What Is a Radius?

How radius behaves

All radii of the same circle have equal length. That simple fact explains why the circle stays perfectly round and why the diameter is always twice the radius.

On this page the radius is shown as a live segment, not just as a number in a formula. That makes it easier to connect the definition to circumference, area, and tangent geometry.

For example, a circle with radius 4 units has diameter 8 units. The radius is not a line that must point upward or to the right; it can aim in any direction from the center to the boundary. Its job is defined by its endpoints, not by its slant.

• A radius is a segment from the center of a circle to a point on the circle.
• In one circle, every radius has the same length.
• A diameter is made from two radii placed end to end through the center.
• A tangent is perpendicular to the radius drawn to the point of tangency.

Where radius is used

• Use radius when finding circumference, area, sector area, or arc length.
• Use it in compass constructions because the chosen radius sets the size of the circle.
• Use it in circle theorems where a radius meets a tangent or helps form a central angle.

Radius mistakes to avoid

• Do not confuse radius with diameter; the radius reaches from center to edge, not from edge to edge.
• Do not call any interior segment a radius unless one endpoint is the center and the other lies on the circle.
• Do not switch length units when moving from the radius to formulas for circumference or area.