Ping Pong Balls in a 747 Answer: About 23 Million [Solved]

About 23 million ping pong balls fit in a Boeing 747. The ping pong balls 747 answer is about 23 million, and you can reach it with four quick steps: the volume of one ball, the volume of the plane, one division, and a fix for the gaps between the balls.

This is a Fermi estimation question, the kind tech firms asked through the 2000s to test how candidates handle a question with no exact answer. It is widely listed as a Google interview question from that era, and it appears in William Poundstone’s book Are You Smart Enough to Work at Google?, which collected the brain teasers Google used in its early recruiting. Google later dropped brain teasers, but estimation rounds still use questions like this one.

Before any numbers, state your assumptions out loud. The interviewer is listening for them. This answer uses an empty passenger 747-400, seats and fittings removed, with balls filling the passenger cabin plus the lower cargo holds. The fuel tanks are not counted, since they hold fuel, not balls.

The Ping Pong Balls 747 Answer in 4 Steps

Step 1: Find the volume of one ping pong ball

A standard ping pong ball is 40 millimetres across, so its radius is 2 centimetres. The volume of a sphere is 4/3 x pi x radius cubed, which gives 4/3 x 3.14 x 8, or about 33.5 cubic centimetres per ball.

One cubic foot holds 28,317 cubic centimetres. Divide 28,317 by 33.5 and you get about 845 balls per cubic foot, if the balls could fill the space with no gaps at all. Step 4 fixes the gaps.

Step 2: Find the volume of the plane

Boeing lists the 747-400 passenger cabin at 31,285 cubic feet. The lower cargo holds add 5,536 and 835 cubic feet. Add them together and the usable interior is 37,656 cubic feet, or about 1,066 cubic metres. Use that number, not the outside size.

Step 3: Divide the plane by the ball

Multiply 37,656 cubic feet by 845 balls per cubic foot and you get about 31.8 million balls. That is the answer if balls were cubes that stacked perfectly. They are spheres, so the real number is lower.

Step 4: Fix the packing

Spheres always leave gaps. The densest neat packing of equal spheres fills 74 percent of a space. Balls poured in at random fill about 64 percent. Apply those two rates to the 31.8 million ceiling:

Packing	Balls per cubic foot	Total in the 747
No gaps (impossible)	845	31.8 million
Neat packing, 74 percent	625	23.5 million
Random pouring, 64 percent	541	20.4 million
Passenger cabin only, neat packing	625	19.6 million

The realistic range is about 20 to 24 million, and the headline answer is about 23 million. That matches the figure quoted in the interview books, from 625 balls per cubic foot times 37,656 cubic feet.

Why the Ping Pong Balls 747 Answer Is About 23 Million

The exact digit is not the point. Every input here is approximate: the cabin volume is rounded, the packing rate is an estimate, and the plane is treated as empty. A candidate who says 23 million with clean working has answered the question. A candidate who says 50 million or 5 million has a broken step somewhere.

Two sanity checks prove the answer is in the right range. First, the weight. A ping pong ball weighs 2.7 grams, so 23.5 million balls weigh about 63.5 tonnes, close to the 747-400’s structural payload of about 67 tonnes. The plane could never take off loaded like this. It is a volume question, not a flight plan, and saying so out loud earns marks. Second, the cabin-only check. Count only the passenger cabin and you get 19.6 million, still in the same range, which tells you the answer is stable. Small changes in the inputs move the answer by millions, not by an order of magnitude.

The Traps That Catch Candidates

Trap 1: using the outside size of the plane. A 747 is about 70 metres long, 6 metres wide and 6 metres high. Multiply those and you get 2,520 cubic metres, which gives more than 50 million balls. That is wrong, because the fuselage is not a solid box. Most of that box is air outside the cabin, and the cabin is a tube, not a rectangle. Always use interior volume.

Trap 2: forgetting the gaps. Dividing the two volumes directly gives 31.8 million. That step is necessary but not finished. Balls are round, so a quarter to a third of the space stays empty. Stopping at 31.8 million skips the step the interviewer most wants to see.

Trap 3: counting only the passenger cabin. The cargo holds add 6,371 cubic feet, which is about 4 million balls at neat packing. Forgetting them drops the answer to about 20 million. It is still in range, but the interviewer will ask where the rest of the plane went.

Trap 4: fake precision. Quoting 23,538,000 balls pretends the inputs are exact. They are not. Give the range, name the packing rate you used, and say which parts of the plane you counted.

What the Interviewer Is Testing in the Ping Pong Balls 747 Puzzle

This puzzle tests four skills at once, and the interviewer watches how you use each one.

First, it tests whether you can break a huge question into small parts. The whole problem is two volumes and one division. Candidates who freeze at “23 million balls” usually never split the question. Say the split out loud before you touch a number.

Second, it tests whether you can pick numbers you can defend. You need the ball size, the plane volume and a packing rate. A 40 millimetre ball is a fact you should know or estimate well. The plane volume is a number to estimate from the cabin length and width if you do not know it. The packing rate is the one most candidates forget.

Third, it tests clean arithmetic under pressure. The numbers here are friendly on purpose: 33.5 cubic centimetres, 845 per cubic foot, 625 at neat packing. Work them out loud, round at each step, and keep the units visible. If a number looks wrong, say so and redo it.

Fourth, it tests whether you check your own answer. The weight check and the cabin-only check take ten seconds and they prove the answer is sane. Candidates who finish with a check look finished. Candidates who stop at the division look like they ran out of ideas.

Try This One Next

If you liked the ping pong balls in a 747 puzzle, try How Many Golf Balls Fit in a School Bus? Answer [Solved]. It uses the same Fermi method with a smaller container and a bigger ball, and the same packing fix decides the answer. For a different kind of estimate, try Piano Tuners Chicago Answer: About 100 [Solved], which estimates a workforce instead of a volume.

Frequently Asked Questions

Is the ping pong balls 747 answer always 23 million?

No. It is an estimate, and the honest answer is a range of about 20 to 24 million, depending on the packing rate and whether the seats stay in. The 23 million figure is the neat-packing answer for an empty 747-400, and it is the number the interview books quote.

Do the seats change the answer?

Yes, by about 10 to 15 percent if they stay in the cabin. Seats, galleys and overhead bins take up space that balls cannot fill. Most worked answers assume an empty plane and say so. If your interviewer keeps the seats in, state the deduction and give the lower figure.

What if the interviewer asks about tennis balls instead?

Use the same four steps. A tennis ball is about 6.7 centimetres across, so its volume is about 157 cubic centimetres, roughly five times a ping pong ball. That gives about 180 balls per cubic foot with no gaps, about 133 at neat packing, and about 5 million balls in the whole 747. The method never changes, only the inputs.

Where was this question asked?

The ping pong balls 747 question is a classic Fermi question from the tech interview era, documented in William Poundstone’s 2012 book Are You Smart Enough to Work at Google?, which collected the estimation questions Google used in its early recruiting. Google later moved away from brain teasers, but estimation rounds still use questions like this one.

Sources

Boeing 747-400 volume figures: passenger cabin 31,285 cubic feet with lower holds of 5,536 and 835 cubic feet, as published in 747 estimates and the Answers.com calculation. Freighter hold volumes cross-checked against the Atlas Air 747-400F specification sheet. Ping pong ball size, 40 millimetres diameter and 2.7 grams, is the ITTF standard. Question history: William Poundstone, Are You Smart Enough to Work at Google? (2012). All arithmetic was recomputed from the raw figures.