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Triangle Area and Perimeter from Cartesian Vertices

No. The absolute determinant removes the orientation sign. Perimeter adds the three point distances. Collinear vertices return zero area, and repeated vertices are allowed as degenerate cases.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

Example in initial displayed units: x₁ (A) 0, y₁ (A) 0, x₂ (B) 4, y₂ (B) 0, x₃ (C) 0, y₃ (C) 3 gives Area 6, Perimeter 12.

A = |determinant|/2; P = AB+BC+CA

Worked example

Enter these known values and leave the other values blank.

x₁ (A): 0
y₁ (A): 0
x₂ (B): 4
y₂ (B): 0
x₃ (C): 0
y₃ (C): 3

Area: 6
Perimeter: 12

Assumptions and limitations

Coordinates share one Cartesian scale. Area and perimeter are read-only forward results. Signed coordinates and either orientation are accepted. Collinear or repeated vertices give zero area; that is a degenerate outline rather than a nonzero-area triangle.
Use compatible units and enough independent values. Clear unknowns before solving backward. Original reference drawings are schematic and do not scale to entered values.

Common questions

Does reversing the vertex order change triangle area?