Triangle Centres Calculator (Centroid, Circumcentre, Incentre, Orthocentre)

What this tool does

Give the three corners and the calculator finds where the medians meet (centroid, the balance point), where the perpendicular bisectors meet (circumcentre, the centre of the circle through all three corners), where the angle bisectors meet (incentre, the centre of the largest circle that fits inside) and where the altitudes meet (orthocentre). In any triangle the centroid, circumcentre and orthocentre lie on one straight line, the Euler line, with the centroid a third of the way from the circumcentre to the orthocentre. In an obtuse triangle the circumcentre and the orthocentre fall outside the triangle, and in a right triangle the orthocentre sits on the right-angle corner.

Formula

G = (A + B + C) ÷ 3 · O: 2(B − A)·O = |B|² − |A|² · I = (aA + bB + cC) ÷ (a + b + c) · H = A + B + C − 2O · R = abc ÷ 4S · r = S ÷ s

Variables

Worked example

Limitations

• Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
• The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.