# Math For Measurments: Introduction

All maps are made with measurements. These measurements might be taken from an aerial photograph or satellite image, or from the instruments used by land surveying and GIS professionals. Even the quick map you sketch on a napkin to give directions to a friend are made from crude measurements in your mind. Measurements are a critical element of the map making process, and they are the foundation upon which all maps, and other types of spatial data, are built.

## What Types Of Measurements Are We Talking About?

We are going to examine 2 basic types of measurements in this section of the Math for Maps chapter of the Free Gis Book. Both of these measurements are “spatial” measurements. This means they are basically measurements of location. (You can measure a lot of other things besides location. For example, if you are interested in predicting the weather you might measure temperature, air pressure, and wind speed. We won't be talking about any of these other types of measurements.) The first type of measurement we are going to look at are distance measurements. The second type of measurement we are going to look at are angle measurements.

## The Act Of Measuring, Or The Result Of Measuring

“Measurements” can be a tricky word. When I use it in this section I typically mean the “result” of the measurement, not the actual act of measuring. In the English language you can say, “The surveyor made a measurement with his instrument.” This isn't the manner in which we are typically going to use the word “measurement”. Instead, we will typically use it as shown in this English language statement: “The surveyor's measurement was 101.23 feet.” So when I say “measurement” I want you to think “the result of measuring”. If I mean to use the word in a different sense, I'll point it out.

## A Quick Note About Unit Systems

I won't be going into great depth about unit systems and unit conversions in this chapter. Measurements can be made in all types of unit systems. In this chapter I will be using the unit system I most commonly work with here in the United States. That means I'll be working with Unites States survey feet, acres, miles, and with angles in degrees-minutes-seconds format. I know most of the world uses metric, and if someone decides to translate this work they are more than welcome to change the units and unit system where applicable. I will clearly state the unit of any measurement value in this section of the chapter.