Draw triangles, quadrilaterals, circles, and segments — see angles, lengths, area.
Click on the canvas to place the selected point, or drag existing vertices.
Formulas used
Distance between two points
The length of a segment from (x1, y1) to (x2, y2) comes from the Pythagorean theorem:
Used for all side lengths, segment length, circle radius (when defined by two points), and Euclidean distance between any two vertices.
Heron's formula (triangle area)
With side lengths a, b, c and semi-perimeter s = (a + b + c) / 2:
This calculator also cross-checks triangle area with the coordinate (shoelace) form, which does not require computing sides first.
Shoelace formula (polygon area)
For a polygon with vertices (x1, y1), (x2, y2), ..., (xn, yn) listed in order:
Works for any non-self-intersecting polygon — triangles and quadrilaterals included. Sign of the unsigned sum tells you the orientation (clockwise vs counter-clockwise).
Law of cosines (interior angles)
For a triangle with sides a, b, c opposite vertices A, B, C:
Applied at each vertex to get all three interior angles. The three angles always sum to 180° — any deviation indicates input that is not a valid triangle (collinear points).
Circle — circumference and area
With radius r:
When circle is defined by center (cx, cy) and a point (px, py) on the circumference, the radius is the distance from center to that point.
Line segment — slope and midpoint
For points (x1, y1), (x2, y2):
Slope is undefined when x1 = x2 (vertical line). A slope of 0 means the segment is horizontal.
FAQ
How do I input points — by typing or by clicking?
Both work. Type X and Y coordinates into the number fields and the shape updates live, or select which point to place next and click anywhere on the canvas. You can also drag existing vertices to move them. Coordinates accept decimals and negative values.
Which shapes are supported?
Four shape types via tabs: triangle (three vertices), quadrilateral (four vertices, any non-self-intersecting polygon including trapezoids, parallelograms, kites), circle (center plus radius or center plus point on circumference), and line segment (two endpoints). Each tab computes a different set of measurements.
Why does my triangle show an area of zero?
Zero area means the three points are collinear — they lie on the same straight line, so there is no enclosed region. Move any one vertex off that line and the area becomes positive. Angles will also become undefined (NaN) in the degenerate case because side c equals a + b.
Why use Heron's formula instead of (1/2) × base × height?
Heron's formula only needs the three side lengths, which are easy to get from coordinates via the distance formula. It avoids having to pick a base and drop a perpendicular from the opposite vertex, which needs extra steps. The coordinate (shoelace) form is even more direct when vertex coordinates are known.
What units does the calculator use?
The canvas is unit-agnostic — coordinates are pure numbers. Treat them as centimeters, meters, inches, or any consistent unit. Lengths and perimeter inherit that unit; area comes out in squared units (for example, if X and Y are meters, area is in m²). Angles are always in degrees.
Interactive geometry tool that draws shapes from coordinates and reports every measurement at once. Pick a shape tab — triangle, quadrilateral, circle, or line segment — then type vertex coordinates or click on the SVG canvas to place points. Drag any vertex to reshape live.
For a triangle with vertices A(0,0), B(4,0), C(0,3) the calculator returns side lengths AB=4, BC=5, CA=3, perimeter 12, area 6, and interior angles 90°, 53.13°, 36.87° — a classic 3-4-5 right triangle. A circle centered at (0,0) with radius 5 gives circumference 31.416 and area 78.540. A segment from (-3,-2) to (4,3) has length 8.602, slope 0.714, and midpoint (0.5, 0.5).
Toggle grid, axes, and labels for a cleaner view. Copy results copies all coordinates and measurements as plain text for homework, reports, or CAD notes.