# Ball Weight and Density

## How much will a ball of a given diameter in a certain material weigh?

The answer is calculated by multiplying the volume of the ball by the density of the material.

$\text"Weight" = \text"Volume" ⋅ \text"Density"$

For example, calculate the weight of a two inch diameter lead ball:

$\text"Volume" = {4 ⋅ π ⋅ R^3 }/ 3$

$π$, a universal constant $= 3.1416$

$4 ⋅ π = 12.566$

$R = \text"Radius"$

$R = \text"Diameter" / 2 = 2 / 2 = 1$

$R^3 = R ⋅ R ⋅ R = 1$

$12.566 ⋅ 1 = 12.566$

$12.566 / 3 = 4.1887$ cubic inches (is the volume of a 2 inch ball)

4.1887 times the density of lead, which is 0.409 pounds per cubic inch, gives a weight of 1.713 pounds.

## What would a three inch diameter lead ball weigh?

The radius of 1.5 inches cubed equals $3.375 ⋅ 4 ⋅ π = 42.410$, divided by 3, equals 14.137 cubic inches, times 0.409 ( the density of lead ) gives 5.782 pounds.

$\text"Weight" = \text"Volume" ⋅ \text"Density"$

$\text"Weight" = {4 ⋅ π ⋅ R^3/ 3 } ⋅ 0.409$

$\text"Weight" = {4 ⋅ 3.1416 ⋅ {3/2}^3} ⋅ 0.409$

$\text"Weight" = 5.782 \text"pounds"$

Notice that only one inch increase in diameter caused a 4 pound increase in weight. This three inch diameter ball is more than triple the weight of the two inch diameter ball.

Common Ball Material Density (Metric Units)
Material |
Density ( grams / cm³) |

300 Stainless Steel |
8.02 |

Aluminum Alloy |
2.73 |

Brass |
8.47 |

Copper |
8.91 |

Gray Iron |
7.2 |

Lead |
11.35 |

Magnesium |
1.77 |

Monel |
8.9 |

Steel |
7.86 |

Titanium |
4.51 |

Water ( liquid ) |
1.00 |

Zinc |
7.14 |

Common Ball Metal Density (English Units)
Material |
Density ( pounds / cubic inch ) |

Aluminum |
0.0975 |

Brass |
0.3048 |

Cast Iron |
0.26 |

Copper |
0.321 |

Lead |
0.409 |

Magnesium |
0.0628 |

Steel |
0.283 |

Titanium |
0.162 |

Zinc |
0.254 |

*See Also, Sphere Mathematics

**See also: A density measurement conversion tool that is available at http://www.easyunitconverter.com/density-unit-conversion/density-unit-converter.aspx , for density unit conversions of various materials such as brass, copper, steel, and aluminum.

http://www.convertauto.com from Lilly Hammond at NCSU.