# Sizing a tree shaped world [closed]

I want to build a world tree, literally.

The realm of the dead would be in the roots, the realm of the gods at the treetop.

Each leaf would hold at least a small town (let's say 15km²) and at best a big country (700 000km²). They would mostly have arable land on them for humans to live and prosper. The first habitable leaves would be way above ground so no human could imagine there is one. The biome would vary from leaf to leaf. The branches and the trunk would be arid highways between leaves.

The problem is: I'm having a hard time sizing it all. (I'm mostly asking about lengths.)

How tall would the tree be? How wide? How big would be the trunk? How many leaves will it have?

You can assume any species of tree, even a fantasy one. It only needs to have realistic proportions.

• What exactly is your problem? Those calculations seem pretty straight forward. If you want to know how many 15km² leaves yield a total area of 700 000 km², you have to divide that number by 15 for example. You can easily google "leaves per tree" then, selecting any kind of tree you'd like for your world and then do some straight-foward scaling of it all. I'm guessing physics are out the window anyways ? If not, this is simply not possible – Raditz_35 Feb 20 '18 at 13:52
• Given that physics does not apply at all, it would be as tall as your story requires, have as many leaves as you want it to, and trunk will be exactly big enough to be spectacular but small enough to be recognized as a trunk, not a wall. Right? – Mołot Feb 20 '18 at 13:53
• May I suggest that instead of "one big leaf" for major cities, you use a cluster of leaves instead. This way you would not have such discrepancies between leaves size. – Matthieu M. Feb 20 '18 at 16:03
• Branches would be major trade routes, which might mean that major cities would appear at large tree forks. – Hans Z Feb 20 '18 at 16:59

Some quick Googling produced the following statistics for Oak Trees:

• Oak trees grow to an average height of about 50 to 70 feet when fully grown. They tend to have a spread of as much as 50 feet from branch to branch.

• 200,000 to half a million leaves for a mature oak

• Leaves: around 10cm long with 4-5 deep lobes with smooth edges

• 60 year oak tree has trunk girth of 12-18 inches

So lets assume your world tree is a giant oak. We'll also assume the leafy part of the tree is perfectly spherical. Taking numbers from above, lets say a generic tree is 20m tall and 15m spread, with 350,000 leaves.

If the average leaf on your world tree is 350,000km2, then on average it'll be about 600km long (assuming it's a square shaped leaf). This gives us a scalar of 600km (for our world tree) compared to 10cm (for our oak tree). Thus the World Tree is roughly sixty million times bigger than an oak tree.

It will thus be 1.2 million km tall, nine hundred thousand km wide and have a total leaf surface area of 122.5 billion km2. The Earth has about 500 million km2, so your world tree is about a thousand times bigger than Earth, considering surface area only.

You will also have three hundred thousand kms of trunk between the roots and the lowest branches and a trunk diameter of 2,400 kms.

• Since the minimum leaf size is only 15 km, perhaps you should also include numbers for the smallest possible tree. Doing the same calculations, a 15 km^2 leaf tree has a leaf surface area of 5 million km^2, and a scalar of about 4 km to 10 cm. I would consider this a more reasonable tree. – kingledion Feb 20 '18 at 14:49
• @kingledion: Indeed I could, however as I have demonstrated the method to get whatever size of tree you desire, I feel it is best left as an exercise for the reader. – Kyyshak Feb 20 '18 at 16:08
• I'd also like to point out that this multiplier makes a typical bough 10x longer than the circumference of the Earth. Travelling between leaves is going to be hard. – Tin Wizard Feb 20 '18 at 17:41