Compute spring force, spring constant, or displacement — F = −k·x
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Have you ever pressed down on a spring and felt it push back? That resistance isn’t random, it follows a beautifully simple rule called Hooke’s law. Whether you’re designing a suspension system, analyzing a simple harmonic oscillator, or just curious about how springs work, understanding the relationship between force, spring stiffness, and displacement is essential.
This Hooke’s law calculator computes spring force, spring constant, or displacement depending on which variables you already know. Choose from three modes: Force, Spring Constant, or Displacement and the tool solves for the missing value using F = k·x. It handles multiple unit systems, includes presets for common spring stiffnesses, and provides instant results with full unit conversions. All calculations run locally in your browser, keeping your data completely private.
Choose your calculation mode: Force, Spring Constant, or Displacement using the buttons at the top of the section.
For Force mode: enter the spring constant (k) and the displacement (x) to find the force.
For Spring Constant mode: provide the force (F) and displacement (x) to calculate stiffness.
For Displacement mode: input the force (F) and spring constant (k) to determine the displacement.
Select the appropriate units for each input N/m or lb/ft for spring constant; m, cm, mm, ft, or in for displacement; N, kN, or lbf for force.
Click Calculate or simply wait for automatic updates, the result appears instantly.
Review the solved value, along with the spring constant and displacement displayed in multiple unit systems.
The calculator applies Hooke’s law, which states that the force required to extend or compress a spring is directly proportional to the displacement from its equilibrium position. The negative sign indicates that the spring force opposes the direction of displacement.
Formula: F = −k·x
Where F is the spring force in newtons, k is the spring constant (stiffness) in N/m, and x is the displacement from equilibrium in meters. The magnitude of the force is simply |F| = k·x, which is what the calculator computes.
The spring constant k measures a spring’s stiffness — a higher k means a stiffer spring that requires more force for the same displacement. The displacement x is the distance the spring is stretched (positive) or compressed (negative) from its natural length.
When solving for spring constant: k = F/x
When solving for displacement: x = F/k
All inputs are converted to SI base units before computation: force to newtons, displacement to meters, and spring constant to N/m. Results are then displayed in multiple unit systems for convenience.
A spring has a spring constant of 500 N/m and is stretched by 0.2 meters. What force does the spring exert?
Step 1: Identify the known values
k = 500 N/m
x = 0.2 m
Step 2: Apply Hooke’s law
F = k·x = 500 × 0.2 = 100 N
Interpretation: The spring exerts a force of 100 newtons. This is the force required to hold the spring at that displacement, and it’s also the force the spring will exert when released.
If we wanted to find the spring constant instead:
Suppose a 100 N force stretches the spring by 0.2 m. What is k?
k = F/x = 100 / 0.2 = 500 N/m
If we wanted to find the displacement:
Suppose a spring with k = 500 N/m is pulled with 100 N. What is x?
x = F/k = 100 / 500 = 0.2 m
Computes force, spring constant, or displacement with a single click, depending on your needs.
Handles multiple units for force (N, kN, lbf), spring constant (N/m, lb/ft), and displacement (m, cm, mm, ft, in).
Includes spring presets for common stiffnesses (5 to 1000 N/m) to quickly get started.
Displays results in multiple unit systems simultaneously — no manual conversions needed.
Shows a clear diagram illustrating the spring, mass, and applied force.
Runs entirely client-side with no server communication, keeping your data private.
Free to use on any device with responsive design.
Hooke’s law says that the force needed to stretch or compress a spring is proportional to how far you stretch or compress it. A stiffer spring requires more force, and stretching it further requires more force. The relationship is linear double the stretch, double the force.
The spring constant (k) is a measure of a spring’s stiffness. It’s the force required to stretch or compress the spring by one unit of distance (typically one meter). Higher k means a stiffer spring. It’s measured in N/m (newtons per meter) or lb/ft (pounds per foot).
The negative sign indicates that the spring force always opposes the displacement. If you stretch the spring (positive x), the spring pulls back (negative F). If you compress it (negative x), the spring pushes outward (positive F). The calculator gives the magnitude of the force, which is the absolute value.
The elastic limit is the maximum stress a material can withstand without permanent deformation. If you stretch a spring beyond its elastic limit, it won’t return to its original shape when the force is removed — it becomes permanently stretched or bent. Hooke’s law only applies within the elastic limit.
Yes, Hooke’s law applies to both stretching (extension) and compression. When you compress a spring, x is negative, and the force F is positive (pushing outward). The magnitude of the force is still |F| = k·|x|.
A ballpoint pen spring: ~100 N/m, a trampoline spring: ~1000 N/m, a car suspension spring: ~30,000 N/m, a mattress spring: ~10,000 N/m, a garage door spring: ~5,000 N/m. The calculator’s presets cover a wide range of these applications.
The spring constant is determined by the material (shear modulus), wire diameter, coil diameter, and number of active coils. Thicker wire, smaller coil diameter, and fewer coils all increase the spring constant. Engineers use these parameters to design springs with specific stiffness values.
A spring is a single elastic element. A spring system can include multiple springs in series or parallel. In series, springs add compliance (lower overall k); in parallel, they add stiffness (higher overall k). The calculator assumes a single ideal spring.
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