Tangent Length Calculator

About this calculator

When a straight line is drawn from a point outside a circle so that it touches the circle at exactly one point, the segment from the external point to that point of tangency is the tangent length, and it follows directly from the fact that a tangent line is always perpendicular to the circle’s radius at the point of contact. That perpendicularity creates a right triangle with the radius, the tangent segment, and the line from the external point to the center, so by the Pythagorean theorem the tangent length equals the square root of (distance to center squared minus radius squared).

This relationship is used in geometry classrooms, in CAD and technical drafting when constructing tangent lines to circular features, and in surveying and machining where tangent lengths determine clearances or transition curves between straight and circular paths.

Enter the distance from the external point to the circle’s center and the circle’s radius, and this calculator returns the exact tangent length using the Pythagorean relationship.