Spring Constant and Force: Understanding the Relationship

A spring does not generate force on its own. Instead, it reacts only when an external load stretches, compresses, or twists it. This reactive push or pull, the force in a spring, is what we call spring force, and it is governed by a key parameter: the spring constant, k.

What Is the Spring Constant?

The spring constant, also known as force constant or spring force constant, measures how stiff a spring is. It tells you how much force of a spring will react for every unit of deformation.

The relationship between force and deformation is expressed by Hooke’s Law:

F = kx

• F: Force applied (newtons, N)
• x: Spring deformation (meters, m); how much the spring is stretched or compressed.
• k: Spring constant (N/m)

When discussing the restoring force (springs pulling or pushing back), we write:

F = －kx

The negative sign simply means the spring reacts in the opposite direction of the deformation.

What Affects the Spring Constant?

Several design and material characteristics determine the coil spring constant – the stiffness of a spring:

• Material Properties

  Different spring steels – carbon steel, stainless steel, or alloy steel – have different elastic moduli, directly affecting stiffness.

• Wire or Strip Thickness

  A thicker wire (or thicker steel strip, for flat springs) increases stiffness and produces a larger k value.

• Number of Active Coils

  More active coils spread the load over a longer path, making the spring softer and lowering k.

• Free Length

  A longer spring stretches more easily, resulting in a smaller k value.

• Coiling Method and Geometry

  Cylindrical, conical, barrel-shaped, or variable-pitch designs all change how the spring distributes force and therefore change stiffness.

Spring Constant in Flat Spiral Strip Springs

While the formula F = kx applies mainly to compression, extension, and torsion springs made with round wire, strip-based flat spiral springs behave differently because they store and release energy as torque, not as linear force.

For these spiral springs, stiffness is described using a torque constant, which relates the torque output to the angle through which the spring is wound or unwound:

T = kθ

• T: torque (N·m)
• θ: angular displacement (radians)
• k: torque constant that indicates how much torque increases per unit of rotation.

A higher torque constant means the spring becomes “stiffer” rotationally and requires more force to wind. The torque constant depends on factors such as strip thickness, width, material, tempering, mandrel diameter, and total number of coils. These geometric and material properties determine how much energy the spring can store and how smoothly it can release that energy during operation.

Partner with Teng Yao for Precision Spring Solutions

Understanding spring constants – whether linear force in wire springs or torque response in flat spiral strip springs – is essential for designing safe, reliable, and long-lasting mechanisms. At Teng Yao, we specialize in producing high-quality strip-based springs with consistent performance, strict dimensional control, and materials suited for demanding applications. If your projects require customized force curves, torque output, or unique end-tab designs, our engineering team can support you from concept to production.

Contact us to develop spring solutions tailored to your device’s performance and durability requirements.