Inputs
Example data table
| Scenario | Rate | Working deflection | Preload | Total deflection | Force | Energy |
|---|---|---|---|---|---|---|
| Metric (basic load) | 15.0 N/mm | 10.0 mm | 2.0 mm | 12.0 mm | 180 N | 1.08 J |
| Metric (high preload) | 12.0 N/mm | 5.0 mm | 8.0 mm | 13.0 mm | 156 N | 1.01 J |
| Metric (light spring) | 3.0 N/mm | 25.0 mm | 0.0 mm | 25.0 mm | 75 N | 0.94 J |
| Metric (rate from geometry) | 4.84 N/mm | 16.53 mm | 0.00 mm | 16.53 mm | 80 N | 0.66 J |
| Imperial (basic load) | 8.0 lbf/in | 0.60 in | 0.10 in | 0.70 in | 5.6 lbf | 0.22 J |
| Imperial (stiffer spring) | 25.0 lbf/in | 0.40 in | 0.00 in | 0.40 in | 10.0 lbf | 0.23 J |
| Geometry example inputs (metric) | |||||||
|---|---|---|---|---|---|---|---|
| Wire diameter (d) | Mean diameter (D) | Active coils (Na) | Shear modulus (G) | Spring index (C) | Wahl factor (K) | Estimated rate | Shear stress @ 80 N |
| 2.0 mm | 16.0 mm | 8 | 79.3 GPa | 8.0 | 1.184 | 4.84 N/mm | ≈ 482 MPa |
Formula used
- Hooke’s law (linear spring): F = k × x
- With preload: F = k × (x + x₀)
- Energy stored: U = ½ k (x + x₀)²
- Spring rate from geometry: k = G d⁴ / (8 D³ Nₐ)
- Shear stress (round wire): τ = (8 F D)/(π d³) × K
- Wahl factor: K = (4C−1)/(4C−4) + 0.615/C, where C = D/d
How to use this calculator
- Select a unit system (Metric or Imperial).
- Choose what you want to solve: force, rate, or deflection.
- Enter the required two values; add preload if your spring is pre-compressed.
- Optionally enable lengths to compute deflection from free and installed lengths.
- Optionally enable geometry to estimate rate, stress, and coil-bind limits.
- Click Calculate and export results as CSV or PDF if needed.
Compression spring force guide
Linear force prediction
A compression spring follows Hooke’s law: force equals rate times total deflection. Using the metric example, k=15 N/mm and working deflection x=10 mm with 2 mm preload gives x_total=12 mm, so F=180 N. The same approach works in imperial units using lbf/in and inches.
Preload and installed length
Preload shifts the load curve upward and is common in valves and clamps. If you enable free and installed lengths, deflection is x = L0 − Li. For instance, L0=80 mm and Li=68 mm yields 12 mm deflection before any extra preload input.
Choosing the right spring rate
When you already know the required force, rearrange the formula to k = F / x_total. A target of 120 N at 8 mm total deflection needs k=15 N/mm. Rate selection affects feel, vibration response, and how quickly loads rise near end travel. For stacked springs, convert each element rate before combining.
Rate from spring geometry
With geometry enabled, the calculator estimates k = G d^4 /(8 D^3 Na). For d=2.0 mm, D=16.0 mm, Na=8, and G=79.3 GPa, the estimated rate is about 4.84 N/mm. This helps compare catalog springs when published rates are missing.
Stress and Wahl correction
Spring stress grows quickly as wire diameter decreases because τ ∝ 1/d^3. The Wahl factor K accounts for curvature; it depends on the spring index C = D/d. In the geometry example, C=8 and K≈1.184. At 80 N, shear stress is roughly 482 MPa, so you can judge margin versus an allowable value.
Coil bind and travel margin
Coil bind happens when coils stack solid. Using total coils Nt = Na + inactive coils, a quick solid-length estimate is Ls ≈ Nt·d. Leaving 1 mm clearance prevents hard contact. The calculator reports deflection-to-solid and the corresponding force so you can keep working travel safely below bind.
Energy for system checks
Energy stored U = ½ k x_total^2 is useful for impact and latch behavior. The 15 N/mm, 12 mm example stores about 1.08 J, while an 8 lbf/in spring at 0.70 in stores about 0.22 J. Higher energy can increase rebound and noise, so confirm damping and guides. Check guides and tolerances always.
FAQs
1) What is spring preload in this calculator?
Preload is the initial deflection already applied before the working stroke. The tool adds preload to your working deflection to get total deflection, then computes force. Use it for assemblies that clamp, seat, or keep parts in contact.
2) When should I use free and installed lengths?
Use lengths when you know the spring’s free length and the installed length in the mechanism. The calculator sets deflection as free minus installed length. It’s helpful for packaging checks and reduces mistakes from typing deflection directly.
3) Why can geometry rate differ from the rated spring rate?
Geometry rate uses an ideal round-wire formula and assumes active coils, mean diameter, and shear modulus are accurate. Real springs vary due to end effects, tolerances, heat treatment, and material lot changes. Use geometry as an estimate and prefer manufacturer data when available.
4) What spring index values work well?
Spring index C = D/d influences stress concentration and manufacturability. Many designs target roughly C=6 to C=12. Low C raises stress and is harder to wind; very high C can reduce stability and increase buckling risk.
5) How do I prevent coil bind?
Provide free length and coil data to estimate solid length. Keep your maximum total deflection below the deflection-to-solid value and leave clearance (for example, 1 mm or 0.04 in). If you approach bind, reduce stroke or choose a longer spring.
6) What does the energy stored value mean?
Energy stored is the work required to compress the spring to the total deflection, U = ½ k x². It helps compare how much “kick” or rebound a spring can deliver. Higher energy can demand better guides, stops, and damping.