Wednesday, March 29, 2017

Calculating the size of Hyrule in Breath of the Wild

Spoiler warning: This post contains minor spoilers for The Legend of Zelda: Breath of the Wild. If you're very sensitive to spoilers, and you don't want to know anything about the map or characters or Link's abilities in the game, then don't read this.

I bought The Legend of Zelda: Breath of the Wild and I love it! One of the coolest things about it is the massive open world. There's just so much to explore, and you can have hours of fun exploring an area, only to find that it is only a tiny fraction of the whole of Hyrule, which is all entirely open to exploration. I wondered exactly how big the world is, so I made a fairly precise calculation of exactly how big the world is, in real-world units.

If I'm even going to start a task like this, I better have a frame of reference so I can relate the game world with the real world. Luckily there's this minigame in Breath of the Wild.


Branli is a researcher who is interested in learning about "bird people". (I guess he's referring to the Rito.) He is located at the top of Ridgeland Tower. Because of Link's ability to paraglide, he thinks that Link is a bird-man. If you pay him a deposit of 20 rupees, he will have you glide off the tower, and measure the distance you travel. (If you're wondering, he does pay you back if you go far enough.) Fortunately for me, the distance is measured in meters, and we can see it live, as Link is gliding.


So when I reached 500 m (actually 500.1 m but whatever), I immediately paused the game to look at the map.


Above is the map at the most zoomed out level. (I've annotated it to point out the tower and Link.) Wow, you can see that 500 meters is pretty small when compared to the whole of Hyrule! In fact, the above map can't even show the entirety of Hyrule, just the north part! I took another screenshot where the map shows the south part:


I don't like dealing with 2 images, so I used image editing magic to combine them into a single image:


Now THIS is the entirety of Hyrule. Neat! From this point, I used Web Plot Digitizer to find the total size. This cool web app lets you click on points, and it tells you their coordinates. It even scales pixels into arbitrary units, if you have a reference (which I have, thanks to Branli!).

First I uploaded my image with the entire Hyrule map. This tool can handle all sorts of plots, but I chose "Map with Scale Bar". Well, in this case there is no actual scale bar on the map, but the 500 meters between the tower and Link is effectively a scale bar.

Then I had to click 2 points to use as a scale to calibrate the axes. Here I clicked on the tower I jumped from, and on Link's current location, which is 500 meters away. Then I entered the distance and the unit. I entered it in kilometers because that's probably a better unit to measure Hyrule.


Now I can pick any number of points, and then view their coordinates in km. I chose the top left corner of the map, and the bottom right corner. The map fades out at the edges, so I tried to choose the points where the fading started.


Finally we can calculate the east-west distance and north-south distance of Hyrule by subtracting these coordinates. The width is about 10.271 km by 7.905 km. Approximately 10 km by 8 km. Amazing!