Attention! Input results shown will be +/- 10% from middle value. Hint: The closer your min and max inputs are, the more accurate your results will be!

Attention! Input results shown will be +/- 10% from middle value. Hint: The closer your min and max inputs are, the more accurate your results will be!

Attention! Input results shown will be +/- 10% from middle value. Hint: The closer your min and max inputs are, the more accurate your results will be!

Attention! Input results shown will be +/- 10% from middle value. Hint: The closer your min and max inputs are, the more accurate your results will be!

# Helical Spring Formulas and Equations

There are several different helical compression spring formulas and equations required to complete a design. First, you must focus on your spring’s requirements when it comes to physical dimensions, material type, and working loads. After you’ve set those parameters, the next step is to match the dimensions correctly to achieve the spring’s required function in your application.

When you’ve measured your spring’s surroundings and figured out its environmental requirements, you must set your spring’s tolerances and work within them to achieve the ideal spring design. To the right is a diagram pointing out the term for each dimension. You will also find the formulas used to calculate certain spring dimensions which will help you stay within limits.

#### Wire Diameter

You can measure the tolerances on outer diameter and inner diameter, but your maximum wire diameter must be calculated. You do this by subtracting the minimum inner diameter from the maximum outer diameter and dividing the result by 2.

d = (Douter – Dinner) ÷ 2

• d = wire diameter
• Douter = outer diameter
• Dinner = inner diameter

#### Solid Height

Then you have total coils, which you want to keep at an intermediate number so you can have elasticity. If you have too many, your spring may be elastic but weak. However this is an option some opt for because it allows for a taller solid height. The formula to calculate solid height is total coils plus 1, multiplied by the wire diameter.

With all types of ends (except ground):

Lsolid = d(N+1)

With ground ends:

Lsolid = dN

• Lsolid = solid height
• d = wire diameter
• N = total coils

#### Pitch

You can then calculate the pitch in between the coils using the free length and the amount of coils you decided to use. You do so by subtracting the amount of wires in the closed coils from the free length and then dividing the result by the active coils.

Closed Ends

p = (L–3d) ÷ Na

Closed and Ground

p = (L–2d) ÷ Na

Double Closed Ends

p = (L–5d) ÷ Na

Open Ends

p = (L–d) ÷ Na

• p = pitch
• L = free length
• d = wire diameter
• Na = active coils

#### Use these coil spring calculation equations to make sure your spring fits.

After setting and calculating the physical dimensions, you must move on to your working loads. Your spring’s working loads will determine your spring rate. Find out how much load you will be placing on your spring as well as how much you expect it to deflect under that force.

Both of these factors make up the formula to calculate the required coil spring rate. This formula is dictated in Hooke’s Law where he states “as the extension, so the force”. Hooke’s law simply means that, as your spring compresses/deflects, the load increases proportionally.

k = L ÷ x

• k = Rate
• x = Travel

The full equation to calculate the rate of an already established spring design is the following. This formula requires more information than the previous. The material type and its properties have a lot to do with your spring’s rate.

D = D outer – d
G = E ÷ 2(1 + V)
k = Gd^4 ÷ (8D^3 x na)

• d = Wire Diameter
• D outer = Outer Diameter
• D = Mean Diameter
• E = Young's Modulus of Material
• G = Shear Modulus of Material
• k = Spring Rate
• na = Active Coils
• V = Poison's Ration of Material

If you have a hard time gathering the information, you may simply enter your spring’s dimensions and material type into our spring calculator. Spring Creator will calculate all of the above formulas as well as the elastic limit and maximum load. You may also contact our team to schedule a consultation with our engineers if you’re having a hard time adjusting the design.