# 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
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
Magnesium 0.0628
Steel 0.283
Titanium 0.162
Zinc 0.254