Ping Pong Balls to Fill a Pool Calculator
Calculate how many ping pong balls it takes to fill a swimming pool. Enter pool dimensions and see the answer — plus the math behind it.
PING PONG BALLS NEEDED
2,163,247 balls
POOL VOLUME
4,000 ft³
GALLONS
29,922 gal
PACKING
64% (random)
Standard ping pong ball: 40 mm diameter, ~2.7 g. Random packing efficiency for spheres is approximately 64% (Bernal packing).
💡 How to Calculate Ping Pong Balls to Fill a Pool
The Ping Pong Ball Pool Problem
How many ping pong balls does it take to fill a swimming pool? This classic math and physics problem combines geometry, volume calculations, and an important concept called packing efficiency. It is a common job interview and physics class question that demonstrates practical application of density and volume concepts.
How to Calculate It
Step-by-Step Method
Step 2: Ball volume = (4/3) × π × r³ = 33.51 cm³ (40 mm diameter)
Step 3: Apply random packing efficiency ≈ 64% (Bernal packing)
Step 4: Number of balls = Pool volume × 0.64 / Ball volume
A regulation ping pong ball has a diameter of 40 mm and weighs 2.7 grams. When you randomly fill a container with spheres, only about 64% of the space is occupied by the spheres — the remaining 36% is air gaps between them. This is known as random (Bernal) packing.
Worked Example
A standard residential pool (20 ft × 40 ft × 5 ft average depth):
Pool volume = 20 × 40 × 5 = 4,000 ft³ = 113.27 m³ = 113,270,000 cm³
Usable space = 113,270,000 × 0.64 = 72,492,800 cm³
Balls = 72,492,800 / 33.51 ≈ 2.16 million ping pong balls