Compression Spring Calculator

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Our compression spring calculator helps you find the force, spring constant, or deflection of a spring with ease.

Springs work on a simple rule known as Hooke’s Law — the force needed to compress or stretch a spring is directly proportional to how far it is moved. T

his means the stiffer the spring (higher spring constant), the more force you need for the same deflection.

Are you looking for clear examples that show exactly how Hooke’s law works in real situations? This guide and calculator will walk you through it all!

🌀 Compression Spring Calculator

🧰 Compression Spring — Formula Explanation & Worked Examples

Hooke's Law (Basic spring relation)
F = k × x
Where:
  • F = Force applied on the spring (units: N).
  • k = Spring constant / stiffness (units: N/m).
  • x = Deflection (compression or extension) measured from the spring's free length (units: m).
Rearranged forms
k = F / x
x = F / k
Units check example: N = (N/m) × m → units match. Hooke's law is linear — valid while the spring remains in its elastic (non-yielding) range.
Optional: Elastic potential energy stored in a spring
U = ½ × k × x²
Use when you want the energy stored due to compression/extension.
Worked Example — Narrative + Step-by-step solution
Problem (Calculate Force):

A compression spring has stiffness k = 200 N/m. It is compressed by x = 0.05 m. What is the force the spring exerts?

  1. Step 1 — Write the formula: Hooke's law: F = k × x.
  2. Step 2 — Substitute the given values: F = 200 × 0.05.
  3. Step 3 — Compute: 200 × 0.05 = 10.
  4. Step 4 — Add units: F = 10 N.
Final answer: F = 10 N
Problem (Calculate spring constant k):

A spring is compressed by x = 0.10 m when a force of F = 25 N is applied. Find the spring constant k.

  1. Step 1 — Use rearranged formula: k = F / x.
  2. Step 2 — Substitute: k = 25 / 0.10.
  3. Step 3 — Compute: 25 ÷ 0.10 = 250.
  4. Step 4 — Units: k = 250 N/m.
Final answer: k = 250 N/m
Problem (Calculate deflection x):

A force of F = 40 N compresses a spring with stiffness k = 800 N/m. How much is the deflection x?

  1. Step 1 — Use rearranged formula: x = F / k.
  2. Step 2 — Substitute: x = 40 / 800.
  3. Step 3 — Compute: 40 ÷ 800 = 0.05.
  4. Step 4 — Units: x = 0.05 m.
Final answer: x = 0.05 m
Tip: use the calculator above for quick checks — these steps show how the arithmetic and units work.

FAQs

What is a compression spring?

A compression spring is a mechanical device that resists a force when it is compressed. The more you push it, the more it pushes back.

What does the spring constant (k) mean?

The spring constant tells you how stiff the spring is. A big k value means the spring is harder to compress, while a small k means it’s easier to compress.

What are the units used in spring calculations?

Force (F) is measured in Newtons (N), deflection (x) in meters (m), and the spring constant (k) in Newtons per meter (N/m).

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