Project success with torsion springs is rooted in comprehension of the torsion spring coefficient. This article aims to demystify this intricate concept, providing a guiding resource for engineers at all career levels. Considerations include spring-loaded door systems. A recurring misstep involves underestimating the stored energy in springs - this can raise safety issues. Comprehensive knowledge of torsion spring coefficients enables precise calculations, promoting safe design. The torsion spring coefficient changes based on various spring factors like material, wire diameter, and coil diameter. This article covers torsion spring coefficient basics, their real-life uses, and explains their variability.

What is a Torsion Coefficient?

The torsion coefficient, also known as spring constant, quantifies a torsion spring's resistance to deformation from twisting or rotational force. Specifically, the torsion coefficient measures the change in rotational angle caused by the applied force. Commonly denoted by the Greek letter Kappa (κ), or sometimes referred to as stiffness, it uses units of Newton-meters per radian (Nm/rad) or pound-feet per degree (lb-ft/°). Higher coefficients indicate springs with greater resistance to deformation, i.e., they need more force to twist.

The application of torsion springs, for instance, in a door mechanism, relies on correct torsion coefficient selection. The spring needs to withstand the weight of the door transmitted through the torsion bar, with no excessive deformation or failure. The force encountered in the application, labeled as (X), and the torsion coefficient of the available springs, labeled as (Y), guide the selection of the appropriate spring to handle the expected forces (Z).

The torsion coefficient depends on the spring's material and design. While a larger load might require a spring with a high torsion coefficient, the practical constraints of spring dimensions and materials must suit the application, and adjustments need to consider these factors.

How to Calculate Torsion Coefficient of a Torsion Spring

To compute the torsion coefficient of a torsion spring, apply the formula: κ = E·d^4 / 64·D·N. Each variable in the equation corresponds to a distinct physical measure relevant to spring design.

The symbol E symbolizes the elastic modulus of the spring material, d is the wire's diameter, D is the mean coil's diameter, and N implies the quantity of active coils.

The elastic modulus (E) relies on the spring material. Different materials such as stainless steel, bronze, and spring steel each possess unique moduli of rigidity, accessible from the data provided by material manufacturers. The selection of the material weighs the rigidity against aspects including cost and resistance to corrosion.

The diameter of the wire (d) is ascertained by direct measurement using a caliper. It's important to note that the wire diameter in the formula is raised to the power of four, thus even small inaccuracies in measurement can impact the torsion coefficient calculation. Therefore, precise measurements are necessary for accurate calculations.

The mean coil diameter (D) is found by subtracting one wire diameter from the outer diameter. As an illustration, if a spring has an outer diameter of 10mm and a wire diameter of 1mm, the mean coil diameter becomes 10mm - 1mm = 9mm.

The number of active coils (N) refers to those coils that are able to twist within the spring. 'Passive' coils, such as the ones held in place at the spring ends, are not included in this count. The total count of active coils can influence properties like the spring's energy storage capability, size, and weight, which are all accounted for in spring designs by engineers.


The torsion spring coefficient is fundamental in spring design and aids in prolonging the life of your springs. In this article, we discussed what it is and provided a method for calculating it. Using these principles can help in improving the performance of your spring. Following these techniques can better ensure the overall function and longevity of your torsion springs.