# Spring Rate

on . Posted in Fastener

Spring rate, abbreviated as $$n_s$$, is not the same as spring load.  The spring rate is based on the spring's working load.  Spring rate is the rate of force or weight required to travel one unit of measurement.  The lower the spring rate, the softer the spring.  The softer the spring, the smother the ride.  Spring load is the amount of weight a spring is designed to carry when compressed to a certain height.

## Spring Rate Formulas

$$\large{ n_s = \frac{ P }{ d_s } }$$

$$\large{ n_s = \frac{ P \;-\; T_i }{ d_s } }$$

$$\large{ n_s = \frac{ G \; d^4 }{ 10.8 \; D \; n_a } }$$     (rate per 360 degrees)

$$\large{ n_s = \frac{ G \; d^4 }{ 8 \; D^3 \; n_a } }$$     (pitch angle is less than 15 degrees or displacement per turn is less than D/4.)

Symbol English Metric
$$\large{ n_s }$$ = spring rate $$\large{ \frac{lbf}{in} }$$ $$\large{ \frac{kg}{mm} }$$
$$\large{ P }$$ = load  $$\large{ lbf }$$ $$\large{ kg }$$
$$\large{ D }$$ = mean coil diameter $$\large{ in }$$ $$\large{ mm }$$
$$\large{ n_a }$$ = number of active coils $$\large{ displacement }$$
$$\large{ G }$$ = shear modulus of material  $$\large{ \frac{lbf}{in^2} }$$  $$\large{ Pa }$$
$$\large{ d_s }$$ = spring displacement $$\large{ in }$$ $$\large{ mm }$$
$$\large{ T_i }$$ = initial tension  $$\large{ lbf }$$ $$\large{ N }$$
$$\large{ d }$$ = wire diameter $$\large{ in }$$ $$\large{ mm }$$

Tags: Spring