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How do I calculate triangle measurements?

Calculate area, perimeter, and angles of triangles. Enter side lengths to find all triangle properties.

What This Calculator Is

A triangle calculator computes the missing properties of a triangle when you know its three sides. Using the law of cosines and Heron's formula, it calculates all angles, the perimeter, area, and determines the triangle type (acute, right, or obtuse).

Who This Calculator Is For

Students studying geometry and trigonometry, engineers and architects calculating triangular structures, surveyors measuring land, and anyone working with triangular shapes who needs accurate measurements.

When to Use This Calculator

Use this calculator when you know three sides of a triangle and need to find angles or area, for geometry homework, in construction and design projects, or when verifying whether three lengths can form a valid triangle.

Inputs

Side A

Side B

Side C

Results

Area

Perimeter12

Angle A (degrees)36.87

Angle B (degrees)53.13

Results are for informational purposes. Verify calculations for critical applications.

Insights

Triangle properties

This triangle has an area of 6.00 sq units and perimeter of 12.00 units with angles of 36.9° and 53.1°.

How Triangle Is Calculated

Using Heron's formula and the Law of Cosines, the calculator determines area from three sides and calculates interior angles. It validates that the sides can form a valid triangle.

Perimeter = a+b+c
Area (Heron's formula): s=perimeter/2; area = sqrt(s(s-a)(s-b)(s-c))
Angles (Law of Cosines): cosA=(b^2+c^2-a^2)/(2bc); cosB=(a^2+c^2-b^2)/(2ac); angle = acos(cos)*180/pi
Where:
sideA, sideB, sideC = triangle side lengths (defaults 3,4,5)
Assumptions:
Returns all zeros if sides are non-positive or violate triangle inequality
cos values clamped to [-1,1] before acos to avoid NaN from floating-point error
Only angleA and angleB are returned/computed directly (angleC = 180-A-B, not explicitly output); values rounded to 2 decimals

Key Takeaways

•Triangle inequality: sum of any two sides must be greater than the third
•All angles must sum to 180 degrees
•A 3-4-5 triangle is always a right triangle
•Equilateral: all sides equal; Isosceles: two sides equal; Scalene: no sides equal
•Use Pythagorean theorem for right triangles: a² + b² = c²

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