About Helical Springs & Calculating the Formula

In the manufacture of custom springs for an application, engineers must first accurately calculate a helical spring formula to achieve the ideal spring design. Formulas and equations vary, too, for each type of helical spring. For example, a lot to do with calculating the formula for a helical spring relates as much to the type of spring required for an application as it does in selecting the material with the necessary properties for the application. There may be optional configurations or certain finishing requirements to consider as well.

Helical SpringHelical springs are those familiar spiral wound, coil-shaped, mechanical components. Think Slinky. Often referred to as a coil spring, a helical spring is essentially an elastic coil formed by tightly winding a piece of wire into a cylinder. The elastic properties of a helical spring allow it to deflect the action of a load and then, when that load is removed, return to its original shape. Given that there are only three types of helical springs—compression, tension, or torsion springs—what type of load the spring carries will determine what type of spring will be used in an application.

Types of Helical Springs

Compression springs are the most widely used helical springs. As the name suggests, compression springs are designed to carry a load when compressed, providing a buffer between two objects or absorbing energy from a load. By design, the spaces between a compression spring’s coil are visible and open when unloaded. These springs are used as shock absorbers, vibration dampers, pure energy accumulators and as force generators. Compression springs come in a variety of shapes, too—conical, hourglass, convex, and barrel—with the uniform cylindrical shape being the more common design.

Designed to resist the tension created by a pulling force, tension springs, also called extension springs, are used to create a resistance against a directional force when pulled or stretched or for storing potential energy. They are characterized by tightly wound coils that touch each other when the spring is unloaded. Loops or hooks configured on either end of the spring are attached to separate objects or components that, when loaded by an external force, counter with a pulling force while simultaneously creating the required energy necessary to carry the load while the spring is being pulled or stretched.

Torsion springs are another type of helical spring. Much like other helical springs, torsion springs store energy. It is achieved when the spring is twisted or rotated, through torque force however, not through compressive or tensile force. When a torsion spring is twisted on its axis it exerts the force equivalent to the amount applied to it but in an opposite direction. In other words, a torsion spring will store the mechanical energy created while being rotated and then release that energy once the rotational load has been removed. Torsion springs can be configured in a single-bodied and double-bodied helical design, with different end configurations including straight, offset, and hinge ends, and can be designed to generate rotational forces in either a clockwise or counterclockwise motion.


Surface treatment for helical springs vary and depend on the application requirements. Frequently used options include anodizing, bead blasting, passivation, electro-polishing, powder coating, rust prevention, deburring, color coding, laser etching, among others. Plating finish options include black oxide, cadmium, chrome, gold, nickel, phosphate, tin, and zinc.

Helical Spring Formula Calculation Functions

Helical spring formulas are calculated to ensure the spring will function in a device or mechanism as expected. The manufacturing of a spring cannot be left to guesswork or approximation.

As mentioned, much to do with calculating the formula for helical springs involves selecting a material with the necessary properties for the application, along with other factors such as its working load, tolerances, cycles, and so forth. The spring’s wire diameter, D, its inner diameter, ID and outer diameter, OD, its mean coil radius, R, the number of active coils, VN, and other variables are calculated to ensure the desired force-deflection response is achieved.

Additionally, the formula for a helical spring, its measurements and specifications, will differ in relation to the type of spring—compression, tension or torsion—too. The measurement of a compression spring will require 4 specifications—the wire diameter, its outer diameter, the free length of the spring, and the number of coils must be factored.

For example, if the spring is designed to be fitted into a shaft or hole, the required dimension for the outer diameter would need to be calculated by multiplying the wire diameter by two and adding that number to the inner diameter. The equation is expressed as such:

2(Wire Diameter) + Inner Diameter = Outer Diameter

2WD + ID = OD

On the other hand, if the spring design is intended to fit over a shaft, the dimension of the inner diameter of the helical spring needs to be calculated. Calculate the dimension by multiplying the wire diameter by two and subtracting it from the outer diameter as expressed:

Outer Diameter – 2(Wire Diameter) = Inner Diameter

OD – 2(WD) = ID

In measuring a tension spring, 5 specifications are needed—the wire diameter, its outer diameter, the length of the inside hook, the type of hook, and the spring’s body length. To accurately calculate the required dimensions for a torsion spring design, first determine the direction of wind—left or right hand. Then measure the wire diameter, the outer diameter, the number of total coils, and the length of leg 1 and the length of leg 2.

Fundamentally, helical springs are a simple mechanical device designed to support various types of loads—compressive, tensile and torque. To ensure their reliability, durability, and precision, engineers calculate helical spring formulas and equations to achieve optimal spring design and functionality.

If you’re looking for helical springs or any other custom spring or wire form, contact the experts at James Spring and Wire.