Orthocenter Calculator
With this orthocenter calculator you'll quickly find out the coordinates of this important triangle center.
Area30
Perimeter21.00015993
Vertices5
Interior angle sum540°
Diagonals5
Shoelace terms
| # | x | y | xᵢyᵢ₊₁ − xᵢ₊₁yᵢ |
|---|---|---|---|
| 1 | 0 | 0 | 0 |
| 2 | 5 | 0 | 20 |
| 3 | 6 | 4 | 28 |
| 4 | 2 | 6 | 12 |
| 5 | -1 | 3 | 0 |
The formula
the shoelace formula, from the vertex coordinates
Why it is called the shoelace formula
Write the coordinates in a column, repeat the first at the bottom, then cross-multiply downwards and subtract the upward products — the pattern of crossings looks like lacing a shoe. Sum them and halve the absolute value.
The vertices must be in order around the outline, or the crossings cancel wrongly and the answer is meaningless. The sign before taking the absolute value tells you the winding direction.