Triangle & Trigonometry Calculator

Triangle & Trigonometry Calculator

Solve any triangle from three known values — enter sides and angles in any valid combination (SSS, SAS, ASA, AAS, SSA) and instantly get all missing measurements, area, perimeter, heights, inradius, circumradius, and triangle classification. Includes step-by-step solutions, an SVG diagram, and a quick reference for special right triangles.

How to Use

Enter at least three known values (sides and/or angles), with at least one side. The calculator auto-detects the configuration (SSS, SAS, ASA, AAS, or SSA) and solves for all unknowns using the Law of Cosines, Law of Sines, and Pythagorean theorem. Toggle between degrees and radians for angle units. Scroll down to see the step-by-step solution showing every formula and intermediate calculation, plus an SVG diagram of your triangle.

Features

• Triangle Solver — Enter any valid combination of 3+ sides and angles. Solves for all 3 sides, all 3 angles, area, perimeter, heights, inradius, and circumradius.
• Auto Configuration Detection — Automatically identifies SSS, SAS, ASA, AAS, or SSA and applies the correct solving method. Handles the ambiguous SSA case with two possible solutions.
• Step-by-Step Solution — See exactly which formulas were used and how each value was calculated. Great for learning or verifying homework.
• SVG Triangle Diagram — Visual representation of the solved triangle with labeled sides and angles, approximately proportional to actual measurements.
• Triangle Classification — By sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).
• Special Right Triangles — Quick reference for common triangles (30-60-90, 45-45-90, 3-4-5, 5-12-13, 8-15-17) with clickable presets to populate the solver.
• Degrees/Radians Toggle — Switch between degree and radian angle units.
• Input Validation — Triangle inequality check, angle sum validation, and clear error messages for impossible triangles.

Formulas Used

Law of Cosines: c² = a² + b² − 2ab·cos(C)
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Pythagorean Theorem: a² + b² = c² (right triangles)
Area (SAS): ½·a·b·sin(C)
Area (Heron’s): √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2
Height: hₐ = 2·Area/a
Inradius: r = Area/s
Circumradius: R = a/(2·sin(A))