Triangle Calculator — Free Geometry Tool
Calculate triangle sides, angles, area and perimeter using advanced geometric theorems.
Sides
Angles
Calculation Results
Side a
5.000
Side b
4.000
Side c
3.000
Angle A
90.00°
Angle B
53.13°
Angle C
36.87°
Triangle Classification
Equilateral
All sides equal (60°)
Isosceles
Two sides equal
Right Angle
One 90° angle
Scalene
No sides equal
Any Triangle, Solved From What You Know
What you have determines the method
Three known pieces (including at least one side) solve any triangle:
| You know | Method | Watch for |
|---|---|---|
| Two legs of a right triangle | Pythagoras: a² + b² = c² | The everyday case |
| Two angles + any side | Law of sines | Third angle is free: angles sum to 180° |
| Two sides + included angle | Law of cosines | The formula people forget first |
| All three sides | Law of cosines for angles; Heron for area | Check triangle inequality first |
| Two sides + non-included angle | Law of sines — carefully | The ambiguous case: sometimes two valid triangles |
Triangles outside the classroom
The 3-4-5 trick gives carpenters and masons a perfect right angle with a measuring tape — scaled to 6-8-10 or 9-12-15 for bigger layouts. Roof pitch, ramp gradients, ladder safety angles (the 4-to-1 rule is a triangle), land plot areas from three boundary measurements via Heron's formula, and the height-from-shadow trick (similar triangles) all run on the same handful of relationships.
The toolkit around it
Trig functions for manual work live in the scientific calculator (mind the degree/radian mode), quadratics that geometry problems generate solve in the quadratic solver, and unit mixing — feet measured, meters required — sorts out in the unit converter.