Triangle Calculator
Calculate triangle area, perimeter, angles, and sides. Solve any triangle using SSS, SAS, ASA methods or right triangle calculations.
Area = ½ × base × heightTriangle Properties
Area
6.00
square units
Perimeter
12.00
units
What do you know?
Enter Values
Triangle Visualization
Complete Results
Side a
3.0000
Side b
4.0000
Side c
5.0000
Angle A
36.87°
Angle B
53.13°
Angle C
90.00°
Area
6.0000
Perimeter
12.0000
Height (to c)
2.4000
Type
Scalene Right
Inradius (inscribed circle)
1.0000
Circumradius (circumscribed circle)
2.5000
Triangle Formulas
Area Formulas:
Area = ½ × base × height
Area = ½ × a × b × sin(C)
Area = √[s(s-a)(s-b)(s-c)] (Heron's)
Pythagorean Theorem (right triangles):
c² = a² + b²
Law of Cosines:
c² = a² + b² - 2ab·cos(C)
Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Common Special Triangles
3-4-5 Right Triangle
Sides: 3, 4, 5
Angles: 36.87°, 53.13°, 90°
Multiples work too: 6-8-10, 9-12-15
45-45-90 Triangle
Sides ratio: 1 : 1 : √2
Isosceles right triangle
Example: 1, 1, 1.414...
30-60-90 Triangle
Sides ratio: 1 : √3 : 2
Half of equilateral triangle
Example: 1, 1.732, 2
Equilateral Triangle
All sides equal, all angles 60°
Area = (√3/4) × side²
Height = (√3/2) × side
Triangle Properties
Area
6.00
square units
Perimeter
12.00
units
?How to Calculate Triangle Properties
Triangle area = (base x height) / 2, or using Heron's formula: sqrt(s(s-a)(s-b)(s-c)) where s is semi-perimeter. The sum of interior angles always equals 180 degrees. Use Law of Sines (a/sinA = b/sinB = c/sinC) and Law of Cosines (c squared = a squared + b squared - 2ab cosC) to solve triangles.
What is a Triangle?
A triangle is a polygon with three sides and three angles. The sum of interior angles is always 180 degrees. Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Triangle calculators use trigonometric laws to find unknown measurements from given values.
Key Facts About Triangles
- Sum of interior angles always equals 180 degrees
- Area = (base x height) / 2, or use Heron's formula with three sides
- Perimeter = sum of all three sides (a + b + c)
- Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
- Law of Cosines: c squared = a squared + b squared - 2ab*cos(C)
- Triangle inequality: any side must be less than the sum of the other two
- Equilateral: all sides and angles equal (60 degrees each)
- Isosceles: two equal sides and two equal base angles
Quick Answer
Triangle area = (base x height) / 2, or using Heron's formula: sqrt(s(s-a)(s-b)(s-c)) where s is semi-perimeter. The sum of interior angles always equals 180 degrees. Use Law of Sines (a/sinA = b/sinB = c/sinC) and Law of Cosines (c squared = a squared + b squared - 2ab cosC) to solve triangles.
Frequently Asked Questions
For base and height: Area = ½ × base × height. For three sides (Heron's formula): s = (a+b+c)/2, Area = √[s(s-a)(s-b)(s-c)]. For two sides and included angle: Area = ½ × a × b × sin(C).
For right triangles: a² + b² = c², where c is the hypotenuse (longest side opposite the right angle). This lets you find any side if you know the other two. Example: 3² + 4² = 9 + 16 = 25 = 5².
c² = a² + b² - 2ab·cos(C). This generalizes Pythagorean theorem to any triangle. Use it to find a side when you know two sides and the included angle, or to find angles when you know all three sides.
a/sin(A) = b/sin(B) = c/sin(C). Each side divided by the sine of its opposite angle gives the same ratio. Use it when you know a side-angle pair plus one other measurement.
By sides: Equilateral (all equal), Isosceles (two equal), Scalene (none equal). By angles: Acute (all < 90°), Right (one = 90°), Obtuse (one > 90°). A triangle can be described by both, e.g., "Isosceles Right".
Last updated: 2025-01-15
Triangle Properties
Area
6.00
square units
Perimeter
12.00
units