How to Calculate Tension in a Constant Force Spring

Conastant force spring

When designing retractable mechanisms such as cable reels, seatbelt systems, or industrial assemblies, accurately calculating the tension of a constant force spring is critical. A correct calculation ensures stable performance, consistent output force, and long service life.

Basic Tension Formula for a Single Constant Force Spring

The tension force (N) of a constant force spring can be estimated using the following formula:

$\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">T</span>}<span\; style="font-size:\; 14px;\; color:\; \#000000;">=</span>\frac{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">19400</span>}<span\; style="font-size:\; 14px;\; color:\; \#000000;">\cdot </span>{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">t</span>}}^{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">3</span>}}<span\; style="font-size:\; 14px;\; color:\; \#000000;">\cdot </span>\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">w</span>}}{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">6.6</span>}<span\; style="font-size:\; 14px;\; color:\; \#000000;">\cdot </span>{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">d</span>}}^{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">2</span>}}<span\; style="font-size:\; 14px;\; color:\; \#000000;">\cdot </span>\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">1.2</span>}}$T = \frac{19400 \cdot t^3 \cdot w}{6.6 \cdot d^2 \cdot 1.2}T=6.6⋅d2⋅1.219400⋅t3⋅w

Parameters:

• T = Tension force (Newton, N)

• t = Material thickness (mm)

• w = Spring width (mm)

• d = Coil diameter (mm)

Key Insight:

• Tension increases significantly with material thickness (t³ relationship)

• Larger coil diameter reduces force output

• Width contributes linearly to total force

Tension Calculation for Multiple Springs (Parallel Configuration)

In many applications, multiple constant force springs are combined to achieve higher output force or redundancy.

Total Tension Formula:

${\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">T</span>}}_{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">t</span>}\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">o</span>}\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">t</span>}\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">a</span>}\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">l</span>}}<span\; style="font-size:\; 14px;\; color:\; \#000000;">=</span>{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">T</span>}}_{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">1</span>}}<span\; style="font-size:\; 14px;\; color:\; \#000000;">+</span>{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">T</span>}}_{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">2</span>}}<span\; style="font-size:\; 14px;\; color:\; \#000000;">+</span>{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">T</span>}}_{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">3</span>}}<span\; style="font-size:\; 14px;\; color:\; \#000000;">+</span><span\; style="font-size:\; 14px;\; color:\; \#000000;">\cdots </span><span\; style="font-size:\; 14px;\; color:\; \#000000;">+</span>{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">T</span>}}_{\mathrm{<span\; style="font-size:\; 14px;\; color:\; \#000000;">n</span>}}$T_{total} = T_1 + T_2 + T_3 + \cdots + T_nTtotal=T1+T2+T3+⋯+Tn

Example: Three-Spring System

For a system using three springs in parallel:

1. Calculate each spring’s tension individually

2. Sum all values to get total system force

Result:
A predictable and stable combined force output, ideal for:

• Cable retractors

• Hose reels

• Motorized assemblies

• Industrial automation systems

Practical Design Considerations

When applying this formula in real projects, consider:

• Material selection (e.g., stainless steel for corrosion resistance)

• Fatigue life requirements

• Space constraints (coil diameter vs housing size)

• Force tolerance and consistency

Applications of Constant Force Springs

Constant force springs are widely used in:

• Cable and wire management systems

• Medical devices

• Automotive components

• Office equipment (printers, scanners)

• Fitness equipment (Pilates reformers)

Need Help with Custom Spring Design?

At Dongguan Seme Precision Hardware Co., Ltd., we provide:

• Custom constant force spring design

• Engineering support & force calculation verification

• Rapid prototyping and sampling

• Mass production with strict quality control

Contact us today for a free design consultation or sample request.