# Calculate Ping Pong Balls Needed to Fill a Swimming Pool

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## How to Find How Many Ping Pong Balls fill a Space

Finding how many ping pong balls will fill a swimming pool involves a few simple math challenges.

### Find the Volume of a Pool

The first is finding the volume of the pool. To find the volume of the pool, simply multiply the length by the width by the height in inches to find the volume in cubic inches.

For circular pools multiply 3.14159 by the pool’s diameter, then divide by 2 to find the area. Multiply the area by the depth in inches to find the volume in cubic inches. Use our volume calculator to find the volume of other shapes.

### Find the Volume of a Ping Pong Ball

Next, we need to find the volume of a ping pong ball. A regulation ping pong ball has a diameter of 40 millimeters. To find the volume, we can use the volume formula for a sphere, which is ^{4}/_{3}πr^{3}.

volume = (4 ÷ 3) × π × r^{3}

volume = (4 ÷ 3) × 3.14159 × 20^{3}

volume = (4 ÷ 3) × 3.14159 × 8,000

volume = 33,510

Now, convert from cubic millimeters to cubic inches., which can be done by multiplying the cubic millimeters by .000061024.

cubic inches = 33,510 × .000061024

cubic inches = 2.045

### Find Ping Pong Ball Fill Density

To correctly solve this problem it’s necessary to determine the maximum density of ping pong balls in a space. This is a necessary part of the problem because ping pong balls are spherical, which means there will inevitably be a void where the rounded balls cannot fill between them.

Assuming the ping pong balls are placed in the maximum density fill pattern the formula to find the density is π ÷ (3 × √3), which roughly equals .74048.

### Putting it All Together

Armed with the volume of the swimming pool, the volume of the ping pong ball, and the maximum ball density, find the number of ping pong balls that can be fit into a pool using the formula pool volume ÷ ball volume × fill density.

balls = pool volume ÷ ball volume × density

balls = pool volume ÷ 2.045 × .74048