Spring Rate Calculator
Estimate round-wire coil spring rate from wire diameter, mean coil diameter, active coils, shear modulus, spring type, preload, travel, end condition, and stress allowance.
Calculation Breakdown
| Material | Typical shear modulus | Good use | Stress note |
|---|---|---|---|
| Music wire ASTM A228 | 11.5 Mpsi / 79 GPa | High strength small springs | Not ideal for corrosion |
| Oil tempered wire | 11.2 Mpsi / 77 GPa | General machine springs | Good rugged choice |
| Chrome silicon | 11.2 Mpsi / 77 GPa | Valve and high stress springs | Better heat and fatigue |
| 302 stainless steel | 10.0 Mpsi / 69 GPa | Corrosion resistant springs | Lower rate than music wire |
| 17-7 stainless steel | 10.5 Mpsi / 72 GPa | Fatigue and heat service | Often precipitation hardened |
| Phosphor bronze | 6.3 Mpsi / 43 GPa | Electrical contacts | Much lower stiffness |
| Spring type | Rate formula use | Preload meaning | Important check |
|---|---|---|---|
| Compression spring | Direct linear force rate | Installed compression force | Solid height and buckling |
| Extension spring | Rate after initial tension | Initial tension or installed pull | Hook stress and loop opening |
| Valve spring | Direct rate with high stress margin | Seat load | Open load and surge margin |
| Die spring | Direct rate for guided compression | Installed clamp force | Percent deflection of free length |
| Torsion spring | Linearized by arm length | Arm-end starting force | Angular rate needs separate design |
| Design check | Preferred range | Problem sign | Adjustment |
|---|---|---|---|
| Spring index C | 4 to 12 | Below 4 is hard to make | Increase mean diameter or reduce wire |
| Bind reserve | 10% to 20% of travel | Coils touch at full travel | Longer free length or fewer coils |
| Stress ratio | Below 80% for cycling | Stress near limit | Larger wire or lower travel |
| Active coils | Usually 3 or more | Rate very sensitive | Add active coils or revise geometry |
| Deflection share | Below 35% of free length | Heavy set risk | Use longer spring or stronger material |
| Formula | Expression | Inputs | Output |
|---|---|---|---|
| Spring rate | k = Gd⁴ / 8D³N | G, wire, mean diameter, active coils | Force per travel |
| Load at travel | F = preload + kx | Preload, rate, travel | Working force |
| Wahl factor | K = (4C - 1)/(4C - 4) + 0.615/C | Spring index C | Stress correction |
| Corrected stress | tau = 8FDK / pi d³ | Load, diameter, wire, Wahl | Shear stress |
| Stored energy | E = 0.5kx² | Rate and total deflection | Energy in spring |
Spring rate is the measurement of how much forces is required to compress or extend a spring by a specific distance. The spring rate is used to determine if a spring will function correct in the device in which it is installed. For instance, the spring rate can help determine whether a valve will open at high rpm or whether the latch on a cabinet will hold without being too stiffly.
Small change to the dimensions of a spring will change the spring rate of that spring. Such changes can be as simple as altering the wire diameter or adding an extra active coil. Because even the smallest changes to a springs dimensions significantly alter the spring rate, the spring rate should be calculated with a calculator instead of guess at from previous springs.
Spring Rate: What It Is and How to Calculate It
The physical dimensions of a spring are the various physical measurement of the spring that alter the spring rate. The wire diameter affect the spring rate significantly, as does the mean coil diameter. Additionally, the number of active coil also affects the spring rate of a spring.
Each added or removed active coil will alter the spring rate of a spring. In order to calculate spring rate, one can enter the number of active coils, the mean coil diameter, and the wire diameter into a calculator to determine spring rate. The material out of which the spring is made will affect the spring rate and the durability of the spring.
For instance, music wire is a material that is strong and provides a high shear modulus to the spring, allowing for a smaller diameter spring to achieve the same spring rate. However, music wire is vulnerable to moisture. Stainless steel is a more durable spring for wet environment, but it trades some of its stiffness for durability.
Chrome silicon is a material that is in between music wire and stainless steel in both stiffness and durability, but it can handle more heat. The shear modulus is a constant value of the spring rate equation that convert the geometry of the spring to a force value. Changing the material within a calculator will change the shear modulus and stress limit of that spring, ensuring that both are using the same spring and material for comparison.
The spring index is the ratio of the mean diameter to the wire diameter of the spring. The spring index can affect how the spring is formed and within what bore size it will fit. A spring index below four will be difficult to form so that the spring does not crack.
A spring index above twelve will cause the spring to either buckle or tangle with other nearby springs. Most springs will fall within an index between four and twelve. A spring rate calculator will display the spring index to the user to ensure that the index is within a realistic range.
Preload and travel are two different measurements that will determine the amount of force that the spring will deliver during operation. Preload is the force that is provided to the spring before any additional force is deliver to it. Travel is the additional deflection of the spring during operation.
By adding these two forces together, one can determine the working load. Additionally, a spring rate calculator will include a design margin to the working load to ensure the spring does not experience the same force that was calculated. Stress result include the Wahl correction factor for the spring.
Wahl factor is included to account for the fact that stress is not equally distributed along the cross section of the spring wire. If the spring index is too small, then the spring may fail despite looking safe. Solid height and bind reserve are two measurements used to ensure that a compression spring will not fail due to lack of clearance between the coils of that spring.
Solid height is the height of the spring when the two ends of the spring are touching. If a spring continues to deflect beyond this point, it will no longer return to its resting position. For this reason, there should be some bind reserve between the springs working height and solid height.
Some percentage of travel, such as ten or fifteen percent, should be reserved as bind reserve to ensure the spring will work correct. Because extension springs feature hooks or loops, they require different consideration than the other types of springs. The hooks or loops to an extension spring will feature high amounts of stress on that spring.
The initial tension on the coils of the extension spring also means that the spring rate only applies once the initial tension is overcome. In extension springs, the stress on the hooks must also be calculated to ensure the loops do not open. Another type of spring to consider are torsion springs.
The output of a torsion spring is generally linear force applied to the end of an arm. The length of the arm can be entered into the spring rate calculator to convert the angular rate of the spring to a linear rate. This will allow the spring designer to compare the two types of springs.
However, the stress within a torsion spring is distributed differently from a linear spring, thus the allowable values of a torsion spring are different than those of a linear spring. There are errors that people can make when calculating spring rate. For instance, one can measure the outside diameter of a spring but not the mean diameter.
In this instance, one must subtract one wire diameter from the outside diameter to determine spring mean diameter. Additionally, the number of turns of a spring can be calculated but the number of active coils must be counted. Any inclusion of the inactive coils will make the spring rate too high.
In the same way, the length of the spring when it is not under tension can be entered into the spring rate calculator. However, it is also important to ensure that the deflection of the spring will not go beyond a safe percentage of the length of the spring. Due to the way that springs store energy, there are some consideration to safety when calculating spring rate.
When a spring is deflected or compressed, its energy is stored. That energy must go somewhere when the spring is released. Therefore, the part to which the spring is attached must be secured with clamps.
Additionally, the person calculating the spring must also protect their eyes and hands when the spring is deflected. Although a spring rate calculator can not replace a fatigue analysis or finite element analysis of the spring, the calculator will provide some information that will allow the spring designer to determine if the spring has a chance of working prior to beginning to wind the spring. This information is especially helpful for those designing springs at a bench with a micrometer and wire.
