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Triangle Orthocenter Calculator

Work out triangle orthocenter instantly with clear inputs, formula shown and shareable results.

About Triangle Orthocenter Calculator

The orthocentre H is where the three altitudes meet. Using the Euler line relation H = A + B + C − 2O, where O is the circumcentre, gives it directly without solving altitude equations.

Formula

Euler line relation

H = A + B + C − 2·O (O = circumcentre)

Worked example

With the default values below, Triangle Orthocenter Calculator returns Orthocentre of (2, 1.6). Change any input above and every figure here is recalculated in your browser.

Inputs used

Vertex A (x, y)
0, 0
Vertex B (x, y)
6, 0
Vertex C (x, y)
2, 5

Results

Orthocentre
(2, 1.6)
Orthocentre x
2.0000
Orthocentre y
1.6000
Circumcentre x (used in Euler line)
3.0000

Step by step

  1. 1Values used
  2. 2Euler line relation
  3. 3Orthocentre= (2, 1.6)
  4. 4Orthocentre x= 2.0000
  5. 5Orthocentre y= 1.6000
  6. 6Circumcentre x (used in Euler line)= 3.0000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Where is the orthocentre of a right triangle?

At the right-angle vertex, because two of the altitudes are the legs themselves.

What is the Euler line?

The straight line through the orthocentre, centroid and circumcentre, with the centroid always between the other two in a 2:1 ratio.

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