Calculate spring velocity from spring constant, displacement, and mass, plus find spring rate from wire diameter, coil diameter, material, and coils.

How far the spring is stretched or compressed from rest. Maximum speed occurs as the mass passes the rest position.

The mass attached to the spring; the spring’s own mass is ignored.

Optional settings

Spring Velocity Formula

For an ideal undamped linear spring and point mass, the following equation gives the maximum speed at equilibrium. The displacement x is amplitude measured from equilibrium, and spring mass is neglected.

Vs = SQRT (k × x² / m)
  • Where Vs is the spring velocity (m/s)
  • k is the spring constant (N/m)
  • x is the maximum displacement (m)
  • m is the mass (kg)

Use v = A√(k/m), with positive spring constant and moving mass. The calculator also solves its inverses and estimates close-coiled compression spring rate from k = Gd⁴/(8D³Na), using mean coil diameter and active turns. Material modulus presets are approximate; choose Custom for a measured or specified modulus.

What is a Spring Velocity?

Definition:

Spring velocity here means the maximum speed of the attached mass as it passes through equilibrium after release from rest at its maximum displacement. For a vertical spring, use amplitude about the loaded equilibrium, not the unloaded spring length.

How to Calculate Spring Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate velocity from redshift.

First, determine the spring constant (N/m). In this example, the spring constant (N/m) is found to be 5 N/m.

Next, determine the maximum displacement. For this problem, the maximum displacement is found to be 3 m.

Next, determine the mass. In this case, the mass is measured to be 2 kg.

Finally, calculate the Spring Velocity using the formula above:

Vs = SQRT ( k*x^2 / m)

Vs = SQRT ( 5*3^2 / 2)

Vs = 4.74 m/s