Helix Volume

The Volume of a Helix calculator computes the bulk volume of a spiral or helix based on the dimensions and the displacement of the helix material as if the helix was placed in a fluid.

INSTRUCTIONS: Choose units and enter the following:

• (H) Helix Height 
• (P) Helix Pitch: distance between turns
• (D) Helix Diameter
• (SD) Strand Diameter

Volume of Helix (V): The calculator returns:

• (HV) Helix Bulk Volume of the helix . 
• (HD) Helix Material Displacement, as if the helix was place in a fluid.

Both volumes are returned in cubic centimeters.  However these can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The bulk volume of a helix is the equivalent to the volume of a cylinder in which the helix could fit.  The formula for the volume a helix is:

`HV = pi(D/2)^2*H`

where:

• HV = Volume of Helix cylinder
• H = Height of Helix
• D = Diameter of Helix

The formula for the length of a helix is:

      `L = H/P * sqrt( (pi*D)^2 + P^2)`

where:

• L = Length of Helix
• H = Height of Helix
• P = Pitch of Helix
• D = Diameter of Helix

Note: The number of turns (n) is equal to (H/P)

The Helix Displacement is:

`HD = pi*((SV)/2)^2 * L`

where:

• HD - Helix material displacement
• SD - Strand Diameter.  This would be the diameter of the spring material.
• L - Elongated Length of Helix

A HELIX is a three dimensional spiraling circular object.  The most common application of the helix shape is in the common spring.  A helix has a height or length, diameter and pitch, where pitch is the measurement between the spirals (see diagram).

Helix Calculators:

• Length of Helix - Computes the length of the material composing the helix if elongated.
• Height of Helix - Computes the height of a helix based on length of material, pitch and diameter.
• Volume of Helix - Computes the total displacement of helix cylinder and the displacement of the helix material as if in liquid.