Triangle Calculator
Solve any triangle using sides and angles. Calculate area, perimeter, heights, and identify triangle types (SSS, SAS, ASA, AAS).
A triangle calculator solves any triangle given a combination of sides and angles (SSS, SAS, ASA, AAS), computing all missing measurements, area, and perimeter using the Law of Sines and Law of Cosines.
Examples
Right Triangle (3-4-5)
SAS Triangle
Frequently Asked Questions
What is the sum of angles in a triangle?
Key Terms
- SSS
- Side-Side-Side
- SAS
- Side-Angle-Side
- ASA
- Angle-Side-Angle
Quick Tips
- •Double-check your inputs — small errors in angles or sides lead to large errors in the solved triangle.
- •Use the step-by-step breakdown to verify intermediate calculations.
- •When given a choice, prefer the SAS or SSS method over ASA/AAS to minimize cumulative rounding.
A triangle calculator solves any triangle given a combination of sides and angles (SSS, SAS, ASA, AAS), computing all missing measurements, area, and perimeter using the Law of Sines and Law of Cosines.
How to Use This Calculator
Enter the sides and angles you know (e.g. two sides and one angle, or three sides). The calculator uses the Law of Sines and Law of Cosines to find the missing sides, angles, area, and perimeter. Select the layout that matches your given information, fill in the values, and click Calculate.
Understanding the Formula
Law of Cosines: c² = a² + b² - 2ab cos(C). Area (Heron's): √[s(s-a)(s-b)(s-c)].
Examples
Right Triangle (3-4-5)
Sides a = 3, b = 4, c = 5. Angles: 36.87°, 53.13°, 90°. Area = 6 square units. Perimeter = 12.
SAS Triangle
Sides a = 8, b = 6, included angle C = 60°. Side c ≈ 7.21, Area ≈ 20.78 square units using the formula ½ab sin(C).
Frequently Asked Questions
What is the sum of angles in a triangle?
The sum of internal angles in any Euclidean triangle is always exactly 180 degrees.
Assumptions & Limitations
- Assumes Euclidean geometry — the sum of interior angles is always 180 degrees.
- Inputs must form a valid triangle; the calculator will reject impossible combinations (e.g., side lengths that violate the triangle inequality).
- Angle inputs are in degrees unless otherwise specified.
Key Terms
- SSS
- Side-Side-Side
- SAS
- Side-Angle-Side
- ASA
- Angle-Side-Angle