Quadrilateral Area Calculator

Work out quadrilateral area instantly with clear inputs, formula shown and shareable results.

About Quadrilateral Area Calculator

Any quadrilateral splits into four triangles along its diagonals, and summing them gives A = ½·d₁·d₂·sin θ where θ is the angle between the diagonals. The enclosing parallelogram formed by lines through the vertices parallel to the diagonals has exactly twice this area.

Formula

Area from diagonals

A = ½ · d₁ · d₂ · sin θ

Worked example

With the default values below, Quadrilateral Area Calculator returns Area of 34.6410. Change any input above and every figure here is recalculated in your browser.

Inputs used

Diagonal 1minimum 0: 10
Diagonal 2minimum 0: 8
Angle between the diagonalsaccepts 0–180 °: 60 °

Results

Area: 34.6410
Product of diagonals: 80.0000
sin of the angle: 0.866025
Area of the enclosing parallelogram: 69.2820

Step by step

1Values used
2Area from diagonals
3Area= 34.6410
4Product of diagonals= 80.0000
5sin of the angle= 0.866025
6Area of the enclosing parallelogram= 69.2820

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does this work for a non-convex quadrilateral?

It works whenever the diagonals actually intersect inside the figure. For a re-entrant shape use the shoelace formula with the four vertices instead.

What happens at θ = 90°?

sin θ = 1 and the formula reduces to ½·d₁·d₂, the rhombus and kite case.