Enter three vertices to analyze a triangle accurately. Get inradius, incenter, perimeter, area, and validation. Download reports and inspect the plotted triangle with confidence.
1. Side lengths from coordinates
a = √[(x₃ - x₂)² + (y₃ - y₂)²], b = √[(x₃ - x₁)² + (y₃ - y₁)²], c = √[(x₂ - x₁)² + (y₂ - y₁)²]
2. Area from coordinates
Area = |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)| ÷ 2
3. Semiperimeter
s = (a + b + c) ÷ 2
4. Inradius
r = Area ÷ s
5. Incenter coordinates
I = ((ax₁ + bx₂ + cx₃) ÷ (a + b + c), (ay₁ + by₂ + cy₃) ÷ (a + b + c)) where a, b, and c are opposite side lengths.
| Example | A | B | C | Area | Inradius | Incenter |
|---|---|---|---|---|---|---|
| Example 1 | (0, 0) | (6, 0) | (2, 4) | 12.0000 | 1.4880 | (2.4076, 1.4880) |
| Example 2 | (1, 1) | (5, 2) | (3, 7) | 11.0000 | 1.3895 | (3.1187, 2.9619) |
| Example 3 | (-2, 1) | (4, 1) | (1, 6) | 15.0000 | 1.6986 | (1.0000, 2.6986) |
The inradius is the radius of the largest circle that fits inside a triangle and touches all three sides. In coordinate geometry, that value helps connect algebra, distance, perimeter, and area in one clean result. It is useful in classwork, geometry checks, drafting problems, and coordinate verification tasks.
This page accepts three coordinate pairs and builds a full triangle analysis. It measures all side lengths, computes the perimeter, finds the semiperimeter, and determines the enclosed area from the coordinate formula. It then applies the inradius formula r = A ÷ s, where A is the area and s is the semiperimeter.
The incenter is the point where the three angle bisectors meet. In coordinate form, that point is found with weighted averages based on the opposite side lengths. Because the incenter is equally distant from every side, the common distance from that point to the sides is exactly the inradius.
Not every set of three points forms a proper triangle. If the points overlap or fall on the same straight line, the area becomes zero and the incircle does not exist. This calculator checks those cases before showing the numeric result, which helps prevent misleading answers.
The graph gives a visual check of the triangle and its incircle. This is helpful when you want to verify point order, compare narrow and wide triangles, or inspect whether the result feels reasonable. A plotted figure often catches entry mistakes faster than reading a table alone.
It is the radius of the circle inscribed inside the triangle. That circle touches all three sides exactly once.
Yes. The calculator accepts integers and decimals, then returns rounded results based on your chosen precision setting.
The points may overlap or lie on one straight line. A valid triangle needs three unique points and positive area.
Yes. It returns the incenter coordinates because the incenter is directly connected to the inscribed circle and inradius.
It uses the coordinate area formula based on the determinant pattern. This method works directly from the three vertex pairs.
No. The unit label is optional. Add one when you want saved results to show units such as cm, m, or ft.
They tell whether the triangle is scalene, isosceles, or equilateral, and whether it is acute, right, or obtuse.
Yes. Use the CSV button for spreadsheet work or the PDF button for a quick printable summary.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.