Barycentric Coordinates
Click anywhere to see barycentric coordinates. Drag vertices to reshape the triangle.
λ₁ dominant
λ₂ dominant
λ₃ dominant
Centroid G
Circumcenter O
Orthocenter H
Incenter I
Click inside the triangle to see coordinates
Barycentric coords sum to 1. Negative values mean the point is outside the triangle.
About: Barycentric coordinates (λ₁, λ₂, λ₃) express any point P as a weighted average of triangle vertices: P = λ₁A + λ₂B + λ₃C with λ₁+λ₂+λ₃=1. They were introduced by Möbius in 1827. The centroid is (1/3, 1/3, 1/3); the incenter has weights proportional to side lengths (a:b:c); the circumcenter and orthocenter have elegant forms involving the side lengths and angles. Points outside the triangle have at least one negative coordinate — they're still valid barycentric representations.