physics for beekeepers

Physics for beekeepers: heat loss from spheres

. . . or “learning about bees from your cat”

Here is something any feline will tell you: a sphere is a shape with a high volume to surface area ratio. The surface of an object is the part exposed to air, so it’s the surface where things gain or lose heat. Things wrapped up in a ball—like your cat on a cold day—lose less heat to the atmosphere than things stretched out in all directions—like the same cat on a summer afternoon. Basically, your cat is a shape-shifter, changing his volume to surface area ratio depending on the temperature.

Beekeepers often worry about their bees being cold in winter, but bees are brilliantly adapted to staying warm. As the temperature begins to fall they form a cluster to keep warm, as the outside temperature becomes even colder, the cluster becomes tighter and rounder—just like your cat.

But for bees to survive the winter, the cluster must also be large enough. A large cluster contains more bees generating heat, but equally important, a large cluster has a higher volume to surface area ratio than a small one. The reason is simple: as the radius of a sphere increases, the surface area increases with the square of the radius while the volume increases with the cube of the radius. In plain English it means that as your cluster gets bigger, the volume increases more than the surface area.

The lower amount of surface area per volume of bees means the big cluster loses heat at a slower rate than a little cluster, the same way your cat loses heat at a slower rate than the mouse he is stalking, but at a faster rate than the German shepherd stalking him. Small objects lose heat faster than big objects of similar shape and density. (We all know mice shiver, but to know whether they shiver from cold or from fear, you’ll have to consult a mouse.)

In a large cluster, more bees are producing heat and a greater percentage of the bees are on the inside of the cluster where it’s warm and comfy. Conversely, tiny clusters have a small chance of making it through the winter—it is best to combine these with another colony if possible. And in spring, when temperatures are erratic, you should avoid breaking a cluster into smaller units. Reversing boxes when it divides the nest, or opening the brood nest too much, can cause the bees to separate into small clusters or spread themselves into a non-spherical shape. Either one could compromise the health of your colony.


Too warm to be decent.


  • I was searching for the Physics series, when I stumbled upon the English series first. I found that to be so helpful and vow to be very deliberate in my terminology from here forward. Then I came to where I really wanted to learn more and couldn’t help but notice the last paragraph of this blog. Should references to “hive” actually be “colony” or do we seek a healthy house? I bet I am going to be so annoying to my fellow beekeepers. 🙂

    • Dennis,

      Ha! You are golden! I fixed it.

      I have the recurring thought (delusion?) that I am going to go back through all my posts and correct spelling, grammar, usage, diction, and punctuation until I realize there are 1000 posts. I really wanna do it, but it ain’t gonna happen. Instead, I have to rely on people like you!

  • Okay, I’ll admit it is early here and the first cuppa is in the present tense. However, I’m confused. It seems that you either have to have a lot of cats or borrow the neighbors’, which isn’t going to help the cooperation level. Add to that that I don’t have one cat, but even if I did, I don’t remember them being all that cooperative most of the time. You have to move some frames for extra room too.

    Does the cat go on the outside or the inside of the cluster?


  • Rusty,
    Well played. 🙂
    Applicable to handling bees in a general sense, “A man who carries a cat by the tail learns something he can learn in no other way.”, Mark Twain.


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