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Triangle Area Calculator – Base, Height & Heron's Formula

Geometry Math area calculator geometry triangle
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Triangle Area Calculator

Calculate triangle area instantly using Base & Height or Heron's Formula — with interactive visualization.

Enter Measurements
units
Please enter a positive number.
units
Please enter a positive number.
Formula: Area = ½ × b × h
Enter Three Sides
units
units
units
Valid triangle — all side lengths satisfy the triangle inequality.
Formula: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2
Triangle Area
40.00
square units
Scalene

Frequently Asked Questions

What is the formula for triangle area using base and height?
The area of a triangle is ½ × base × height (A = ½·b·h). The height must be perpendicular to the base. This is the most straightforward method when you know the base length and the altitude to that base.
What is Heron's Formula?
Heron's Formula calculates triangle area from the lengths of all three sides: Area = √[s(s−a)(s−b)(s−c)], where s is the semi-perimeter: s = (a+b+c)/2. It's named after Heron of Alexandria (c. 60 AD) and is extremely useful when the height is unknown.
How do I know if three sides can form a triangle?
The Triangle Inequality Theorem states that the sum of any two sides must be greater than the third side. All three conditions must hold: a + b > c, a + c > b, and b + c > a. If any condition fails, a triangle cannot exist with those side lengths.
What are the different types of triangles?
By sides: Equilateral (3 equal sides), Isosceles (2 equal sides), Scalene (all sides different). By angles: Acute (all angles < 90°), Right (one angle = 90°), Obtuse (one angle > 90°). Our calculator automatically identifies the triangle type based on your inputs.
Can Heron's Formula handle very large or small numbers?
Yes, Heron's Formula works for any valid triangle regardless of scale. However, for extremely thin triangles (where the area is very small relative to side lengths), numerical precision can become an issue. Our calculator uses double-precision floating-point arithmetic to maintain accuracy across a wide range of values.
What are some real-world applications of triangle area calculations?
Triangle area calculations are essential in architecture (roof trusses, structural analysis), land surveying (dividing irregular plots), engineering (force diagrams, truss design), computer graphics (3D mesh rendering), navigation (triangulation), and construction (material estimation for triangular sections).
Why does the calculator also show semi-perimeter and angles?
The semi-perimeter (s) is the key intermediate value in Heron's Formula. The interior angles (calculated via the Law of Cosines) provide additional insight into the triangle's shape. Knowing both area and angles gives you complete geometric information about the triangle from just three side lengths.
Is the base & height method always accurate?
Yes, the formula A = ½·b·h is mathematically exact for any triangle, provided the height is measured perpendicular to the base. In practice, measurement errors in base or height will propagate to the area calculation. For irregular triangles where you only know side lengths, Heron's Formula is the preferred method.
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