Mechanics
Hooke's Law
Spring force is proportional to displacement, opposite in direction.
Variables
FN
Spring force
Restoring force
In SI units: kg·m/s²
kN/m
Spring constant
Spring stiffness
In SI units: kg/s²
Allowed values: greater than 0
xm
Displacement
Extension from equilibrium
Derivation
Empirical law for elastic materials within elastic limit.
Your notes
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Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- k = 2 N/m (Spring constant)
- x = 3 m (Displacement)
Result: F = -6 N
Where this formula is listed
- Mechanics formulas, under Dynamics, alongside Newton's Second Law, Weight, Friction Force, Drag Force and Terminal Velocity.
- In the mechanics list it comes after Friction Force and before Drag Force.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Hooke's Law formula?
Hooke's Law is written F = −kx. Spring force is proportional to displacement, opposite in direction. It belongs to Mechanics, under Dynamics.
What are the units in F = −kx?
In SI units, F is spring force, measured in kg·m/s²; k is spring constant, measured in kg/s²; x is displacement, measured in m.
How is the Hooke's Law formula derived?
Empirical law for elastic materials within elastic limit. The result is F = −kx.