Triangle Calculator
Solve a triangle from SSS, SAS, ASA, AAS or SSA (including the two-solution case) or base and height: all sides, angles, area, perimeter and type.
Interactive calculator · Method TRIANGLE-SOLVER-1.0 · Last reviewed: 2026-11-04
Calculate your scenario
Sides a, b, c sit opposite angles A, B, C.
Your inputs
Default worked example. Edit the inputs to calculate your scenario.
Default worked example
c² = a² + b² − 2ab cos C; area by Heron's formula = 6 sq units.
How to use the calculator
Pick the combination of values you know, enter those sides and angles using the a/b/c and A/B/C labels (each angle sits opposite the side with the same letter), and read all the remaining parts.
What the result means
Sides 3 and 4 with a 90° angle between them close with a third side of 5: a right triangle with area 6 and perimeter 12.
Formula and units
Sides a, b, c sit opposite angles A, B, C. SAS uses the law of cosines c² = a² + b² − 2ab cos C; ASA and AAS find C = 180° − A − B and then the law of sines a ÷ sin A = b ÷ sin B = c ÷ sin C; SSA solves sin B = b sin A ÷ a, which can give zero, one or two triangles. All angles are then found from the three sides with the law of cosines, and area by Heron's formula: √(s(s − a)(s − b)(s − c)) with s half the perimeter. Base-height mode uses area = base × height ÷ 2.
Worked examples
SAS: sides 3 and 4 with a 90° angle: Side a (opposite angle A): 3 length unit; Side b (opposite angle B): 4 same length unit; Side c (opposite angle C): 5 same length unit; Angle A: 36.87 degrees; Angle B: 53.13 degrees; Angle C: 90 degrees; Height to base a (base-height mode): 4 same length unit; Known values: sas.
Example result: Area: 6 sq units; Sides a, b, c: a = 3, b = 4, c = 5; Angles A, B, C: 36.8699°, 53.1301°, 90°; Perimeter: 12 units; Triangle type: scalene, right; Solutions: 1.
SSA: a = 7, b = 10, A = 40° (two triangles): Side a (opposite angle A): 7 length unit; Side b (opposite angle B): 10 same length unit; Side c (opposite angle C): 5 same length unit; Angle A: 40 degrees; Angle B: 53.13 degrees; Angle C: 90 degrees; Height to base a (base-height mode): 4 same length unit; Known values: ssa.
Example result: Area: 33.5283 sq units or 15.7121 sq units; Sides a, b, c: a = 7, b = 10, c = 10.4322 or a = 7, b = 10, c = 4.8887; Angles A, B, C: 40°, 66.6742°, 73.3258° or 40°, 113.3258°, 26.6742°; Perimeter: 27.4322 units or 21.8887 units; Triangle type: scalene, acute or scalene, obtuse; Solutions: 2 (ambiguous SSA case).
Limitations and common mistakes
Only the inputs named by the selected mode are used; the other side and angle boxes are ignored. Angles are in degrees and every side uses one length unit. A triangle whose sides fail the triangle inequality, or whose two given angles reach 180°, has no solution. Base and height alone fix the area but not the shape, so sides and angles are not reported in that mode. Displays round half-up to four decimals.
Using SAS when the known angle is not between the two known sides; that is the SSA case, which may have two answers or none.
Sources and assumptions
Method TRIANGLE-SOLVER-1.0; last formula review 2026-11-04. Sources and their supported claims. Calculation methodology.