Hooke's Law Calculator

Force grows linearly with stretch but energy grows with the square, which is why the second centimetre of stretch stores three times as much energy as the first. Stretch a spring twice as far and you store four times the energy, not twice. The minus sign in F = −kx says the force opposes the displacement — it always points back towards rest. It is dropped here because the magnitude is what gets measured. Hooke's law only holds up to the elastic limit. Past that the spring deforms permanently and the linear relationship stops applying entirely, which is why a stretched-out spring never quite returns.