# Compression Spring

Written by Jerry Ratzlaff on . Posted in Fastener

A compression spring is a open-coil helical springs wound to resist the compression force along the wind axis.  The spring will always resist and pushing back the compression force to its origional length.

### Compression Spring Deflection formula

$$\large{ d_s = \frac{ 64 \; n_a \; r^3 \; F }{ d^4 \; G } }$$

Where:

$$\large{ d_s }$$ = spring deflection

$$\large{ n_a }$$ = number of active coils

$$\large{ G }$$ = shear modulus of material

$$\large{ F }$$ = spring force

$$\large{ r }$$ = spring radius  ( $$\large{ \frac{D}{2} }$$ )

$$\large{ d }$$ = wire diameter

### Compression Spring Diameter formula

$$\large{ D = D_o - d }$$

$$\large{ D = D_i + d }$$

Where:

$$\large{ D }$$ = mean coil diameter

$$\large{ D_i }$$ = inside diameter

$$\large{ D_o }$$ = outside diameter

$$\large{ d }$$ = wire diameter

Solve for:

$$\large{ D_i = D_o - 2 \; d }$$

$$\large{ D_o = D_i + 2 \; d }$$

### Compression Spring Force formula

$$\large{ F = \frac{ \pi }{ 16 } \; \frac{ d_{s}{^3} }{ r } \; \tau }$$

Where:

$$\large{ F }$$ = spring force

$$\large{ d_s }$$ = spring deflection

$$\large{ \pi }$$ = Pi

$$\large{ \tau }$$ (Greek symbol tau) = shear stress

$$\large{ r }$$ = spring radius  ( $$\large{ \frac{D}{2} }$$ )

$$\large{ d }$$ = wire diameter

### Compression Spring index formula

$$\large{ C = \frac{ D }{ d } }$$

Where:

$$\large{ C }$$ = spring index

$$\large{ D }$$ = mean coil diameter

$$\large{ d }$$ = wire diameter

### Compression Spring load when compressed to length formula

$$\large{ P = T \; n_s }$$

$$\large{ P = n_s \; \left( l_i - l_f \right) }$$

Where:

$$\large{ P }$$ = load when compressed to length

$$\large{ l_f }$$ = final length (compressed)

$$\large{ l_i }$$ = initial length (free)

$$\large{ T }$$ = travel length

$$\large{ n_s }$$ = spring rate

### Compression Spring Mean Coil Diameter formula

$$\large{ D = ID + d }$$

Where:

$$\large{ D }$$ = mean coil diameter

$$\large{ ID }$$ = inside diameter

$$\large{ d }$$ = wire diameter

### Compression Spring Rate formula

$$\large{ n_s = \frac{ G \; d^4 }{ 8 \; n_a \; D^3 } }$$

Where:

$$\large{ n_s }$$ = spring rate

$$\large{ D }$$ = mean coil diameter

$$\large{ n_a }$$ = number of active coils

$$\large{ G }$$ = shear modulus of material

$$\large{ d }$$ = wire diameter

### Compression Spring Solid Coils Height formula

$$\large{ h = d \; \left( n_t + 1 \right) }$$

$$\large{ h = d \; n_t }$$   (for ground ends)

Where:

$$\large{ h }$$ = solid height

$$\large{ n_t }$$ = total number of coils

$$\large{ d }$$ = wire diameter

### Compression Spring Travel length formula

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

Where:

$$\large{ T }$$ = travel length

$$\large{ P }$$ = load when compressed to length

$$\large{ n_s }$$ = spring rate

### Compression Spring Wire Length formula

$$\large{ L_c = D \; \pi }$$   (coil wire length)

$$\large{ L_t = L_c \; n_t }$$   (total wire length)

Where:

$$\large{ L_c }$$ = coil wire length

$$\large{ L_t }$$ = total wire length

$$\large{ D }$$ = mean coil diameter

$$\large{ \pi }$$ = Pi

$$\large{ n_t }$$ = total number of coils

### Compression Spring Wire Stress formula

$$\large{ S = \frac{ 8 \; p \; D \; K }{ \pi \; d^3 } }$$

$$\large{ S = \frac{ 8 \; n_s \; D \; K \; d_s }{ \pi \; d^3 } }$$

Where:

$$\large{ S }$$ = wire stress

$$\large{ D }$$ = mean coil diameter

$$\large{ \pi }$$ = Pi

$$\large{ p }$$ = pitch

$$\large{ d_s }$$ = spring deflection

$$\large{ n_s }$$ = spring rate

$$\large{ K }$$ = stress correction factor

$$\large{ d }$$ = wire diameter

Tags: Equations for Spring