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Triangle Incenter Calculator

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

About Triangle Incenter Calculator

The incentre is the meeting point of the three angle bisectors and the centre of the inscribed circle. It is the side-length-weighted average of the vertices, and the inradius equals area divided by the semiperimeter.

Formula

Incentre

I = (a·A + b·B + c·C) / (a + b + c), r = Area / s

Worked example

With the default values below, Triangle Incenter Calculator returns Incentre of (2, 2). 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)
0, 8

Results

Incentre
(2, 2)
Incentre x
2.0000
Incentre y
2.0000
Inradius r
2.0000

Step by step

  1. 1Values used
  2. 2Incentre
  3. 3Incentre= (2, 2)
  4. 4Incentre x= 2.0000
  5. 5Incentre y= 2.0000
  6. 6Inradius r= 2.0000

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

What are a, b and c here?

They are the side lengths opposite vertices A, B and C respectively, computed automatically from the coordinates you enter.

Is the incentre ever outside the triangle?

Never. The incircle is inscribed, so its centre always lies inside.

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Triangle Incenter Calculator | Calcrivo