Spring Calculator -- Hooke's Law
Calculate any variable in Hooke's Law instantly. Pick a calculation mode, adjust the sliders or type values, and see results in real time.
Spring Type Presets
Series and Parallel Springs
Calculate the equivalent spring constant for multiple springs connected in series or parallel.
Spring Constants
Formula Reference
F = force (N or lbf)
k = spring constant (N/m, N/mm, or lbf/in)
x = displacement from equilibrium
PE = potential energy (J or ft-lbs)
k = spring constant
x = displacement from equilibrium
Springs in series are softer -- the equivalent spring constant is always less than the smallest individual spring.
Springs in parallel are stiffer -- the equivalent spring constant is the sum of all individual constants.
About Hooke's Law
Hooke's Law describes the behavior of springs and elastic materials. It states that the force required to compress or extend a spring is directly proportional to the displacement from its natural length.
The Spring Constant (k)
The spring constant measures spring stiffness. A higher value means a stiffer spring that requires more force to compress or extend. Common units:
- N/m (Newtons per meter) -- SI unit
- N/mm (Newtons per millimeter) -- common in engineering
- lbf/in (pounds-force per inch) -- imperial unit
Compression vs. Extension
Hooke's Law applies to both compression springs (pushed together) and extension springs (pulled apart). The displacement x is always measured from the spring's natural (unloaded) length. By convention, compression is often negative displacement and extension is positive, though the magnitude is what matters for force calculation.
Linear Elastic Region
Hooke's Law is accurate only within the elastic limit of the spring. Beyond this point, the spring may deform permanently or the relationship becomes non-linear. Most springs are designed to operate well within their linear elastic region.
Potential Energy Storage
When you compress or extend a spring, you store elastic potential energy. This energy can be released to do work, which is why springs are used in mechanical systems from car suspensions to watches. The energy stored increases with the square of displacement, so doubling the compression quadruples the stored energy.
Common Applications
- Suspension Systems: Car and bicycle suspensions use springs to absorb shock. Spring constants are carefully chosen to balance comfort and handling.
- Mechanical Scales: Traditional scales measure weight by how much a spring compresses under load.
- Watches and Clocks: Mainsprings store energy that powers mechanical timepieces.
- Shock Absorbers: Damped spring systems absorb impacts in machinery and structures.
- Vibration Isolation: Springs isolate sensitive equipment from vibrations.
- Energy Storage: Spring-based systems store mechanical energy in toys, tools, and industrial equipment.
Frequently Asked Questions
What is Hooke's Law?
How do I find the spring constant?
What happens when springs are combined in series?
What happens when springs are combined in parallel?
How much energy is stored in a compressed spring?
When does Hooke's Law break down?
How do I convert between spring constant units?
What is the difference between a compression and extension spring?
Can I use this for non-metal springs?
How accurate are these calculations?
Privacy & Limitations
- All calculations run entirely in your browser -- nothing is sent to any server.
- Results are computed using standard formulas and should be verified for critical applications.
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Spring Calculator FAQ
What is Hooke's Law?
Hooke's Law states that the force needed to extend or compress a spring is proportional to the distance from its rest position: F = kx. This linear relationship holds true within the elastic limit of the spring material.
How do I find the spring constant?
Measure the force required to produce a known displacement, then calculate k = F/x. Alternatively, hang known weights from the spring and measure how far it stretches. The slope of a force-displacement graph gives you the spring constant.
What happens when springs are combined in series?
Springs in series (end-to-end) act like a softer spring. The equivalent spring constant is found using 1/k_total = 1/k1 + 1/k2. Two identical springs in series have half the stiffness of a single spring.
What happens when springs are combined in parallel?
Springs in parallel (side-by-side) act like a stiffer spring. The equivalent spring constant is simply k_total = k1 + k2. Two identical springs in parallel have twice the stiffness of a single spring.
How much energy is stored in a compressed spring?
Elastic potential energy is calculated using PE = 1/2 x k x x-squared. Energy increases with the square of displacement, so compressing a spring twice as far stores four times the energy.
When does Hooke's Law break down?
Hooke's Law is valid only in the linear elastic region. Beyond the elastic limit, the spring may permanently deform or break. Very large displacements can also cause non-linear behavior even before permanent deformation.
How do I convert between spring constant units?
Common conversions: 1 N/m = 0.001 N/mm = 0.00571 lbf/in. The calculator handles these conversions automatically. Remember to also convert displacement to matching units.
What is the difference between a compression and extension spring?
Compression springs resist being pushed together (coil springs in car suspensions). Extension springs resist being pulled apart (springs on garage doors). Hooke's Law applies to both, but their physical construction differs.
Can I use this for non-metal springs?
Yes. Hooke's Law applies to any elastic material within its linear range -- rubber bands, plastic springs, even biological materials like tendons. Each has its own spring constant based on material properties and geometry.
How accurate are these calculations?
Results are mathematically exact for ideal springs following Hooke's Law. Real springs have manufacturing tolerances, temperature sensitivity, and may show slight non-linearity. This calculator provides theoretical values assuming ideal linear elastic behavior.