Find Force, Spring Constant, or Extension — instantly. Built for Class 11 & beyond.
Choose what you want to find, fill in the other two values, and hit Calculate.
Struggling to rearrange the formula? The triangle trick is your best friend. Cover the variable you want to find — the remaining two show you what to do.
Cover F → you see k×x | Cover k → you see F÷x | Cover x → you see F÷k
Measured in Newtons (N). The push or pull applied to the spring. This is the restoring force the spring exerts back.
Measured in N/m. It tells you how stiff the spring is. A higher k means a stiffer spring.
Measured in metres (m). How much the spring stretches or compresses from its natural length.
Imagine you stretch a rubber band. The more you pull it, the harder it pulls back. Hooke's Law says exactly this — but for springs and elastic materials.
Robert Hooke, an English scientist, discovered this principle in 1676. He wrote it in Latin as "ut tensio, sic vis" — which means "as the extension, so the force."
Click a ballpoint pen. That click? It's Hooke's Law. The tiny spring inside compresses when you push, and springs back with the exact same force. Every time, predictably.
Same thing happens in:
Hooke's Law is written as a precise mathematical equation. Understanding each part of the formula helps you use it correctly — especially the negative sign, which students often miss.
Where each symbol means:
Before the equation, the law is stated as a proportionality:
This means: double the extension → double the force. Triple the extension → triple the force. The spring constant \(k\) is the constant of proportionality that converts the ∝ into an = sign: \(F = kx\).
The spring constant k is the backbone of Hooke's Law. It tells you how stiff or flexible a spring is.
A car suspension spring: k ≈ 15,000–30,000 N/m. Needs a huge force for a small compression.
A slinky toy: k ≈ 1–2 N/m. A tiny force creates a large extension.
A typical mattress coil: k ≈ 500–2000 N/m. Balanced for comfort and support.
If a mass m (in kg) is hung from a spring and it extends by x metres, the spring force equals the weight of the object:
Problem: A 500 g mass (0.5 kg) hangs from a spring and stretches it by 10 cm (0.1 m). Find the spring constant.
Weight (F) = m × g = 0.5 × 9.8 = 4.9 N
k = F ÷ x = 4.9 ÷ 0.1
∴ k = 49 N/m
These are the types of problems you'll see in Class 11 exams. Work through each one step by step.
Problem: A spring with k = 300 N/m is compressed by 8 cm. What force does it exert?
Convert: 8 cm = 0.08 m
F = k × x = 300 × 0.08
∴ F = 24 N
Problem: A 15 N force stretches a spring by 5 cm. What is the spring constant?
Convert: 5 cm = 0.05 m
k = F ÷ x = 15 ÷ 0.05
∴ k = 300 N/m
Problem: A spring with k = 500 N/m has a 25 N force applied to it. How far does it stretch?
x = F ÷ k = 25 ÷ 500
∴ x = 0.05 m = 5 cm
Problem: A bungee cord has k = 100 N/m. A 70 kg person jumps. At the lowest point the cord is stretched 8 m. What is the spring force pulling them back up?
F = k × x = 100 × 8
∴ F = 800 N (vs their weight = 70 × 9.8 = 686 N — they bounce back!)
Hooke's Law doesn't just apply to springs. It applies to any elastic material — metal rods, rubber bands, even bones. In this form, we use stress and strain instead of force and extension.
σ = F / A
Force per unit area. Measured in Pascals (Pa) or N/m².
ε = ΔL / L₀
Extension divided by original length. It has no unit — it's a ratio.
E = σ / ε
The "stiffness" of the material itself. Measured in Pa or GPa.
In the green region, stress ∝ strain — Hooke's Law holds. Beyond the elastic limit, the material doesn't return to its original shape.
Hooke's Law is brilliant, but it has a boundary. Stretch a spring too far and it won't spring back to its original length. This boundary is called the elastic limit.
A spring that has exceeded its elastic limit is said to have undergone plastic deformation. Hooke's Law no longer applies. This is why engineers always design springs to work well within the elastic limit — with a safety margin.
Material returns to its original shape. Hooke's Law is valid here. Stress ∝ Strain.
Permanent deformation occurs. Hooke's Law no longer applies. The spring is "ruined."
You've solved the equations. But here's the exciting part: Hooke's Law isn't just a textbook formula. It's quietly running your car, saving your life in an earthquake, keeping planes in the sky, and even pumping blood through your heart. Let's look at each field.
Every time something stretches, compresses, bends, or bounces back — and returns to its original shape — Hooke's Law is the reason why. Engineers, doctors, architects, and product designers all rely on it daily.
The formula is always the same: F = kx. Only the scale changes — from a tiny watch spring (k = 0.01 N/m) to a skyscraper's foundation damper (k = 50,000,000 N/m).
Your mattress has hundreds of tiny springs. Each one compresses under your body weight proportionally. Heavier sections sink more, lighter sections sink less — giving your spine perfect support every night.
A typical mattress spring: k ≈ 800–1,500 N/m
Click a pen. That satisfying click? A tiny spring compresses when you push, then pushes the ink tip out. When you click again, the spring pulls it back in. This happens millions of times without wearing out — because it stays well within its elastic limit.
Pen spring constant: k ≈ 10–30 N/m
A spring balance is Hooke's Law made visible. Place an object on the scale — the spring stretches by exactly x = F/k. The dial reads that stretch as weight. This is how every mechanical scale has worked for 300 years.
This is also how doctors' weighing machines and kitchen scales work at their core.
That spring mechanism that slowly closes your door? It's a torsional spring (a spring that twists instead of stretches). As you push the door open, the spring stores elastic potential energy. When you let go, it releases that energy — closing the door gently.
This is Hooke's Law at its most dramatic. Your car hits a pothole — the suspension spring compresses by x metres. The spring absorbs the impact force (F = kx) so your body doesn't. A stiffer spring (high k) gives a sportier, bumpier ride. A softer spring (low k) gives a smoother, more comfortable ride.
Car suspension spring: k ≈ 15,000–35,000 N/m
The front forks of a motorcycle contain two large springs. When you brake hard, the bike dips forward — the fork springs compress, absorbing the braking force. Without them, the wheel would lock up and you'd go over the handlebars.
Fork spring constant: k ≈ 8,000–20,000 N/m
When a 300-tonne aircraft lands at 250 km/h, the landing gear springs must absorb an enormous impact force in milliseconds. Engineers use Hooke's Law to design oleo-pneumatic struts — a combination of springs and gas — so passengers feel only a gentle thud.
Landing gear stiffness: k ≈ 1,000,000+ N/m
At the ends of train carriages are large buffer springs. When carriages couple together or a train decelerates, these springs compress and absorb the shock. Without them, connecting carriages would send passengers lurching forward violently.
A trampoline is a giant Hooke's Law demonstration. Jump on it — the springs stretch by x metres under your weight (F = mg). The springs then pull the mat back up with the same force, launching you upward. More weight = more stretch = higher bounce.
Olympic trampoline spring: k ≈ 2,000–4,000 N/m per spring (100+ springs)
Pull back an arrow. The bow limbs bend — this is elastic deformation following Hooke's Law. The further you pull (x), the more force (F = kx) stored as elastic potential energy. Release the string — all that energy transfers to the arrow as kinetic energy. Olympic archers pull with forces of 150–220 N.
A bungee cord is an elastic rope. As you fall, the cord stretches proportionally to the force (your weight + momentum). At maximum stretch, the cord pulls back with F = kx — where x is how far it's stretched. Engineers calculate the exact k value needed so you stop just before hitting the ground.
Resistance bands are elastic bands that follow Hooke's Law. Stretch them further — resistance increases. The "light," "medium," and "heavy" bands you see at the gym are just different spring constants (k values). Physiotherapists use them because the resistance is predictable and proportional.
Modern skyscrapers in earthquake zones are built on giant spring-like isolators called base isolators. These rubber-and-steel pads absorb seismic vibrations. When the ground shakes violently, the building sways gently instead of crumbling — because engineers designed the base isolators using Hooke's Law.
Base isolator stiffness: k ≈ 5,000,000–50,000,000 N/m
The cables of a suspension bridge stretch slightly under the weight of traffic — this is elastic deformation. The cables act like giant springs with an incredibly high k value. Engineers measure this elastic stretch precisely to ensure the bridge never reaches its elastic limit under maximum load.
Heavy industrial machines (generators, compressors, motors) vibrate when running. Engineers mount them on spring-damper systems. The springs absorb vibration using Hooke's Law — preventing damage to the machine and the floor, and reducing noise. The "anti-vibration pads" under washing machines work the same way.
When a bolt is tightened, it stretches slightly — this is preload. The bolt acts as a spring. Engineers calculate exactly how much to tighten it using Hooke's Law, so the bolt is always under tension (preventing loosening) but never past its elastic limit (preventing breakage). Aeronautical bolts are torqued to precise values for this exact reason.
Your aorta (the main artery from the heart) stretches with every heartbeat and springs back. This elastic behaviour follows Hooke's Law. The artery walls have a specific spring constant — if it becomes too stiff (atherosclerosis), the heart has to work much harder. Cardiologists measure arterial stiffness as a health indicator.
Your bones and tendons are elastic materials with Young's Modulus values (the material-level form of Hooke's Law). Tendons store elastic energy when you walk or run — like little springs. The Achilles tendon stores up to 35% of the energy of each step and returns it, making walking far more efficient than it would be otherwise.
Braces use metal wires that apply a continuous, gentle spring force to your teeth. The wire has a specific spring constant (k) — the orthodontist chooses the wire thickness to apply just the right force (F = kx) to move the tooth by x millimetres per month. Too much force damages the root; too little does nothing.
Cardiac stents — tiny mesh tubes placed inside blocked arteries — are made from shape-memory alloys that behave elastically. They compress for insertion and spring open to the exact diameter needed (x = F/k). Hooke's Law is literally keeping hearts beating.
Mechanical keyboards use a tiny spring under each key (k ≈ 40–80 cN/mm — centinewtons per millimetre!). Each keypress compresses the spring by x millimetres. The spring force F = kx gives the "tactile feel" you sense when typing. Premium keyboards use stiffer springs for more resistance; gaming keyboards use softer ones for speed.
Modern smartphones use piezoelectric force sensors under the screen. When you press the display, it micro-deflects (x is tiny — just micrometres). The sensor detects this deformation via Hooke's Law and distinguishes a light tap from a hard press. This is how 3D Touch and Force Touch technology work.
Scientists use an Atomic Force Microscope to image surfaces at the atomic level. It works by scanning a tiny cantilever spring (k ≈ 0.01–100 N/m) over a surface. When the tip deflects by x nanometres due to atomic forces, F = kx gives the force. This lets scientists literally feel individual atoms — and Hooke's Law is the instrument's entire operating principle.
A mechanical watch runs on a coiled mainspring — a ribbon of metal that stores energy when wound. As it unwinds, it releases force proportionally (Hooke's Law). The hairspring (the tiny spiral spring in every watch) vibrates at a precise frequency controlled by its spring constant k. This is what keeps time accurate.
Hairspring constant: k ≈ 0.001–0.01 N/m
Here's how the spring constant (k) varies enormously depending on application:
| Application | Typical k Value | What x Represents | Why It Matters |
|---|---|---|---|
| Watch hairspring | 0.001–0.01 N/m | Tiny rotation of spring | Controls timekeeping frequency |
| Resistance band | 50–200 N/m | How far you stretch it | Controlled workout resistance |
| Mattress spring | 800–1,500 N/m | How much it sinks under weight | Comfortable, supportive sleep |
| Bike suspension | 5,000–15,000 N/m | Compression on rough terrain | Rider comfort and control |
| Car suspension | 15,000–35,000 N/m | Compression over bumps | Safety and ride quality |
| Aircraft landing gear | 500,000–2,000,000 N/m | Compression on touchdown | Survive massive impact forces |
| Building base isolator | 5,000,000–50,000,000 N/m | Horizontal sway in earthquake | Prevent building collapse |
The SI unit of spring constant is Newton per metre (N/m). It tells you how many Newtons of force are needed to stretch or compress the spring by one metre.
Yes! Hooke's Law applies to both stretching (extension) and squashing (compression). In both cases, the spring exerts a restoring force — a force that pushes or pulls it back to its natural length. The formula F = kx works for both, where x is the magnitude of compression or extension.
Spring constant (k) is a property of a specific spring — it depends on the material, shape, coil diameter, wire thickness, and number of coils. Young's Modulus (E) is a property of the material itself — it doesn't depend on the shape. Steel always has E ≈ 200 GPa, regardless of whether it's a thin wire or a thick rod.
When you hang a mass m from a spring and it extends by x, the spring force equals the weight:
k = mg / x
Where g = 9.8 m/s². For example, hanging a 1 kg mass that extends the spring 0.2 m: k = (1 × 9.8) / 0.2 = 49 N/m.
No! Hooke's Law applies to any elastic material within its elastic limit — rubber bands, wood, bone, tendons, and even the Earth's crust during small seismic events. The key condition is that the material must return to its original shape after the force is removed.
Series (end to end): 1/k_total = 1/k₁ + 1/k₂. The system is softer (lower k).
Parallel (side by side): k_total = k₁ + k₂. The system is stiffer (higher k).
Think of it like resistors in a circuit — the rules are similar!
In many textbooks, Hooke's Law is written as F = –kx. The negative sign means the spring force acts in the opposite direction to the displacement. If you pull the spring to the right (+x), the spring pulls back to the left (–F). This is the restoring force concept. For magnitude calculations in problems, you can ignore the sign and use F = kx.