Mass-Spring System (constant)

The Spring Constant calculator computes the spring constant based on the mass of an object on a spring and the period.

INSTRUCTIONS: Choose units and enter the following:

• (m)  Mass of the object on the spring
• (T)  Period of the mass-spring system.

Spring Constant (k): The calculator returns the constant in Newtons per Meter (N/m).  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula for a spring's constant is:

    `k = m / (T / (2*PI) )^2`

where:

• k = spring constant
• m = mass on a spring
• T = period of the mass spring system

The Mass-Spring System (period) equation solves for the period of an idealized Mass-Spring System.  For more information and context on this equation, please see the Mass-Spring System Calculator page.

Spring Equation Calculators

• Period of an Oscillating Spring: This computes the period of oscillation of a spring based on the spring constant and mass.
• Mass of a Spring: This computes the mass based on the spring constant and the period of oscillation. 
• Angular Frequency of a Spring: This computes the angular frequency based on the spring constant and the mass.
• Spring Constant: This computes a spring's constant based on the mass and period of oscillation.
• Work done on a Spring: This computes the work based on the spring constant and the two positions of a spring.
• Hooke's Law: This computes the force to change the length of a spring based on the spring constant and length of displacement.
• Force to Fully Compress a Spring: This computes the force required to fully compress a spring based on the spring's physical attributes including the Young's Modulus, wire diameter, length of spring, number of windings, Poisson ratio, and outer diameter of the spring.