How many ants does it take to change a lightbulb? Or carry off a small child?

A few weeks ago I was considering the important question of whether ants could — and if so, how many it would take to — carry off a small child. And are there enough ants in a colony to make it happen.

This is a pure back of the envelope, questionably sourced, calculation.

Let's say the child weighs 25 pounds or 55 kilos which is 55,000 grams. The average ant weighs 3 milligrams or 0.003 grams (and is 3 millimeters long).

An ant can carry 10-50 times its own weight; let's say 33x, so a 3 milligram ant can lift 0.1 grams. So, it takes 10 ants to lift a gram and it would take 550 thousand ants to carry off a child.

Estimates on the number of ants in an ant mound vary considerably, 10,000 to 50,000 or so. Not enough. Of course, there are claims that an ant supercolony, with billions of members, has largely conquered the world. They could certainly muster the troops needed to carry off a child.

But army ants seem more promising. When they swarm, they might send out over 200,000 raiders. And they are 3-4x as long as an average ant. So, assuming weight increases cubically we can estimate that an army ant weighs about 30 milligrams. It's ability to lift should decrease relative to its increase in size, but estimates for their lifting ability seem to still be in the 10-50x body weight range, so let's say 20x or the ability to lift ~0.5 grams. So now you only need 50 thousand or so army ants to carry off the child. Only 1/4th the ants in a swarm. Quite feasible.

Still, getting sufficient ants to actually lift a child, given the surface area, seems difficult, so they would need a rope or something.

* Update. Using the Mosteller formula for body surface area, estimating the child's height at 24 inches or 60 centimeters gives you:
SQRT((61 cm * 55 kg) / 3600) = ~1 square meter.

If we assume the ants have access to 40% of that surface area we get 4000 square centimeters. Let's say the army ants, at 10 millimeters in length, are 2 millimeters wide. So you could get 5 ants in a square centimeter, and 20 thousand ants on the exposed surface area. This would probably be 6x for average ants. But the ants would lift up their heads and part of their thorax, tightening the spacing by say 25% getting us to 25 thousand ants. With some more squeezing and some layering, the army ants should pretty much be there. And for regular ants we are probably now at 300 thousand ants.

So maybe no rope or other lifting apparatus is required. Keep an eye on your children.