Concave vs. Convex – How to Use Each Correctly

/ October 14, 2019/ Usage

What’s the Difference Between Concave and Convex?

Concave and convex are closely related words. They are both common in mathematics and physics, and one of these is the inverse of the other.

Concave is an adjective that refers to a thing that has an inward indentation. Think of a round disk that curves inward as an example. In geometry, it means a polygon that has one or more angle that is over 180 degrees.

• The inside of the girl’s lenses, for her glasses, is concave.

Convex is the opposite of concave. Therefore, the same disk from the earlier example would be concave from one direction, and convex from the other. Convex means curving outward. In geometry, convex can also mean all interior angles of a polygon are 180 degrees or less.

• The outer side of the camera lens is convex.

Now that you know the differences between these two words, let’s look at them in context to ensure you don’t confuse one for the other.

Using Concave in a Sentence

When to use concave: Concave means that the surface of something is curving inwards, or that the middle is thinner than the edges. This usually refers to something glass, such as a lens. This has important applications in physics. Within mathematics, concave refers to a polygon that has one or more interior angles greater than 180 degrees.

For example,

• The math teacher wanted the students to identify which polygons were concave.
• The physics students needed to use a concave and a convex lens to see how each affected the light passing through it.

Another way to think of concave is to think of the inner surface of a sphere.

Using Convex in a Sentence

When to use convex: Convex is an adjective that means a surface that curves outward. Another way to describe this is that the middle is thicker than the edges. Within mathematics, it means a polygon in which all the interior angles are equal to or less than 180 degrees.

• The magnifying glass has a convex lens.
• When a convex lens is close to your eyes, the image on the other side is right side up. However, when you move the convex lens away, the image becomes inverted.

Yet another way to describe this is as the outer edges of a globe.

Remembering Concave vs. Convex

These words sound similar and are used in the same contexts. However, they are opposites of one another so it is important to keep them straight.

One easy way to remember that concave means curving inwards is to use the spelling. Concave contains the word cave. When you think of a cave, you think of a hole in a mountain that opens inward.

Additionally, the crisscrossing symbol of the letter x in convex can help you remember that convex is the opposite of concave.

Outside Examples

• Bedford is painting the concave interior walls of a vintage 1948 Airstream trailer into a colorful canvas depicting scenes from national parks across the country. –Washington Times
• Programming the laser cuts in just the right way enabled the rubber to inflate not only outwardly, like a kickball, but as a 3-D structure with concave regions. –Washington Post
• At $3,100-per-truck for side-guards and $400 for each pair of “convex rear-view mirrors,” Fleet and Facilities Management Commissioner David Reynolds pegged the cost of retrofitting the city’s 1,700 trucks at $5 million. –Chicago Sun Times
• Edgy, from Walker Zanger’s Kaza collection, features a recurring hexagonal base with alternating convex and concave patterns. –Houston Chronicle

Quiz: Concave vs. Convex

Instructions: Fill in the blank with the correct word, either concave or convex.

• You need to turn your magnifying glass around. You are using the __________ side, which make everything look smaller. If you flip it over you’ll be using the _______________ side which will make everything look bigger.
• The car’s side rearview mirror is ___________________, which can make objects appear closer than they really are.
• The top surface of the cake is ______________________ which makes it look like it’s bulging out of the pan.

See answers below.

Article Summary

Should I use concave or convex? Remember that these words are two sides of the same coin, or more literally speaking, two sides of a curved disk. Each one is an inverse of the other.

• Convex means curving inward, much like a cave.
• Convex means curving outward.

Because these two words are used in science and mathematics, two fields in which accuracy is of the utmost importance, make sure you know which is which.

Answers

1. concave, convex
2. convex
3. convex