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Quadrilateral calculator
A quadrilateral is two triangles glued along a diagonal, and a triangle cut by a line is the same thing with one angle opened out flat. Type into either half and whatever it determines is handed to the other.
How to use it
- Pick what you are looking at: a quadrilateral, or a triangle with a line drawn across it.
- Type any measurement onto the figure. Each half needs three values, and the shared edge counts for both — so a quadrilateral takes five and a cut triangle four.
- Anything one half works out is passed to the other, so you rarely have to type six numbers. A passed value is shown with a dashed outline.
- In the cut-triangle mode the two angles where the line meets the base always add to 180°, so typing one gives you the other.
Why a quadrilateral and a cut triangle are the same picture
Draw the diagonal of any quadrilateral and it falls into two triangles that share that diagonal. Draw a line from one corner of a triangle to a point on the opposite side and you get two triangles that share that line. The two situations look different on paper and are the same object underneath: two triangles hinged along a common edge. The only difference is the angle where they meet. In a quadrilateral the two halves of that corner make some ordinary angle; in the cut triangle they open out to exactly 180° and the corner flattens into a straight side.
That is why one tool does both, and why the cut-triangle mode needs no extra arithmetic — only the extra fact that the two angles at the cut add to 180°. Type 98° on one side of it and 82° appears on the other, which is the single most common step in school geometry problems built on this figure.
Four sides do not fix a quadrilateral
A triangle is rigid: give its three sides and there is exactly one triangle, which is why a triangular brace stiffens a gate and why three lengths are enough to solve one. A quadrilateral is not. Four given sides describe a linkage that flexes — you can push it from a square towards a flat rhombus without changing a single side length, and every position along the way has the same four sides. So four sides are not an answer, and a tool that draws one anyway has picked a shape out of infinitely many and told you nothing.
What makes it rigid is a fifth measurement that ties the halves together: the diagonal, or one of the angles. That is exactly the shared edge in this tool, and it is why a quadrilateral needs five values here rather than four.
What it refuses
The shared edge is one length belonging to both halves, so it cannot be two different numbers, and pinning it twice to disagreeing values is refused rather than drawn from two incompatible halves. In the cut-triangle mode, angles at the cut that do not come to 180° are refused too, because the outer edge would not be straight and the figure would not be the one on screen.
A half with two sides and an angle that is not between them can describe two different triangles — the ambiguous case — and rather than picking one, the tool says which half is unsettled and asks for one more measurement. Nothing is passed across from a half that has not settled, and a half that knows only its shape never passes a length, because its sides are ratios and not lengths at all.
Questions
How many values does it need?
A quadrilateral needs five, and a triangle cut by a line needs four. The reason is that each half is a triangle needing three, the shared edge is one length counted by both, and in the cut-triangle mode the two angles at the cut are related by adding to 180°, which removes one more. You will usually type fewer than that in total, because whatever one half works out is passed to the other automatically.
Why can I not just give the four sides of a quadrilateral?
Because they do not determine one. A four-bar linkage with those side lengths flexes through infinitely many shapes, all with the same four sides — unlike a triangle, which is rigid. You need a fifth measurement that pins the two halves relative to each other: the diagonal, or one of the angles.
What do U, S, V and T mean?
S and T are the two ends of the shared edge — the diagonal of the quadrilateral, or the line cutting the triangle. U is the far corner of the upper half and V the far corner of the lower one. In the cut-triangle mode U, S and V lie on one straight line, which is the base of the whole triangle, and T is the corner the cut comes from.
What does a dashed outline on a box mean?
That the value was worked out by the other half and handed across, rather than typed by you or derived inside its own half. It is marked so you can see where a number came from, which matters when you are checking a result rather than just reading it.
Does anything leave my browser?
No. It is a few dozen lines of trigonometry running on this page, with no server involved at any point. Nothing is uploaded, stored or logged.
Updated 2026-08-20. Runs fully in your browser — nothing is uploaded.