Triangle Calculator
Calculate any triangle’s sides, angles, area, and perimeter by entering three known values. Supports all triangle types including right, obtuse, and acute triangles.
Triangle Sides
Triangle Angles
Triangle Calculation Results
Triangle Calculator Guide
How to Use This Triangle Calculator
This comprehensive triangle solver requires exactly three known values to calculate all remaining properties. Simply enter any combination of three sides or angles, and the calculator will determine all missing measurements including area, perimeter, and triangle classification.
Triangle Solving Methods
SSS (Side-Side-Side)
When all three sides are known, the calculator uses the Law of Cosines to determine all angles, then calculates area using Heron’s formula.
SAS (Side-Angle-Side)
With two sides and the included angle, the calculator applies the Law of Cosines to find the third side, then uses the Law of Sines for remaining angles.
ASA (Angle-Side-Angle)
Given two angles and the included side, the calculator first determines the third angle, then uses the Law of Sines to find the remaining sides.
AAS (Angle-Angle-Side)
With two angles and a non-included side, the calculator calculates the third angle, then applies the Law of Sines to solve for missing sides.
Mathematical Formulas
The triangle calculator employs several fundamental geometric principles:
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Area (Heron’s Formula): Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2
Area (SAS): Area = (1/2)ab sin(C)
Perimeter: P = a + b + c
Triangle Classification
The calculator automatically classifies triangles based on their properties:
- By Sides: Equilateral (all sides equal), Isosceles (two sides equal), or Scalene (all sides different)
- By Angles: Right triangle (one 90° angle), Acute triangle (all angles < 90°), or Obtuse triangle (one angle > 90°)
- Special Cases: Identifies common triangles like 30-60-90 and 45-45-90 right triangles
Practical Applications
Triangle calculations are essential in numerous fields:
- Construction and Architecture: Calculating roof angles, structural supports, and foundation layouts
- Engineering: Force analysis, mechanical design, and surveying applications
- Navigation: GPS calculations, maritime navigation, and flight path planning
- Physics: Vector analysis, optics, and wave interference calculations
- Computer Graphics: 3D modelling, game development, and animation
Common Triangle Properties
Every triangle possesses fundamental characteristics that this calculator determines:
- Interior Angles: Always sum to exactly 180 degrees
- Triangle Inequality: The sum of any two sides must exceed the third side
- Exterior Angles: Each exterior angle equals the sum of the two non-adjacent interior angles
- Altitude: Perpendicular distance from each vertex to the opposite side
- Median: Line segment from each vertex to the midpoint of the opposite side
Frequently Asked Questions
What inputs does the triangle calculator accept?
The calculator accepts any three values from six possible measurements: three sides (a, b, c) and three angles (A, B, C). Valid combinations include three sides, two sides with one angle, two angles with one side, or other mathematically valid configurations.
Can this calculator solve right triangles?
Absolutely. The calculator automatically detects right triangles and applies appropriate methods including the Pythagorean theorem. Simply enter 90 degrees for one angle, or let the calculator determine if your triangle is right-angled based on the side lengths.
What happens if my triangle measurements are impossible?
The calculator validates all inputs against geometric principles. If the values cannot form a valid triangle (violating the triangle inequality or angle sum rules), you’ll receive an error message explaining the issue.
How accurate are the calculations?
The calculator provides results with high precision, typically accurate to several decimal places. For practical applications, the accuracy far exceeds most measurement tolerances in construction, engineering, and scientific applications.
Does the calculator work with different units?
Yes, the calculator works with any consistent unit system. Whether you input measurements in metres, feet, centimetres, or any other unit, the results will be expressed in the same units. Just ensure all side measurements use the same unit.