Angle Bisector Calculator

Work out angle bisector instantly with clear inputs, formula shown and shareable results.

About Angle Bisector Calculator

The internal bisector from A cuts side a into pieces proportional to the adjacent sides (BD:DC = c:b) and has length √[bc((b+c)² − a²)] / (b+c).

Formulas

Bisector length

tₐ = √[bc((b+c)² − a²)] / (b + c)

Angle bisector theorem

BD : DC = c : b

Worked example

With the default values below, Angle Bisector Calculator returns Bisector length from A of 8.4327. Change any input above and every figure here is recalculated in your browser.

Inputs used

Side a (opposite the bisected angle)minimum 0: 6
Side bminimum 0: 8
Side cminimum 0: 10

Results

Bisector length from A: 8.4327
Segment adjacent to side b: 2.6667
Segment adjacent to side c: 3.3333
Angle A being bisected: 36.8699 °

Step by step

1Values used
2Bisector length
3Angle bisector theorem
4Bisector length from A= 8.4327
5Segment adjacent to side b= 2.6667
6Segment adjacent to side c= 3.3333
7Angle A being bisected= 36.8699 °

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 is the angle bisector theorem?

The bisector from a vertex divides the opposite side into two segments whose lengths are in the same ratio as the two sides forming the angle.

Do the three internal bisectors meet?

Yes, at the incentre, which is the centre of the inscribed circle.