Solve a triangle from any three known sides/angles, or explore an angle on the unit
circle — with the formula worked out step by step underneath.
Enter exactly three known values (at least one must be a side).
How to use this calculator
Switch between Triangle Solver and Unit Circle above. Both calculate live as you type -
no Calculate button needed.
Triangle SolverFill in any three of the six fields (three sides, three angles) and the rest are
solved for automatically - the calculator figures out which case applies (SSS, SAS,
ASA, AAS, or SSA) from whichever three you filled in.
The ambiguous case (SSA)Two sides plus a non-included angle can match zero, one, or two different
triangles - both are shown when two exist, since there's no way to know which one
you meant from the numbers alone.
Why three angles alone isn't enoughThree angles only fix a triangle's shape, not its size - infinitely many
similar triangles share the same three angles. At least one side is required.
Unit CircleType an angle (or click one of the common angles) to see it plotted on the unit
circle, with cos/sin/tan, the quadrant, and the reference angle - the acute angle
between the terminal ray and the x-axis.
Undefined tangenttan θ is undefined at 90° and 270° (and their equivalents), since it's sin÷cos
and cos is zero there - shown as "undefined" rather than a huge or infinite number.