Spring Constant Calculator

Table of Contents:

• What is the Spring Constant Calculator 
• How to use the spring constant calculator, example
• What is Spring Constant?
• Can I change My Spring Constant?
• How to Find Your Spring Constant Easily
• G-Values for Common Spring Materials
• Compression Spring Constant
• Formula for Compression Spring Constant
• Example of Calculating the Compression Spring Constant
• Formula for Determining the Spring Constant from Load and Travel
• Extension Spring Constant
• Formula for Extension Spring Constant
• Formula for Extension Spring Constant Based on Load and Travel
• Example of Calculating the Extension Spring Constant
• Torsion Spring Constant
• Formula for Torsion Spring Constant
• Example: Calculating Torsion Spring Constant
• Modulus of Elasticity (E) for Common Spring Wire Materials
• Conclusion

What is the Spring Constant Calculator 

The best spring calculator to calculate the spring constant in compression, extension and torsion springs. By entering a few basic spring dimensions such as: wire diameter, outer diameter, free length and total coils the spring constant calculator calculates the spring constant of your spring. Find out your spring constant, your springs maximum load, maximum travel and so much more. Our spring constant calculator can calculate the spring constant in english lbs/in or metric N/mm. Download 3D Blueprints, spec sheets for all your spring designs with the best spring constant calculator.  

How to use the spring constant calculator, example:

Let's assume your Compression Spring has a:

Go to the Spring Constant Calculator  and choose compression springs then enter the following specifications

• Wire diameter of  0.043 inches
• Outer Diameter of  0.250 inches
• Free Length of 1.043 inches
• Total Coils of 13.7 
• End Type: Closed and Squared
• Material Type: Music Wire ASTM A228

Click Calculate

In the 1st Tab of “Preview Springs and Specs”

The Spring Constant calculator has calculated the 

• Spring Rate of 47.328 lbs/in of compression This means your spring has a rate of force of 47.328 per inch of compression, Meaning it will take 47.328 lbs of force or load to move or compress the spring 1 inch of distance. 

• Maximum Load of 16.861 lbs of force. This means the maximum safe force you will obtain from this compression spring is 16.861 lbs of load or force.
• Maximum Travel or Deflection of 0.356 inches of travel. This means that your spring can safely compress, travel or deflect 0.356 inches. This spring CANNOT travel or deflect to its solid height or coil bind height. 

What is Spring Constant?

Hooke’s Law, which is foundational in the study of spring dynamics, states that the force exerted by a spring is proportional to the distance it is stretched, compressed or twisted. This relationship is mathematically represented by F=kx where F is the force applied to the spring, x is the displacement from the spring's original length, and k is the spring constant. This law highlights the linear behavior of springs within the elastic limit, where the deformation is reversible, and the spring returns to its original shape once the force is removed.

The units of the spring constant, such as Newtons per millimeter (N/mm) or pounds per inch (lbs/in), depend on the system of measurement used and indicate the force required per unit of length change in the case of compression and extension springs. Torsion springs constant unit of measure in imperial units is inch-lbs/degree and metric is N-mm/degree . A higher spring constant indicates a stiffer spring, requiring more force to produce the same displacement compared to a spring with a lower spring constant.

Understanding the spring constant is crucial not only for designing mechanical systems like vehicle suspensions and electronic devices but also for applications in biomechanics and architecture. It allows engineers and designers to predict how springs will behave under load, optimize performance, and ensure safety and comfort in their applications. Accurate calculation and application of the spring constant can lead to innovations in product design and improvements in a wide range of technological and industrial fields.

Can I change My Spring Constant?

Yes, The AI behind our spring constant calculator software is different, it designs stronger, weaker and almost identical spring designs at the time of inputs so you don't need to re-plug in more numbers. Just look at the results tab and you will get thousands of similar springs designs that are weaker, stronger and very similar so you can change your spring constant at any time by picking a different spring constant from the thousands of spring options to choose from.

How to Find Your Spring Constant Easily

Go to Spring Creator 5.0 and input just a few spring dimensions and get your spring constant in seconds.

G-Values for Common Spring Materials

Understanding the shear modulus (G) of various materials is crucial for accurately calculating the compression spring constant. The shear modulus, often denoted a G, is a measure of a material's ability to resist shear deformation and is a fundamental property in determining a spring's stiffness. Below is a breakdown of the G-values for common spring materials:

These values reflect the different properties of common spring materials for spring wire, influencing their performance in specific applications. For instance, materials like Music Wire and Inconel have higher G values, indicating a higher stiffness, which is ideal for springs that require significant resistance to deformation under load.

Compression Spring Constant

Compression spring constant or compression spring rate is defined as the rate of force per inch of compression or in metric its Newtons per millimeter of compression. The compression spring constant is a crucial factor in mechanical engineering, playing a pivotal role in applications where springs are compressed by an external load. It quantifies the stiffness of a compression spring, indicating how much force is required to compress the spring by a unit of length.

Formula for Compression Spring Constant

The fundamental formula to calculate the compression spring constant

​k = Gd^4 ÷ (8D^3 * n)

Where:

• G (Shear Modulus of Material): This is a material-specific constant that measures the rigidity or stiffness of the spring material. It is expressed in pounds per square inch (psi) and indicates how much the material resists shear stress.
• d (Wire Diameter): The diameter of the spring wire, typically measured in inches. This dimension greatly affects the spring's overall strength and stiffness.
• D (Mean Diameter): The average diameter of the middle of the spring coil, also measured in inches. This determines the overall diameter size of the spring and influences its compressibility.
• N (Number of Active Coils): The total coils that are actively contributing to spring compression. This count excludes any coils that are squared off or closed.

Example of Calculating the Compression Spring Constant

In this example, we calculate the compression spring constant k for a spring made from Music Wire, a common material known for its high strength and durability. The specifications for the spring are as follows: a wire diameter (d) of 0.035 inches, an outer diameter (OD) of 0.500 inches, a mean diameter (D) of 0.465 inches, and a total of 8 active coils (N). The spring's free length (FL) is 1.000 inch. Given these parameters, we use the spring constant formula k = Gd^4 ÷ (8D^3 * n).

For Music Wire, the shear modulus (G) is 11.5×10^6 psi. Substituting all the known values into the formula, we perform the calculation as follows:

• k = Gd^4 / 8D^3N
• k = (11.5 x 10^6) (0.035)^4) / 8 (0.465)^3 (8)
• k = 17.2571875 / 6.434856
• k = 2.68 lbs / inch

Finally, the spring constant k is computed to be 2.68 pounds per inch. This value signifies that a force of 2.68 pounds is required to compress this specific spring by one inch of distance. In other words the spring needs a force of 2.68 lbs to compress one inch of distance.  This calculation not only helps in understanding the physical characteristics of the spring but also assists in predicting how the spring will perform under various load conditions, crucial for applications requiring precise mechanical movements and load-bearing capacities.

Example used is Part Number:  AC035-500-10000-MW-1000-C-N-IN    

Blueprint for Part Number  AC035-500-10000-MW-1000-C-N-IN    

Formula for Determining the Spring Constant from Load and Travel

Formula for Determining the Spring Constant from Load and Travel
The basic formula to calculate the spring constant for compression springs when you have predetermined the load and the distance traveled it needs to achieve is relatively straightforward:

k = Load / Distance Traveled

This equation derives from Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement caused by that force. Here, k represents the spring constant, indicating the force per unit of distance traveled.

Practical Example

Suppose you are designing a spring mechanism where a specific load needs to result in a precise amount of compression to function correctly. Consider a scenario where:

Using the formula:

This spring constant calculator shows that the compression spring constant k is 2.5 pounds per inch. In practical terms, this means that for every inch that the spring is compressed, it requires 2.5 pounds of force to do so.

Extension Spring Constant

The extension spring constant is a measure of the stiffness of an extension spring, indicating how much force is required to extend the spring by a unit of distance. This characteristic is crucial for ensuring that extension springs function correctly within their intended applications, such as in machinery where parts must return to a specific position after being pulled.

Formula for Extension Spring Constant

The extension spring constant k is calculated using a formula similar to that of compression springs, reflecting Hooke’s Law, which states that the force exerted by a spring is proportional to the displacement of that spring. The formula for the extension spring constant is:

k = Gd^4 ÷ (8D^3 * n)

​

Where:

• G is the shear modulus of the material, representing the material's ability to withstand shear stress.
• d is the diameter of the wire used in the spring.
• D is the mean diameter of the coils.
• N is the number of active coils contributing to the spring's elasticity.

This formula provides the basis for calculating how stiff the spring is per unit of distance traveled which is lbs/in or N/mm of extension, this translates to how much force is needed to extend it by a unit of travel.

Formula for Extension Spring Constant Based on Load and Travel

The formula to calculate the extension spring constant when the desired load and the resulting extension are specified, while also considering any initial tension in the spring, is given by:

 k = Load−Initial Tension / Distance Traveled

This formula allows for a more accurate calculation of the extension spring constant by factoring in the initial tension, which is the force already present in the spring when it is at its relaxed length.

Example of Calculating the Extension Spring Constant

Consider an extension spring that needs to extend under a specific load and within a particular range of extension. For instance, suppose you have a spring with an initial tension of 2.5 pounds, and you want to achieve a load of 10 pounds when the spring is extended by 0.568 inches:

• Load Applied: 10 pounds
• Initial Tension in Spring: 2.5 pounds
• Distance the Spring Travels: 0.568 inches

Using the formula provided:

k = 10 lbs − 2.5 lbs / 0.568 inches =   7.5 lbs / 0.568 inches = 13.204 lbs/in

This result, 13.204 pounds per inch extension spring constant, indicates the extension spring constant. It tells us that each inch of extension requires 13.204 pounds of force, then you factor in the initial tension of 2.5 lbs thus giving you a total extension spring load of 10 lbs at 0.568 inches of extended travel.

Torsion Spring Constant

The torsion spring constant or torsion spring rate defines the stiffness of a rotational torsion spring, indicating the torque required to rotate the spring by one degree of travel. The torsion spring constant in inches is: inch-lbs/degree and metric is N-mm/degree. Unlike compression or extension springs, which involve linear movement, torsion springs work on rotational motion. They are crucial in applications that require rotational force, such as hinges, automotive trunk lids, and various machinery components.

Formula for Torsion Spring Constant

The torsion spring constant is calculated using a unique formula due to the nature of rotational motion:

k = Ed^4 / 10.8DN

Where:

• E is the modulus of elasticity, representing the material's stiffness and measured in psi (pounds per square inch).
• d is the diameter of the spring wire, measured in inches.
• D is the mean diameter of the spring coils, measured in inches.
• N is the number of active coils, contributing to the spring's rotational flexibility.

Example: Calculating Torsion Spring Constant

Let's take a practical example of calculating the torsion spring constant, using a spring made of Music Wire. Assume the spring parameters are as follows:

• Wire Diameter (d): 0.035 inches
• Mean Diameter (D): 0.465 inches
• Number of Active Coils (N): 3
• Modulus of Elasticity (E) for Music Wire: 30×10^6 psi

Substituting these values into the formula gives:

k = 30×10^6×(0.035)^4 / 10.8×0.465×3

Breaking down the calculation:

1. Calculate  d ^4: (0.035)^4 = 0.0000015
2. Calculate D × N: 0.465 × 3 = 1.395
3. Substitute the values: k = 30 × 10^6 × 0.0000015 / 10.8 × 1.395 = 4515.066
4. k = 2.988 lb-in/360°
5. k = 2.988/360° = 0.008 Torsion spring rate per degree of radial travel

This calculation indicates that the torsion spring constant is approximately 2.988 inch pounds per 360 degrees. Let's break it down further and take 2.988 inch-lbs/360 degrees = 0.008 Torsion spring rate per degree of radial travel.

This means if we twist or rotate the torsion spring 90 degrees we will get 0.753 inch-lbs of torque. Formula is torsion spring rate of  0.008 inch-lbs x 90 degrees of radial travel = 0.753 inch-lbs of torque. 

Formula to determine torsion spring constant k :

k = torque / Distance Traveled in degrees.  

So in the above example take the torque of 0.753 inch-lbs / 90 degrees = 0.008 inch-lbs per degree of torsion spring rate. This is how to calculate torsion spring constant by torque or load and knowing the distance in degrees of travel.  

Example spring used for this formula is part number: 

 AT035-500-3000-MW-RH-0750-N-IN

Modulus of Elasticity (E) for Common Spring Wire Materials

The modulus of elasticity, often represented as E, is a crucial property for spring wires because it measures the stiffness of a material when subjected to mechanical stress. This parameter, typically expressed in millions of pounds per square inch (psi × 10^6), provides a reference point for predicting how well a spring will return to its original shape after being flexed or compressed. Different materials have unique modulus values, influencing their behavior in various applications.

• Music Wire: 30 psi×10^6

Renowned for its strength and high tensile properties, music wire is a popular choice for precision springs that require significant force and high resistance to deformation.

• Stainless Steel: 28 psi × 10^6

Stainless steel provides an excellent balance between strength and corrosion resistance, making it suitable for springs exposed to harsh environments or high humidity.

• Chrome Vanadium: 30 psi×10^6

Chrome vanadium is prized for its resilience and durability, providing good resistance to fatigue, which makes it ideal for high-stress applications.

• Chrome Silicon: 30 psi×10^6

Chrome silicon, known for its high tensile strength and stability at elevated temperatures, is a great choice for automotive and aerospace applications.

• Phosphor Bronze: 15 psi×10^6

Phosphor bronze offers excellent flexibility and fatigue resistance, while being more corrosion-resistant than many steel alloys. It is often used in electrical and marine applications.

These modulus values give insight into the mechanical properties of various spring wires, allowing engineers to select the most suitable material for specific performance requirements. Whether designing springs for precision equipment or industrial machinery, understanding the modulus of elasticity is essential to ensure the springs maintain their shape and function over time.

Our spring constant calculator is based on the formulas on this page.

Conclusion

In conclusion, understanding the spring constant calculator is crucial for designing and optimizing mechanical systems. Whether you're working with compression, extension, or torsion springs, accurately calculating the spring constant on our spring constant calculator ensures that your springs perform reliably and meet the desired specifications under varying loads. The modulus of elasticity (E) and shear modulus (G) are fundamental properties that influence spring stiffness, affecting how much force is needed to compress, extend, or rotate the spring. Given the diverse applications and importance of these calculations, utilizing a reliable and user-friendly tool is essential.

Spring Creator 5.0 simplifies these complex calculations, providing accurate spring constants for various spring types and materials. By inputting your spring parameters into the spring constant calculator, you can quickly and easily determine the spring constant you need for your specific design requirements. Embrace the efficiency and accuracy of Spring Creator 5.0 to streamline your spring design process, ensuring that your springs deliver consistent performance in every application.

Created by Alfonso Jaramillo Jr
President Acxess Spring
Over 40 Years of Experience in Spring Engineering and Manufacturing