations (solving for size of force), the sign is often dropped for simplicity.
The spring constant k measures the stiffness of a spring — how much force is required per unit of displacement. A higher k means a stiffer spring. Its SI unit is Newtons per meter (N/m). Different springs have vastly different constants: a soft rubber band may have a low k, while a steel coil spring can have a very high k.
Rubber bands do not strictly follow Hooke's Law. Unlike ideal springs, rubber bands have a nonlinear stress-strain relationship — their stiffness changes as they are stretched. Hooke's Law is most accurate for elastic materials like metal springs that deform linearly within their elastic limit.
When a spring is stretched or compressed beyond its elastic limit (also called the yield point), it undergoes permanent deformation and no longer returns to its original shape. At this point, Hooke's Law no longer applies, and the force-displacement relationship becomes nonlinear.
Once the spring force F is known, you can calculate acceleration using Newton's Second Law: a = F/m, where m is the mass attached to the spring. This calculator includes an optional mass input to compute acceleration alongside the standard Hooke's Law variables.
In SI units, force is measured in Newtons (N), displacement in meters (m), and the spring constant in N/m. In the imperial system, force may be in pounds (lb), displacement in inches or feet, and k in lb/in or lb/ft. Always ensure consistent units across all three variables to get accurate results.
Yes. This calculator lets you choose which variable to solve for. Select 'Force (F)' to calculate force from k and x, select 'Spring Constant (k)' to find stiffness from F and x, or select 'Displacement (x)' to find how far a spring stretches given F and k.