Orthocenter Calculator

This finds the point where the three altitudes of a triangle meet. Enter the three vertices as coordinates, using whole numbers, decimals or fractions, and it returns the orthocenter together with the equation of each altitude, the foot it lands on, and the circumcenter, centroid, nine-point centre and Euler line. Coordinates are carried as exact fractions throughout, so a rational answer comes back as 55/19 rather than a decimal approximation. The orthocenter sits inside an acute triangle, on the right-angle vertex of a right triangle, and outside an obtuse one, which the result says explicitly.