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### Sphericity of Sphere Formulas and Calculator

Engineering Materials

**Tolerances, Engineering Design Limits ans Fits**

**Sphericity of a Sphere Formulas and Calculator **

Sphericity is, naturally, a measure of how spherical an object is. Defined by Wadell in 1932, the sphericity ψ of a particle is the ratio of the surface area of a sphere with the same volume as the given spherical particle to the surface area of the particle.

The sphericity of a nonspherical particle is always less than 1 and a particle that is a perfect sphere has sphericity value of ψ = 1.000 .

Sphericity is a measure of how closely the shape of an object resembles that of a perfect sphere. For example, the sphericity of the balls inside a ball bearing determines the quality of the bearing, such as the load it can bear or the speed at which it can turn without failing.

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**Sphericity of a Sphere** can be calculated by the following formula:

Eq :

Ψ = ( π^{1/3} ( 6 V_{P} )^{2/3}) / A_{p}

Where:

V_{P} = volume of the particle

A_{p} = the surface area of the particle

A particle that is a perfect sphere has sphericity value of ψ = 1.)

Reference:

Machinery's Handbook 30th edition

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