📌 Quick Answer
The spring constant (k) measures the stiffness of a spring — the force required to stretch or compress it by one unit of length.
From Hooke’s law, k = F / x, where F is the applied force and x is the extension or compression. Its SI unit is newton per metre (N/m).
🔹 Key Takeaways
- k = F / x (from Hooke’s law F = kx).
- SI unit is N/m; dimensions [MT−²].
- A higher k means a stiffer spring.
- Springs in parallel add (k = k₁+k₂); in series the reciprocals add.
What Is the Spring Constant?
The spring constant, also called the force constant, is a measure of how stiff a spring is. It tells you how much force is needed to deform the spring by a given amount. A stiff spring has a large spring constant; a soft spring has a small one.
Formula and Hooke’s Law
The spring constant comes directly from Hooke’s law, which states that the restoring force of a spring is proportional to its extension:
F = k x ⇒ k = F / x
where F is the applied force (N) and x is the extension or compression (m).
Unit and Dimensions of Spring Constant
Since k = F/x = newton / metre, the SI unit of spring constant is N/m. Its dimensional formula is [M¹ T−²].
Springs in Series and Parallel
| Arrangement | Effective spring constant | Effect |
|---|---|---|
| Parallel | k = k₁ + k₂ | Stiffer (larger k) |
| Series | 1/k = 1/k₁ + 1/k₂ | Softer (smaller k) |
Worked Example
A force of 20 N stretches a spring by 0.1 m. Its spring constant is k = F/x = 20 / 0.1 = 200 N/m.
Frequently Asked Questions
What is the spring constant?
It is a measure of a spring’s stiffness — the force needed to stretch or compress it by one unit length, given by k = F/x.
What is the SI unit of spring constant?
The SI unit of the spring constant is newton per metre (N/m).
What is the formula for spring constant?
k = F/x, derived from Hooke’s law F = kx, where F is force and x is extension.
Does a higher spring constant mean a stiffer spring?
Yes. A larger spring constant means more force is needed to deform the spring, so it is stiffer.