How this calculator works
Connect the three entered vertices in order and close the outline back to the first vertex. Subtract the sum of the reverse products from the forward products, then halve the result. The sign records orientation and its absolute value gives geometric area. Perimeter is the sum of the three Euclidean distances. Computation translates the coordinates to the first vertex before taking the determinant to reduce cancellation.
Formula
Signed area = [(x₂-x₁)(y₃-y₁) - (x₃-x₁)(y₂-y₁)]/2; K = |signed area|; P = AB + BC + CA.
Worked example
A = (0,0), B = (4,0), C = (0,3) give a forward product sum of 12 and reverse sum of 0. Area is 6 square units, signed area is +6 and perimeter is 12 units.
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Frequently asked questions
Does swapping two vertices change the area?
It changes the sign and orientation, but the absolute area and perimeter remain the same.
Can I enter latitude and longitude?
Convert geographic coordinates to a suitable flat projection first. This tool assumes a Euclidean coordinate plane, not a curved Earth.
What happens with collinear points?
The determinant is zero. The points do not enclose a triangle and the calculator reports an input error.