Area of a Triangle from Coordinates Calculator
Enter the coordinates of the three corners. You get the area, the perimeter and the centroid, and the calculator tells you if the points lie on one line.
- Nothing you type is stored
- Free
- No signup
Area (square units)
9
A → B → C anticlockwise- Perimeter
- 13.9804
- Centroid
- (3, 3)
Show working
- A = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|
- A = ½ |1 × (−4) + 5 × (5) + 3 × (−1)|
- A = ½ × |18| = 9
How to use
- Enter vertex A (x₁, y₁).
- Enter vertices B (x₂, y₂) and C (x₃, y₃).
- Read the area and check the badge for collinear points.
Good to know
Area = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. The bars mean you take the positive value. This formula was in the Class 10 Coordinate Geometry chapter in older NCERT editions and still appears in state boards and competitive exams; the same expression appears as a determinant in higher classes.
If the area is 0, the three points are collinear: they lie on one straight line and do not make a triangle. Questions such as "find k if the points are collinear" set this expression to zero.
The badge also shows the order of the vertices (anticlockwise gives a positive value before the bars). The centroid ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3) is where the medians meet.
Questions
What is the formula for the area of a triangle with coordinates?
½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|.
How do I check if three points are collinear?
Find the area with this formula. If it is 0, the points are collinear.
Why is my answer negative in the working?
The sign depends on the order of the points. Area is the absolute value, so it is always positive.
What units is the area in?
Square units of whatever unit the coordinates use.
Is anything I enter stored?
No. The calculation runs in your browser and nothing is sent to a server.