Spring Constant Calculator

How to use this calculator

1. Enter the applied force in newtons (for example, the force from a weight or a test rig).
2. Enter how far the spring extended or compressed under that load, measured in meters (convert from mm or cm if needed).
3. We divide force by displacement to compute the spring constant k in N/m.
4. Optionally, repeat with multiple measurements and average k values to reduce experimental error.

Inputs explained

Force

Applied load in newtons (N). If you measure mass in kilograms, multiply by g (≈ 9.81 m/s²) to convert weight to force (F = m × g). Use the magnitude only.

Displacement

Spring extension or compression in meters (m) relative to the unloaded length. Convert millimeters to meters by dividing by 1000 (e.g., 20 mm = 0.02 m).

When to use it

• Finding k for an unknown spring in a physics lab by measuring how far it stretches under different loads.
• Checking whether a spring matches design requirements for suspension, vibration isolation, or mechanical linkages.
• Comparing stiffness across different springs when tuning ride quality, keyboard switches, or mechanical assemblies.
• Estimating how much a spring will deflect under a given load once you know k, using Δx = F ÷ k.
• Teaching Hooke’s law and linear elasticity concepts in introductory physics or engineering courses.

Tips & cautions

• Stay within the elastic (linear) range of the spring—measurements taken near coil bind or permanent deformation will give misleading k values.
• Use multiple force–displacement pairs and average the k values if your measurements are noisy or your ruler is coarse.
• Convert millimeters or centimeters to meters before entering displacement to keep units consistent (e.g., 15 mm = 0.015 m).
• Zero the displacement from the spring’s relaxed length, not from an arbitrary reference, to avoid offset errors.
• For very stiff springs, small displacement errors can produce large percentage errors in k; use precise measuring tools where possible.
• Assumes linear elastic behavior; many springs deviate outside small deflections.
• Ignores preload and friction effects in real assemblies.
• No unit auto-conversion—keep inputs in SI units.

Worked examples

Deep dive

FAQs

Does direction matter?

Use the magnitude. Sign indicates compression vs. extension but k is positive.

What units should I use?

Use newtons (N) for force and meters (m) for displacement. The calculator outputs k in N/m. If you start from kilograms and millimeters, convert first.

Can I use this for non-coil springs (like leaf or torsion springs)?

Yes, as long as the force–deflection relationship is approximately linear over the range you’re measuring. For torsion springs, you’d typically use torque and angular deflection with a different k unit (N·m/rad).

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