Racira CAD

Angle Bisector Tool

Input

Angles are measured counter-clockwise from the +X axis. A(1,0), B(0,0), C(0,1) gives a 90° angle at B with a 45° bisector.

Result

Interior angle at vertex90.000°
Half-angle45.000°
Bisector direction (from +X)45.000°
Reflex-sector bisector225.000°

What is Angle Bisector Tool

Angle Bisector Tool finds the bisector of an angle two ways. In Angle value mode you type the angle and it returns the bisector at half that angle, plus the bisector of the reflex sector, which sits 180 degrees opposite. In Three points mode you enter two points and a vertex — A, B and C with B as the corner — and the tool computes the interior angle at B from the two arm vectors, the half-angle, and the direction of the bisector measured counter-clockwise from the positive X axis.
The three-point bisector direction comes from adding the two unit vectors along the arms: the bisector of an angle is the ray that makes equal angles with both sides, and the normalised sum of two unit vectors points exactly along it. The default example — A at (1,0), B at (0,0), C at (0,1) — is a 90 degree corner whose bisector runs at 45 degrees, the classic half-of-a-right-angle check.

How to Use Angle Bisector Tool

  1. Step 1: Choose the Mode — Three points for angles defined by geometry, or Angle value for a plain angle you already know.
  2. Step 2: In three-point mode, enter the X and Y coordinates of A, B and C. B is the vertex — the corner of the angle — and A and C are any point on each arm.
  3. Step 3: In angle-value mode, enter the angle in degrees, from 0 to 360. Values above 360 are normalised onto the circle.
  4. Step 4: Read the Result panel: the interior angle at the vertex, the half-angle, the bisector direction from the +X axis, and the reflex-sector bisector.
  5. Step 5: Verify the default: A(1,0), B(0,0), C(0,1) must give a 90 degree angle, a 45 degree half-angle and a 45 degree bisector.
Angles are measured counter-clockwise from the positive X axis and normalised to 0–360 degrees, so a point straight above the vertex reads 90 degrees rather than a negative number. The reflex-sector bisector is the ray that splits the large sector — for a 90 degree corner it lies at 225 degrees, half of the 270 degree sector that wraps from the second arm back through 180 to the first.

Why Use Angle Bisector Tool

Bisectors are constant drawing chores: centrelines for tapped-hole patterns, the mid-line of a chamfer or roof valley, angular dimension placement, and the angle at which a feature must be rotated to face between two reference edges. Working from coordinates removes the protractor entirely — the direction is exact, not read off a printed drawing at the precision a scale can manage.
The three-point mode is what makes it a CAD tool rather than a calculator: coordinates come straight from the model, and the answer is an angle from the drawing's own X axis, which is exactly the rotation value a CAD command asks for. When you only need to halve a known angle, angle-value mode answers in one field, and the reflex output covers the other side of the corner without a second calculation.

Privacy & Security

This tool runs entirely in your browser — no data ever leaves your device. There is no server round-trip, no upload, no logging, and no account required. Your input is processed locally using client-side JavaScript and is never stored, transmitted, or accessible to anyone else. When you close the tab, everything disappears.

Frequently Asked Questions

Why is the bisector direction measured from the +X axis instead of north?

CAD and Cartesian coordinate systems treat the positive X axis as zero and measure counter-clockwise, which is the convention this tool follows. Survey bearings are measured clockwise from north instead. If you are converting a result to a survey bearing, subtract the reported angle from 90 degrees for the first quadrant, then adjust per quadrant — the value here is the drawing angle, not a compass angle.

What happens if I enter the two points in the reverse order?

Swapping A and C leaves the interior angle exactly the same — the angle between two lines is symmetric — and the bisector direction is unchanged too, because the bisector ray is the same line either way. The angle at B is computed from both arms, so neither endpoint is special beyond defining the two directions.

Can the tool bisect an angle larger than 180 degrees?

The interior angle at a vertex is always the smaller angle between the two arms, from 0 to 180 degrees, so the bisector it reports is always within that sector. The reflex-sector bisector covers the large side: it is exactly 180 degrees opposite the interior bisector, splitting the reflex sector in half. Use the reflex output whenever your feature lies on the outside of the corner.

What does the angle-value mode do with an angle like 450 degrees?

It normalises the input onto the 0 to 360 degree circle before bisecting, so 450 degrees is treated as 90 degrees and reports a 45 degree bisector. This keeps the tool forgiving of inputs that came from wrapped angle arithmetic, such as a rotation that accumulated past a full turn.