Spiral Spring Design

Spiral Spring Design

Introduction.... Nomenclature.... Spring Index .... Spring Rate.... Spring Stress Values.... Compression Spring Formula....
Compression Spring End Designs .... Extension Springs.... Rectangular Section Springs.... Conical Helical Springs....


A spiral spring consists of a strip or wire wound in a flat spiral .     This is subject to a torque to produce an angular deflection.     A typical spiral spring is a clock spring


D = Outside diameter of spring (m)
b = Width of spring strip (m)
d = Inside diameter of spring (m)
t = thickness of spring strip (m)
n = Number of turns of spring
k = Spring rate = M /θ Nm/rad.
E = Young's Modulus (N/m2)
M = Moment/torque on spring = F.D / 2(Nm)
L = Length of strip (m)
G = Modulus of Rigidity (N/m2)
I = Second moment of intertia of spring strip (m4)
F = Force to deflect spring N
y = distance from neutral axis to outer fibre of wire/strip = y/2 (m)
θ = Deflection (radians)
α = Tensile/compressive stress resulting from spring deflection (N/m2

Note: metres (m) have been shown as the units of length in all of the variables above for consistency.   In most practical calculations milli-metres will be more convenient.

Spring Rate

The spring rate k is defined on this webpage as the torque (Nm)per unit angular deflection (θ ).

Spiral Spring Formulae

length of Strip

Spring Rate

Spring sureface stress

Links to Spring Design
  1. tpcdayton ...Anti-Vibration Mountings
  2. Acxess Springs ...Information on Design, Materials etc (Imperial)
  3. Harris Springs ...Information on Design, Materials etc (Imperial) and a catalog
  4. Earthlink- How to Make Springs ...Good simple comprehensive information
  5. Lee Springs ...Spring Supplier + useful technical Information
  6. Springmasters ...Spring Supplier + comprehensive range of springs with sizes and ratings