THE NUMORIX GUIDE
How to use the Spring Force Calculator
Last reviewed September 14, 2026
What this calculator does
The engine applies Hooke's-law magnitude F = k*x and elastic potential energy PE = 0.
Formula and method
The engine applies Hooke's-law magnitude F = k*x and elastic potential energy PE = 0.5*k*x^2. It returns both values in SI units, rounding the force and energy to four decimals; the force follows the sign of the entered displacement rather than adding a separate restoring-force direction.
Variables and inputs
Enter spring constant k in N/m and displacement x from equilibrium in meters. The UI checks only that both values parse as numbers, so it permits negative displacement and even a nonphysical negative spring constant. The result displays force in newtons and spring energy in joules.
Worked example
For k = 100 N/m and x = 0.5 m, F = 100*0.5 = 50 N and PE = 0.5*100*(0.5^2) = 12.5 J. Doubling displacement would double the force but quadruple the stored energy in the ideal model.
How to interpret the result
The force is proportional to extension or compression within the linear range, while stored elastic energy grows with the square of displacement. In the usual sign convention the restoring force is -k*x; the engine's F = k*x output is an algebraic result whose direction must be interpreted separately.
Common mistakes to avoid
Measure displacement from the spring's equilibrium length, not from an arbitrary end point, and use N/m for k. Do not treat spring force as constant across a large extension or confuse the signed force with its magnitude.
Assumptions and limitations
Hooke's law applies only while the spring remains in its elastic linear range. The calculation omits damping, spring mass, hysteresis, preload, fatigue, buckling, nonlinear stiffness, and the direction of the restoring force; negative k is not physically screened by the UI.