Triangle Calculator
Calculate triangle area, perimeter, angles, and sides.
Triangle Dimensions
Triangle Results
Area
10.83
square units
Perimeter
15.00
units
Triangle Type
Equilateral (Acute)
Angles:
A: 60.0°
B: 60.0°
C: 60.0°
Sides:
a: 5.00
b: 5.00
c: 5.00
About This Calculator
The Triangle Calculator helps you calculate various properties of triangles including area, perimeter, angles, and side lengths. You can input either the three side lengths or the three angles to calculate the remaining properties.
The calculator uses Heron's formula for area calculation and the Law of Cosines and Law of Sines to determine angles and sides. It also identifies the triangle type (equilateral, isosceles, scalene) and whether it's acute, right, or obtuse.
Formula & Calculation Method
Triangle Formulas:
Heron's Formula (Area):
s = (a + b + c) / 2
Area = √[s(s - a)(s - b)(s - c)]
Law of Cosines:
a² = b² + c² - 2bc·cos(A)
cos(A) = (b² + c² - a²) / (2bc)
Law of Sines:
a / sin(A) = b / sin(B) = c / sin(C)
Perimeter:
P = a + b + c
The calculator ensures triangle inequality (sum of any two sides must be greater than the third) and that the sum of angles equals 180 degrees. It automatically determines triangle type based on side lengths and angle measures.
How to Use This Calculator
- Select Mode: Choose whether to input side lengths or angles.
- Enter Values: Input three side lengths or three angles.
- View Results: See calculated area, perimeter, angles, sides, and triangle type.
- Triangle Inequality: When using sides, ensure sum of any two sides is greater than the third.
- Angle Sum: When using angles, ensure they sum to 180 degrees.
Frequently Asked Questions
What is the triangle inequality theorem?
The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side. If this condition is not met, the three sides cannot form a valid triangle.
How do you calculate triangle area?
The most common method is Heron's formula, which uses the semi-perimeter and all three side lengths. For right triangles, you can also use Area = ½ × base × height.
What are the different triangle types?
Equilateral: all sides equal. Isosceles: two sides equal. Scalene: all sides different. Triangles can also be classified as acute (all angles < 90°), right (one angle = 90°), or obtuse (one angle > 90°).
Can I calculate a triangle with only two sides and one angle?
Yes, but this calculator currently requires either three sides or three angles. For two sides and one angle, you would use the Law of Cosines or Law of Sines, which could be added as an advanced feature.
Expert Reviewed
This calculator was reviewed by NumCalculators Editorial Team, Multi-disciplinary Expert Team