Extension springs are found in various applications, from everyday objects to sophisticated equipment. A critical component of these springs is the spring rate, which determines how the spring performs when forces are applied to it. This parameter is key to the functionality of your design and ensures its safety. This article offers a step-by-step guide on determining the extension spring rates, interpreting practical outcomes, and selecting suitable springs for your project. Learn about the integral aspects of extension spring rates to enhance your engineering applications.

What is Spring Rate?

Spring rate refers to the resistance provided by an extension spring to a specific load, numerically determining how much force is required to make the spring extend to a certain length. This is typically denoted as force per unit length, which includes measurements like pounds per inch (lb/in) or newtons per millimeter (N/mm).

The spring rate of an extension spring is distinct from that of a compression spring. For extension springs, a low rate means that a spring can extend more under the same force while a high rate signifies a more rigid spring that needs a larger force to stretch to the same length. The relationship between the extension of a spring and the force it exerts is highlighted in Hooke's law, indicating that the level of force a spring applies is directly proportional to its extension, assuming the spring's elastic limit is not exceeded. Hooke's law includes the concept of the spring rate.

Knowledge of the spring rate supports appropriate design and selection of extension springs for specific roles. For instance, in a garage door mechanism, a suitable spring rate aids in maintaining safety and functionality. If the spring rate is excessively low, the door could descend too rapidly. On the other hand, a very high spring rate may impede lifting the door. As a result, understanding spring rates assists engineers in selecting the best spring for their objective.

How to Calculate Spring Rate of an Extension Spring

The spring rate 'k' of an extension spring is determined using the designated formula:

k = (G * d^4) / (8D^3 * n)


While using this formula, ensure the units for all variables are uniform. For instance, if using Imperial units like pounds and inches, correspondingly adjust the Modulus of Rigidity (G) to these units prior to calculation.

If taken for example an extension spring that has: a wire diameter (d) of 0.035 inches, a mean diameter (D) of 0.250 inches, 10 active coils (n), and a modulus of rigidity (G) of 11.5 million pounds per square inch (11,500,000 psi). The spring rate calculation is:

k = (11,500,000 * 0.035^4) / (8 * 0.250^3 * 10) = 13.81 pounds per inch (lb/in)

This spring rate indicates that the force required to stretch this spring by one inch is 13.81 pounds.

Caution: The above computation is based on a linear relationship between the applied force and the extension of the spring, integral to Hooke's Law. This law remains valid within elastic deformation but may not hold true beyond its elastic limit (plastic deformation). Accordingly, this calculated spring rate should be applied within the load and elongation limits of the respective spring, the requirement of the application, and the spring material's mechanical properties.


In closing, extension springs and in particular, their spring rates, form an essential part of many engineer's day-to-day tasks. This isn't solely a theoretical idea, but it also carries practical importance for your designs. The spring rate, representing the spring's response to a load numerically, can be computed with precision for extension springs. Mastering this rate calculation will enable you to forecast the performance of your extension springs with increased accuracy, ultimately improving the reliability of your projects. While the concept might appear intimidating initially, repeated application will make it familiar. This understanding is a valuable asset for competent engineering.