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Hooke's Law Calculator

Calculate the force in a spring

System Parameters

N
N/m
m

Hooke's Law states that the force (F) needed to extend or compress a spring by some distance (x) is directly proportional to that distance. [1, 2] This is a fundamental principle of physics and elasticity.

  • Restoring Force: The force exerted by the spring is a "restoring force" as it always acts in the opposite direction of the displacement, trying to return to its equilibrium position. [3, 4] This is why the formal equation is F = -kx.
  • Spring Constant (k): A measure of the spring's stiffness. A higher k value means a stiffer spring. [1, 5]
  • Elastic Potential Energy: The energy stored in the spring due to its deformation. [6, 7]

F = -kx

PE = ½kx²

Enter parameters and click Calculate

About Hooke's Law Calculator

About Hooke's Law Calculator

This tool calculates the force, spring constant, or displacement for a spring system using Hooke's Law (F = -kx). It also computes the elastic potential energy stored in the spring. Use this calculator to explore the relationship between force, displacement, and spring stiffness in elastic systems.

  • Force (F): The restoring force exerted by the spring (in Newtons).
  • Spring Constant (k): A measure of the spring's stiffness (in N/m).
  • Displacement (x): The distance the spring is stretched or compressed from equilibrium (in meters).

The calculator also visualizes force and potential energy as a function of displacement using interactive charts.

Frequently Asked Questions

What is a Hooke's Law calculator?
A tool that calculates spring force (F), displacement (x), or spring constant (k) using the formula F = -kx.
What is Hooke's Law?
The principle that the force needed to extend/compress a spring is proportional to the displacement (F = -kx), valid within the elastic limit.
What are the units of spring constant (k)?
Newtons per meter (N/m) in SI units, or pounds-force per inch (lbf/in) in imperial units.
How do you calculate spring force?
F = -kx, where x is displacement from equilibrium (negative sign indicates restoring force direction).
What is the elastic limit?
The maximum stress a material can withstand without permanent deformation - Hooke's Law only applies below this limit.
How do you find the spring constant experimentally?
Measure displacement (x) under known weights (F), then k = F/x from the slope of the force-displacement graph.
What is typical spring constant range for car suspensions?
15-30 N/mm (15,000-30,000 N/m) for passenger vehicles, varying by vehicle weight and design.
How does spring length affect the spring constant?
For a given spring material and coil diameter: k ∝ 1/L, so longer springs are less stiff (smaller k).
What is the formula for springs in series?
1/k_total = 1/k₁ + 1/k₂ + ... + 1/k_n (resulting in lower equivalent stiffness).
What is the formula for springs in parallel?
k_total = k₁ + k₂ + ... + k_n (resulting in higher equivalent stiffness).
How do you calculate potential energy in a spring?
U = ½kx² (energy stored when compressed/stretched by distance x).
What is the spring constant of a DNA molecule?
~0.1 pN/nm (10⁻⁴ N/m) when stretched, varying with salt concentration and stretching mode.
How does wire diameter affect spring constant?
k ∝ d⁴ (for helical springs), so doubling wire diameter makes a spring 16× stiffer.
What is the spring constant of human cartilage?
~500-1000 N/mm (varies by joint and degeneration state - much stiffer than metal springs).
How do you calculate natural frequency of a spring-mass system?
f = (1/2π)√(k/m) where m is the attached mass (assuming no damping).
What is typical k for a Slinky toy spring?
~0.5 N/m (very soft - stretches under its own weight when held vertically).
How do temperature changes affect spring constant?
k increases with lower temperatures (stiffer material) and decreases with higher temperatures.
What is the spring constant of a diving board?
Typically 5,000-20,000 N/m (depends on material, length, and cross-section - treated as cantilever beam).
How do you calculate work done to compress a spring?
W = ½kx² (same as stored potential energy - area under F-x curve).
What is the spring constant of human tendon?
~100-300 N/mm (Achilles tendon stores ~35J energy during running).
How does coil diameter affect spring constant?
k ∝ 1/D³ (for helical springs), so larger diameter coils make much softer springs.
What is the spring constant of a trampoline?
~3,000-8,000 N/m (for individual springs - multiple springs work in parallel).
How do you calculate the elastic limit force?
F_max = kx_max where x_max is maximum displacement before yielding (from material properties).
What is the spring constant of a piano wire?
~8,000-30,000 N/m (for vibrating strings, treated as tensioned 'springs').
How do you calculate spring constant for non-linear springs?
Use tangent stiffness k = dF/dx (instantaneous slope of the force-displacement curve).
What is the spring constant of a rubber band?
~50-200 N/m (varies with thickness and stretch - often non-Hookean behavior).
How do you calculate equivalent k for a cantilever beam?
k = 3EI/L³ where E is Young's modulus, I is area moment of inertia, L is beam length.
What is the spring constant of a mattress?
~100-300 N/m per coil (with hundreds of coils working in parallel).
How do you calculate k for a conical spring?
Use modified formula k = Gd⁴/(8nD³) where G is shear modulus, d is wire diameter, n is active coils, D is mean diameter.
What is the spring constant of a bow limb?
~300-800 N/m (compound bows use non-linear 'cam' systems to modify effective k).
How do you calculate k for a torsion spring?
k = Ed⁴/(64Dn) where E is Young's modulus, d is wire diameter, D is coil diameter, n is number of turns.
What is the spring constant of a suspension bridge cable?
~10⁷-10⁸ N/m (treated as tension spring - extremely stiff due to massive cross-section).
How do you calculate k for a leaf spring?
k = nEbt³/(6L³) where n is number of leaves, b is width, t is thickness, L is length.
What is the spring constant of a graphene sheet?
~1-5 N/m (2D material - measured as force per unit width rather than traditional k).
How do you calculate k for a bungee cord?
Measure force at maximum safe extension (F_max) and use k = F_max/x_max (non-linear in practice).
What is the spring constant of a car valve spring?
~30-50 N/mm (must operate at high frequencies without fatigue failure).
How do you calculate k for a gas spring?
k ≈ γPA²/V where γ is adiabatic index, P is pressure, A is piston area, V is gas volume.
What is the spring constant of a watch hairspring?
~0.0001-0.001 N·m/rad (torsional stiffness for precise timekeeping).
How do you calculate k for a belleville washer?
k = (4Eδ³)/((1-ν²)D²) where δ is washer thickness, D is diameter, ν is Poisson's ratio.
What is the spring constant of a human lung?
~1-5 cmH₂O/L (≈100-500 N/m³ - measured as compliance rather than traditional k).
How do you calculate k for a rubber bushing?
Use dynamic testing to find complex stiffness k* = k' + ik'' (includes storage and loss moduli).
What is the spring constant of a MEMS cantilever?
~0.01-10 N/m (ultra-sensitive for AFM applications - depends on microscopic dimensions).
How do you calculate k for a progressive-rate spring?
Specify initial and final k values - actual k(x) varies with displacement (non-linear design).
What is the spring constant of a climbing rope?
~2,000-5,000 N/m (designed to stretch 30-40% under 80kg fall to absorb impact).
How do you calculate k for a composite spring?
Use rule of mixtures: k_total = ΣV_ik_i where V_i is volume fraction of each component.
What is the spring constant of a spider's silk?
~1-10 N/m (varies by silk type - capture silk stretches 200-300%, dragline ~30%).
How do you calculate k for a conical compression spring?
Treat as variable diameter spring - k varies along length, requiring integration for total deflection.
What is the spring constant of a piezoelectric actuator?
~10⁶-10⁸ N/m (very stiff but tiny displacements - typically micrometers).
How do you calculate k for a non-prismatic beam?
Use energy methods or numerical integration since k varies along the length.
What is the spring constant of a suspension seat?
~2,000-5,000 N/m (designed to isolate vibrations at 1-5 Hz frequencies).

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