Calculator Inputs
Formula Used
Spring index: C = D / d
Wahl correction: Kw = ((4C - 1) / (4C - 4)) + (0.615 / C)
Spring rate: k = Gd⁴ / (8D³Na)
Extension: y = (F - Fi) / k
Corrected coil stress: τ = Kw × 8FD / (πd³)
Allowable shear stress: τallow = UTS × shear factor × cycle factor / safety factor
Stored energy: E = Fi × y + 0.5 × k × y²
The calculator treats the spring as a close-coiled extension spring. Hook stress is estimated with a user-selected multiplier.
How to Use This Calculator
Choose the unit system first. Enter wire diameter, mean coil diameter, active coils, and free length. Select a material or choose custom material values. Add initial tension, working load, maximum load, and travel limit. Then set safety, shear, cycle, and hook factors. Press the calculate button. The result section appears above the form. Review the rate, stress, extension, energy, and warning notes. Use the chart to compare extension against load. Export the design as a CSV file or PDF report.
Example Data Table
| Case | Wire Diameter | Mean Diameter | Active Coils | Initial Tension | Working Load | Use Case |
|---|---|---|---|---|---|---|
| Light return spring | 1.2 mm | 10 mm | 22 | 3 N | 12 N | Small latch |
| Medium mechanism | 2.5 mm | 20 mm | 18 | 12 N | 55 N | Lever return |
| Heavy pull spring | 4 mm | 32 mm | 16 | 45 N | 180 N | Industrial fixture |
Tension Spring Design Guide
What This Tool Checks
A tension spring stores energy when it is pulled. It also needs enough initial tension to stay closed before load is applied. This calculator checks force, extension, spring rate, coil stress, hook stress, body length, and safety margin. It helps compare early design options before making prototypes.
Why Geometry Matters
Wire diameter and mean coil diameter strongly affect rate and stress. A small wire gives low force and high flexibility. A larger wire increases force, but it also raises forming difficulty. The spring index shows this balance. A common index range is often easier to manufacture and inspect.
Understanding Load and Travel
Extension begins after the applied load is greater than initial tension. The spring then follows a near linear load path. The calculator uses this relation to find working extension and maximum extension. It also compares the maximum extension with the entered travel limit.
Stress and Safety
Coil stress is corrected with the Wahl factor. This factor accounts for curvature effects in the wire. The allowable stress is reduced by shear factor, cycle factor, and safety factor. A conservative factor is useful for repeated cycles, shock loads, uncertain material data, or rough operating conditions.
Hook Review
Extension springs often fail near hooks, loops, or formed ends. Hook geometry may create local stress concentration. This calculator uses a hook stress factor to estimate that risk. Increase the factor for sharp bends, small loops, or demanding service. Reduce the working load if hook utilization is high.
Using the Results
Start with a safe stress margin. Then review extension, outside diameter, inside diameter, and body length. Adjust one variable at a time. Increase active coils to reduce rate. Increase wire diameter to raise strength. Increase mean diameter to lower rate, but check space limits. Use the chart and exports to document each design version.
FAQs
1. What is a tension spring?
A tension spring is a spring that resists pulling force. It extends under load and returns when the load is removed.
2. What is initial tension?
Initial tension is the built-in force that keeps coils closed before outside load creates extension.
3. Why is spring index important?
Spring index compares mean coil diameter with wire diameter. Very low or high values can make production harder.
4. What does the Wahl factor do?
The Wahl factor corrects coil stress for wire curvature. It gives a more realistic stress estimate.
5. Why check hook stress separately?
Hooks and loops can create local stress. They often fail before the main spring body.
6. Can I use custom material values?
Yes. Select custom material, then enter shear modulus and tensile strength in the selected unit system.
7. What is a good safety factor?
A higher safety factor is better for shock, fatigue, uncertain loads, or critical equipment. Use engineering judgment.
8. Is this a final manufacturing design?
No. It is a design estimator. Confirm details with material data, tests, standards, and supplier advice.