Having a degree in architecture can sometimes be mistaken for having a degree in math, but this is not the case! While some people claim that being an architect requires advanced mathematics, this is definitely not true.

Architects are actually paid very well without requiring extensive knowledge of mathematics. Businesses hire architects to design buildings, so they do not need mathematicians to work for them.

Furthermore, engineers train in mathematics as part of their studies, which helps them build upon the mathematical foundations already learned by most architects. This means that many architects have adequate levels of mathematics, making it hard to prove that math isn’t needed.

However, there are certain areas of math that play important roles in how architects practice. These include geometry, trigonometry, calculus, and linear algebra. All these fields apply to things like physics, engineering, and computer science, too.

This article will talk about the importance of math in architectural practices, what each field covers, and some examples of each. Then, we will discuss why practicing architects should learn more math.

Find the area of a rectangle

The term “area” refers to the amount of space an object takes up, which in geometry is usually determined using a formula called the Pythagorean theorem. If you remember this theorem from high school math, then you already have some basic areas under your belt!

The pythagorian theorem says that the equation of the hypotenuse (the longer side) of a right-angle triangle equals the sum of the squares of the other two sides. In plain English, if something is measuring a length equal to its own width, then you can calculate the area it covers by taking the square root of the result.

So, for example, what are we talking about here? Let’s say there is a box with dimensions 3 inches tall, 2 inches wide, and 1/2 inch thick. What is the area of this box? Just take the square root of 4, and you get the answer! This box has a calculated area of 2 square inches or four square centimeters.

Now that we know the definition of area, let's practice applying it to a few examples.

Find the volume of a cube

The volume of a solid is determined by multiplying its three dimensions (length, width, height). The volume of a cube is found by multiplying its length, width, and height each squared.

Example: If the cube has a length of 3 inches, then it would have a volume of 9 square inches.

This applies similarly to other shapes such as a pyramid or cylinder. Just remember that you must multiply all three dimensions!

There are several ways to determine the volume of a sphere. One way is to find the radius of the circle that fits inside the sphere, take this value and add it to the spheres’ diameter, which is the measurement from the center of the sphere to the edge. This value can be multiplied into the equation for volume to calculate the total amount of space in the shape.

Math plays an important role in architecture, but most architects do not use advanced math beyond high school level courses. Some degree programs require additional mathematics like algebra, geometry, and trigonometry, but these subjects are often limited to specific areas like surface area, volumes, and ratios.

Architects who specialize in designing spaces with patterns and curves may learn more about functions and derivatives than those who design buildings with strict rules. Engineers and mathematicians make good architectural professionals because they understand the basics of creating aesthetically pleasing structures.

Find the surface area of a sphere

The most basic way to find the surface area of a solid is by using the formula s = πy, where y is the height of the object above the surface we are calculating the surface area for and s is the surface area.

In our case, this would be looking at the surface area of a sphere. A circle with a radius of one half its diameter has a total surface area of 2πr=2*3.14=6.28 radians or 6.283 radian-sized spheres. In other words, there are six times as much surface area in a sphere that size than there is in a regular circle!

This is because you get an extra layer of space when you include the inner and outer curvatures of the shape. This applies particularly well to spheroids, such as a sphere.

Compute the volume of a sphere

The volume of an object is determined by multiplying its height, width, and depth. For example, if you wanted to know how much space a cylinder would take up in a room, you could find that out using the formula above.

The length of the cylinder does not matter here as it can be extended beyond the wall or not included along the floor, but its diameter (height) does! This will determine how high the cylinder needs to be for it to fit into the room.

Architects must have a solid understanding of this concept in order to work with shapes like cylinders and spheres. They use these formulas frequently when calculating spaces and volumes in architectural drawings.

Find the distance between two points

The term ‘distance’ is used to describe the amount of space that exists in-between two things. In mathematics, we are usually very specific with our definitions so that there is no confusion.

So, what is the definition of distance? A metric or ‘measurement’ length! The measure of the length of a thing is how many more steps it takes to get down to the next shorter part. For example, if you have a yard long stick and a half yard short stick, your longer stick has one less foot than the other piece meaning its length is 1/2 yard shorter.

This concept applies beautifully to architecture. Take any two points, say A and B, and find the distance between them using the formula: d = (b - a) / l where a is the height of point A, b is the height of point B, and l is the depth of point A.

The reason this formula works is because both a and b are lengths measured in feet while l is an unknown length which can be determined by finding the difference in elevation at point A and point B.

Find the angle between two lines

The next concept in linear algebra that you will learn is how to find the angle of line segments. You will do this with several examples, so prepare for some math!

If you were given an equation like x = 5 + 2y then you would have to determine what y equals to give you the solution for x. By doing this with each possible value of y, you can figure out what x equals!

The same goes for finding angles. If you are given two lines, then you will know whether their intersection or divergence is a right angle by looking at both equations and solving them!

There are three cases where this happens: when one line is parallel to the other, either totally vertically or horizontally, or when they form a straight-angled V or U shape. These are referred to as orthogonal intersections/divergences and represent 0 degrees (no degree measure) because it is impossible to calculate a true angle here.

When determining if these situations occur, you only need to check one of the two lines: when one axis becomes zero, the other does too making the calculation easy.

Find the gradient of a line

The term gradient comes from geometry, where you find the slope of a line by taking the ratio of two lines or vectors. In other words, the grade is determined by how steep the line is; the higher the number, the steeper the incline.

The gradient of a line is actually quite useful in architecture. You will frequently need to determine whether an area is increasing or decreasing in size (think roofs), as well as determine if something like a roof has a peak or not. These are all questions that can be answered with a simple test of the gradient of the line!

If the gradient is positive, then the area is rising slowly towards a top, for example a roof that rises very slightly before ending. If it’s negative, then the area is dropping quickly towards nothing, such as a house with a pitched roof that collapses under its own weight. A zero degree gradient means that the line is flat, which doesn’t tell us anything specific about the shape of the object.

Calculate the curvature of a curve

The second concept in geometry that is important to know about curved shapes is how to calculate their approximate degree of steepness or concavity. This is called the first derivative, and you can find it by taking the difference between the two adjacent edges of a shape.

For example, if we take the edge between two lines as our base, then the slope (or first derivative) of any other line would be the difference between those two points. In this case, the slope of the triangle’s top side is just the difference between the endpoints of the bottom side.

This way of calculating slopes applies not only to lines, but also to curves! If there are no restrictions, you could determine the first derivative for anything, which makes sense intuitively because things like squares and circles have very sharp corners and/or vertical walls that get steeper as they go up.

However, when working with architectural designs, there are some rules that apply to keep from going crazy. Two such limitations are the so-called quadratic limit and the circle radius rule.

The quadratic limit says that beyond a certain distance, parallel lines will become infinitely close together and therefore lose significance as separate pieces of the shape. As you might expect, this limits the ability to create really tall buildings, and similarly restricts how far you can make windows and similar openings.