Triangle Calculator

Calculate triangle properties including area, perimeter, angles, and side lengths. Supports various triangle types and calculation methods for comprehensive geometric analysis.

Triangle Input

Enter Three Sides

Quick Presets

Triangle Properties

Basic Properties

6.00
Area (cm²)
12.00
Perimeter (cm)

Side Lengths

3.00
Side a (cm)
4.00
Side b (cm)
5.00
Side c (cm)

Angles

36.9°
Angle A
53.1°
Angle B
90.0°
Angle C

Triangle Classification

Right
By Angles
Scalene
By Sides

Additional Properties

2.50
Circumradius (cm)
1.00
Inradius (cm)
6.00
Semiperimeter (cm)
4.00
Height to side a (cm)

Heights (Altitudes)

4.00
Height to a (cm)
3.00
Height to b (cm)
2.40
Height to c (cm)

Medians

4.27
Median to a (cm)
3.61
Median to b (cm)
2.50
Median to c (cm)

Triangle Types & Classifications

Classification by Angles

Acute Triangle
All angles are less than 90°
Right Triangle
One angle equals exactly 90°
Obtuse Triangle
One angle is greater than 90°

Classification by Sides

Equilateral Triangle
All three sides are equal
Isosceles Triangle
Two sides are equal
Scalene Triangle
All three sides are different

How the Triangle Calculator Works

Calculation Methods

Law of Cosines:

c² = a² + b² - 2ab·cos(C)

Law of Sines:

a/sin(A) = b/sin(B) = c/sin(C)

Heron's Formula (Area):

Area = √[s(s-a)(s-b)(s-c)]
where s = (a+b+c)/2

Additional Formulas

Circumradius:

R = abc/(4·Area)

Inradius:

r = Area/s

Altitude:

h = 2·Area/base

Example Calculations

Right Triangle (3-4-5)

Sides: a = 3, b = 4, c = 5
Area: ½ × 3 × 4 = 6 square units
Perimeter: 3 + 4 + 5 = 12 units
Angles: 90°, 53.13°, 36.87°
Type: Right, Scalene

Equilateral Triangle (side = 6)

Sides: a = b = c = 6
Area: (√3/4) × 6² ≈ 15.59 square units
Perimeter: 6 × 3 = 18 units
Angles: 60°, 60°, 60°
Type: Acute, Equilateral

Frequently Asked Questions

What is the triangle inequality?

The triangle inequality states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This must be true for all three combinations of sides.

When is the SSA method ambiguous?

The SSA (Side-Side-Angle) method can be ambiguous when the given angle is acute and the side opposite to it is shorter than the other given side. This can result in two possible triangles.

How accurate are the calculations?

Our calculator uses precise mathematical formulas and provides results accurate to several decimal places. However, for practical applications, consider rounding to appropriate significant figures.