Triangle Calculator
Amancalc.com
Free Online Triangle Calculator
A triangle calculator computes all properties of any triangle from three side lengths: area, perimeter, all three angles, triangle type (equilateral, isosceles, scalene, right), height, inradius, circumradius, and semiperimeter. Uses Heron's formula for area and Law of Cosines for angles with automatic triangle inequality validation.
Enter any three sides and instantly receive complete geometric analysis for architecture, engineering, construction, surveying, manufacturing, design, and mathematics. Handles all triangle types with high precision, visual classification, and practical measurements for real-world applications from roof truss design to land surveying.
What Does the Triangle Calculator Compute?
From sides a=5, b=5, c=6: Area=12.36, Perimeter=16, Angles A=66.42°, B=66.42°, C=47.16° (isosceles), Height=4.94, Inradius=0.77, Circumradius=3.12. Single input produces 15+ measurements instantly.
Heron's formula: s=(a+b+c)/2, Area=√[s(s-a)(s-b)(s-c)]. Law of Cosines: cosC=(a²+b²-c²)/(2ab). Automatic validation: a+b > c, a+c > b, b+c > a. Invalid triangles flagged immediately.
Perfect for students (geometry proofs), engineers (structural design), architects (roof pitches), surveyors (land division), woodworkers (joinery angles), and manufacturers (quality templates).
Triangle Types & Properties
Equilateral
- All sides equal
- All angles 60°
- Height = (√3/2)×side
Isosceles
- 2 sides equal
- 2 base angles equal
- Height splits base
Scalene
- All sides different
- All angles different
- Most common type
Right
- 90° angle
- a²+b²=c²
- Hypotenuse longest
Core Formulas Explained
Heron's Formula (Area)
Law of Cosines (Angles)
How to Use the Calculator
- 1Enter three side lengths (any order). Supports decimals: 5.5, 12.75, 8.2.
- 2Click Calculate. Automatic triangle inequality check: a+b > c.
- 3View complete results: area, angles A/B/C, perimeter, heights, radii, type.
- 4Copy table, download PDF report, visualize triangle diagram.
Real-World Examples by Industry
Construction & Architecture
Roof Truss (3-4-5)
Gable End (5-12-13)
Surveying & Landscaping
Property Corner
Fence Section
Manufacturing & Woodworking
- Miter Joint: 45-45-63.4° isosceles → Perfect 90° corner
- Brace Angle: 3-4-5 right → 53.1° precise cuts
- Truss Plate: Equilateral 12" → 60° all angles
Advanced Triangle Properties
Height (h)
Inradius (r)
Circumradius (R)
Practical Calculation Examples
Roof Rafter (Right)
Equilateral Sign
Irregular Lot
Triangle Inequality Theorem
a + c > b
b + c > a
Frequently Asked Questions
Sides must form triangle?
Yes—automatic inequality check. Invalid combinations flagged immediately.
Decimals supported?
Full precision: 5.25, 12.75, 8.333 all work perfectly.
Right triangle detection?
Automatic Pythagorean check: a²+b²=c² → 90° angle flagged.
Units matter?
Consistent units only (all meters OR all feet). Angles unitless.
Export results?
Copy table, PDF report, CSV data, diagram PNG.
Related Geometry Calculators
Commercial Disclaimer
Triangle calculator provides precise geometric analysis for commercial construction, engineering design, architectural planning, manufacturing templates, and surveying applications. Verify critical structural calculations with licensed professionals and building codes.
Amancalc.com