Circles
Parts of circles and circumference
Start with the basics and progress through 6 lessons. Each lesson builds on the previous one.
0 of 6 lessons done
Test Your Knowledge
10 questions, new mix each time (from 92)
In This Topic (6 lessons)
Parts of a Circle and Circumference
Learn the essential parts of a circle and how to calculate circumference using pi.
Arc Length
Learn how to calculate the length of an arc using the central angle and radius.
Area of Circles
Learn how to calculate the area of a circle using the formula A = πr².
Area of Semicircles and Quarter Circles
Learn how to calculate the area of semicircles and quarter circles using the circle area formula.
Area of Annulus (Ring)
Learn how to calculate the area of an annulus - the ring-shaped region between two concentric circles.
Area of Circles Word Problems
Learn to solve real-world problems involving the area of circles, from pizza to swimming pools.
Circles are unique among shapes—every point on a circle is exactly the same distance from the center. This perfect symmetry makes circles essential in engineering, design, and nature. From wheels to orbits to ripples in water, circular patterns appear everywhere.
In this topic, you will master the vocabulary of circles: radius, diameter, circumference, arc, chord, and sector. You will discover the magical number π (pi) and use it to calculate circumference and area. Understanding the relationships between these measurements opens doors to geometry and trigonometry.
Our lessons connect circles to real applications: wheels, clocks, pizza, and planetary motion. You will see how π appears naturally when measuring circular objects and develop intuition for circular measurements that applies across mathematics and science.
What You'll Learn
- Identify parts of a circle: radius, diameter, chord, arc
- Calculate circumference using C = 2πr or C = πd
- Calculate area using A = πr²
- Find arc length and sector area
- Understand the relationship between radius and diameter
- Apply circle formulas to real-world problems
- Work with inscribed and central angles
Frequently Asked Questions
What is π (pi)?
Pi is the ratio of any circle circumference to its diameter, approximately 3.14159. It is the same for every circle, no matter the size. Pi is irrational—its decimal never ends or repeats.
What is the difference between radius and diameter?
The radius goes from the center to any point on the circle. The diameter goes all the way across through the center. Diameter = 2 × radius, or d = 2r.
How do I find the area of a semicircle?
A semicircle is half a circle, so find the full circle area (πr²) and divide by 2. Semicircle area = πr²/2.