Coil Spring Rate Calculator
Calculate compression spring rate, working load, coil index, Wahl-corrected shear stress, solid height, and travel margin from wire diameter, coil diameter, active coils, material, and end type.
⚙Named coil spring presets
Load a typical spring, then adjust wire diameter, OD or ID, active coils, shear modulus, end type, and working travel.
📏Spring geometry, material, and working load
Measure the spring wire, not the gap between coils.
Mean diameter is OD minus wire diameter, or ID plus wire diameter.
Use the diameter selected above.
Do not count inactive closed end coils as active coils.
The rate changes directly with shear modulus.
Use Mpsi in imperial or GPa in metric mode.
End type affects solid height and stability notes.
Unloaded spring length.
Length after preload, before working travel.
Shortest expected operating length.
Use your material data, heat treatment, and fatigue requirement.
Coil spring result
🧪Material shear modulus cards
📊Coil spring reference tables
| Material | Shear modulus | Typical use | Rate note |
|---|---|---|---|
| Music wire | 11.5 Mpsi / 79.3 GPa | Small and medium springs | High modulus gives a higher rate for the same geometry. |
| Hard drawn wire | 11.4 Mpsi / 78.6 GPa | Light commercial springs | Close to music wire in stiffness calculations. |
| Oil tempered wire | 11.2 Mpsi / 77.2 GPa | Machinery and larger wire | Slightly lower rate than music wire at the same size. |
| Chrome silicon | 11.5 Mpsi / 79.3 GPa | High stress dynamic springs | Rate is similar to music wire; stress capacity differs. |
| 302 stainless | 10.0 Mpsi / 69.0 GPa | Corrosion resistance | About 13 percent lower rate than music wire. |
| Phosphor bronze | 6.3 Mpsi / 43.4 GPa | Electrical and nonmagnetic uses | Much softer rate for the same coil geometry. |
| Coil index C | Manufacturing meaning | Stress effect | Practical note |
|---|---|---|---|
| Under 4 | Very tight coil | High Wahl factor | Difficult to form and usually high stress. |
| 4 to 6 | Tight but possible | Elevated stress | Use caution for fatigue or heavy deflection. |
| 6 to 10 | Preferred general range | Moderate correction | Good starting range for many compression springs. |
| 10 to 12 | Large coil index | Lower correction | May be easier on stress but less stable laterally. |
| Over 12 | Loose coil geometry | Lower direct stress | Check buckling, tangling, and side loading. |
| End type | Inactive coil estimate | Solid height basis | Use case |
|---|---|---|---|
| Plain ends | 0 extra coils | Active coils x wire | Simple springs where seating is not critical. |
| Plain and ground | 0.5 extra coil | (Active + 0.5) x wire | Improved seating with modest extra solid height. |
| Squared or closed | 1.5 extra coils | (Active + 1.5) x wire | Common when ends need flatter bearing contact. |
| Squared and ground | 2.0 extra coils | (Active + 2.0) x wire | Best seating and squareness for precision work. |
| Check | Formula basis | Good screen | Meaning |
|---|---|---|---|
| Spring rate | G x d^4 / (8 x D^3 x Na) | Matches test data | Linear force per deflection before coil contact. |
| Wahl factor | (4C - 1)/(4C - 4) + 0.615/C | Lower near C 8+ | Corrects direct torsional stress for curvature. |
| Shear stress | Kw x 8 x F x D / (pi x d^3) | Below allowable | Screen stress at the entered working length. |
| Solid margin | Working length - solid height | Positive margin | Prevents coil bind at the shortest operating length. |
| Preload | Rate x installed deflection | Application specific | Load already present at the installed length. |
💡Spring calculation tips and safety
A spring rate is an single number that will indicate whether a coil spring will work or if the spring will fail. The spring rate is the number of pounds of force (or newtons in the metric system) that is required to compress a coil spring either one inch or one millimeter, respective. By selecting the correct spring rate for a given piece of equipment, the spring will be reliable.
However, by selecting the incorrect spring rate, the spring may experience various problem. In order to calculate the spring rate for a given spring, a person can utilize a specific equation. The equation incorporates the shear modulus of the wire, the fourth power of the wire diameter, and the spring is divided by eight times the cube of the mean coil diameter of the spring multiplied by the number of active coil.
How to Calculate a Spring Rate and Check the Spring
Due to the use of the fourth power of the wire diameter in the equation, any change in the wire diameter will have a large effect upon the spring rate. For instance, increasing the diameter of the wire by ten percent will increase the spring rate by almost fifty percent. Due to the impact of the wire diameter upon the spring rate, manufacturers make springs with very strict tolerance regarding the springs wire diameter.
Another of the factors that can impact the spring rate of the spring is the mean coil diameter of the spring. You can obtain the mean coil diameter by measuring either the outside diameter or the inside diameter of the spring. If you measure the outside diameter of the spring, then one wire diameter must be subtracted from that measurement to obtain the springs mean coil diameter.
However, if you measure the inside diameter, then one wire diameter must be added to that measurement to determine the mean coil diameter of the spring. The calculator can perform this calculation after the user selects the diameter that was measured. Additionally, the number of active coils of the spring must be used in the calculation; the springs closed or ground turns will not participate in the springs operation.
The material from which the spring is made will also impact the spring rate of the spring. For example, if music wire is used, the shear modulus will be near eleven and a half million pounds per square inch. Oil-tempered wire has a slightly lower shear modulus, and 302 stainless steel has a shear modulus that is approximately thirteen percent lower than music wire.
Thus, any change in the springs material will impact the spring rate. If corrosion resistance is required from the spring, 302 stainless steel will be required. However, using this material will result in a softer spring.
Thus, the diameter of the spring or the mean coil diameter will have to be altered to compensate for the change in material. Another of the numbers that the spring rate calculator can calculate is the coil index of the spring. The coil index is a ratio of the mean diameter of the spring to the diameter of the wire.
The ideal value of the springs coil index is between six and ten. Coil indices that are below four indicate that the coils of the spring may be difficult to wind during the manufacturing of the spring. Coil indices that are above twelve indicate that the spring may buckle to one side when in operation.
Springs with coil indices above twelve will require extra guidance to prevent buckling. The calculator will indicate these extreme coil indices so that they are avoided after the spring is order. Another of the measurements of the spring is the solid height of the spring.
The solid height is the length of the spring when each of the coils of the spring are touching the next adjacent coil. Thus, the calculator can calculate the solid height by taking the total number of coils of the spring, including inactive end coils, and multiplying that number by the diameter of the springs wire. The working length of the spring must be long enough to cover the solid height of the spring.
The user will provide the working length and will include enough room for manufacturing tolerance. One of the last steps in the process is to stress check the spring. The stress on the spring can be calculated by multiplying the Wahl factor by eight times the load on the spring times the mean diameter of the spring, dividing that value by pi times the cube of the springs wire diameter, and then multiplying that result by the springs service factor.
The result of this calculation can be compared to the allowable shear stress of the spring. If the result is one or close to one, a warning will appear on the calculator that indicates that the spring may need to be changed in its geometry, material, or service factor before it is manufactured. Springs will behave differently than the ideal model indicated in the equation.
For example, the spring may experience a permanent set if it is compressed for the first time. Additionally, the spring may buckle if it is too slenderly. Any side loads that are placed onto the spring will also create additional stresses onto the spring that are not accounted for in the calculation.
However, processes like shot peening, presetting, or end grinding will increase the fatigue life of the spring. These processes is outside of the scope of the calculation. There are also tables that assist in the determination of the various spring factors.
One table indicates the different materials and their shear modulus values, their corrosion resistance, and their cost. Another table indicates the mean coil diameter, the manufacturing difficulty, and the stress of the spring with different coil indices. The third table shows the different end types of springs and how many inactive coils they will have based off that spring end type.
These tables will assist users in understanding the spring and eliminating the need to memorize the different values. The process of entering the various measurements into the calculator to determine the spring rate is a simple process. The user will need to enter the wire diameter of the spring, choose the type of diameter that was measured, enter the number of active coils, the type of material of the spring, and the three lengths of the spring.
Each of these values will appear on the screen after entering them into the calculator. Additionally, the spring rate can be adjusted to find the proper spring, and the result will update on the screen. This rapid updating of the rates will allow the designer to easily find a spring that will respect the physics of the spring and the limits of the machine.
Thus, if all of the rates for the spring are within the limits that is set for those rates, the spring will function correctly within the machine.
