Circles: The Basics

Two words do most of the work here. The radius is the distance from the center of a circle out to the edge. The diameter is the distance all the way across, through the center. The diameter is twice the radius, so if you know one you know the other.

Then there are two formulas. Area, the space inside, is $\pi r^{2}$. Circumference, the distance around the edge, is $2\pi r$. Both use the radius, never the diameter. When a question gives you a diameter, cut it in half first — that one habit prevents most circle mistakes.

On a grid, a circle is written $(x - h)^{2} + (y - k)^{2} = r^{2}$. The center is $(h, k)$, and the signs flip when you read them. The number on the right is the radius squared, so take its square root to get the radius.