So, Angles: Making a Protractor, as Simply as Possible

An irreplaceable tool of the trade: the mighty protractor! Whether you are lost at sea or lost in time, learn how to make one on the go in any time period you find yourself in!


The mighty protractor: an endlessly versatile tool that forms the backbone of any chrononaut’s (government-issued) toolkit. A protractor measures angles–the distance between two diverging lines–making it particularly useful in navigation and astronomy.

The protractor’s design has changed very little from its earliest recorded illustrated form in Thomas Blundeville’s 1589 map-making guide: Briefe Description of Universal Mappes & Cardes. Blundeville illustrated a half circle, but a protractor can be either a full or half circle. A full circle is 360 degrees, based on the base-60 numerical system of the Mesopotamians, which allows the circle to be cleanly divided into six triangles, each 60 degrees. A line separating the circle in half represents 180 degrees. Further segmentation while mirroring the additional lines across the x and y-axis will create 360 evenly separated lines where each curved distance between the lines on the edge of the protractor represent a degree.


Folding a paper in half creates two lines that intersect in the middle, creating an angle with 180 degrees separation. By continuing to fold the paper in half (while keeping all sides of the paper mirrored), each new fold will create an arc along the edge of the protractor that is half the size as the previous. So, 1 fold = 180 degrees, 2 folds = 90 degrees. All angles can be determined as:


Protractors are used in fields ranging from mathematics, cartography, and physics, where the angles can be reported as degrees, arcseconds*, or radians. Degrees are for X, while radians represent Y, and arcseconds display angles on a curved surface like constellations in the sky.

Degrees to radians:

Degrees to arcseconds:


*For more on arcseconds and constellations see: So, You’re Lost in Time: Determine When you Are