Triangle Angle Bisector Calculator
Find the internal angle-bisector length and the two segments it creates on the opposite side. Enter three sides and inspect the labelled triangle.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
The internal bisectorAD dividesBC in the ratioBD:DC=AB:AC=c:b. Use the three side lengths to find angleA and the internal bisector length.
BD=ac/(b+c); DC=ab/(b+c); AD=2bc cos(A/2)/(b+c)
Worked example
WithBC=6cm andAB=AC=5cm, BD=DC=3cm andAD=4cm. For unequal adjacent sides, the bisector generally does not meet the opposite side at its midpoint.
Assumptions and input details
Sides must make a nondegenerate triangle. Known lengths after conversion must be between1e−12 and1e9m, and extremely flat triangles are rejected. A,B,C follow the side labels shown. D lies onBC, andAD is the internal bisector; external bisectors are not included. Decimal lengths and the drawing are approximate.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Solve a triangle from SSS, SAS or ASA measurements. Find all three sides and angles, area and perimeter, with a labeled equal-scale triangle.
Simplify a whole-number ratio and divide a total into proportional shares, or solve the missing value in a:b = c:x. Inspect the shares and calculation steps.
Find the diagonal of a right triangle or rectangle. Mix length units and compare 21 unit conversions with a triangle diagram.
Reserved advertising space.