彈簧的彈性系數k與彈簧的直徑，彈簧的線(xiàn)徑，彈簧的材料，彈簧的有效圈數有關(guān)。具體關(guān)系是：
與彈簧圈的直徑成反比，與彈簧的線(xiàn)徑的4次方成正比，與彈簧的材料的彈性模量成正比，與彈簧的有效圈數成反比。
c=F/λ＝Gd4/8D23＝Gd/8C3n
上式中：
c：彈簧的剛度(即所說(shuō)的彈性系數，中學(xué)物理叫倔強系數k)；
F：彈簧所受的載荷；
λ：彈簧在受載荷F時(shí)所產(chǎn)生的變形量；
G：彈簧材料的切變模量(鋼為8×104MPa，青銅為4×104MPa)；
d：彈簧絲直徑；
D2：彈簧直徑；
n：彈簧有效圈數；
C：彈簧的旋繞比(又稱(chēng)為彈簧指數)。
由上式可知。當其它條件相同時(shí)，C值愈小的彈簧，剛度愈大，亦即彈簧愈硬；反之則愈軟。還應注意到，C值愈小，彈簧內、外側的應力差愈懸殊，卷制愈難，材料利用率也愈低，并且在工作時(shí)將引起較大的扭應力。所以在設計彈簧時(shí)，一般規定C≥4，且當彈簧絲直徑d越小時(shí)，C值越宜取大值。

中譯英：
The elasticity of the spring coefficient K and the diameter of the springs, spring wire, spring material, the effective coil number of the spring. Specific relationship is:
And the spring coil diameter inversely, and the spring wire diameter4 times proportional to the spring, and the elastic modulus of the material is directly proportional to the effective coil number, and the spring is inversely proportional.
c=F/λ＝Gd4/8D23＝Gd/8C3n
Type of:
C:the stiffness of the spring(i.e., the elastic coefficient, high school physics called stiffness coefficient K);
F:spring loads;
Lambda:spring in the load of F generated by deformation of;
G:spring material 's shear modulus(steel is 8×104MPa to 4×104MPa, bronze);
D:spring wire diameter;
D2:diameter of spring;
N:the effective coil number of springs;
C:spring winding ratio(also known as the spring index).
Based on the formula one. When the other conditions were the same, C value is a small spring, stiffness is bigger, namely spring more hard; otherwise the soft. It should also be noted that, C value is small, spring, lateral stress difference is disparate, winding more difficult, the material utilization rate is lower, and the work will lead to larger torsional stress. So in the design of a spring, general provisions of C≥4, and when the spring wire diameter d more hours, C value is to employ large value.
(圖/文http://www.zushanlaojiu.com/)