Find the area of a triangle from base and height, three sides, or two sides and an angle.
Calculated locally in your browser.
How do you calculate the area of a triangle?
Three ways: base and height gives ½ × base × height; three sides use Heron's formula, s = (a+b+c) ÷ 2, area = √(s(s−a)(s−b)(s−c)); two sides and the included angle give ½ · a · b · sin(C). For example, base 10 and height 6 give ½ × 10 × 6 = 30 square units.
Understanding your result
The base-and-height method is simplest when you have a perpendicular height. Heron's formula is ideal when you only know the side lengths, and the two-sides-and-angle method suits surveying. The area is always in square units of the length unit you enter.
Formula and method
Base and height: ½ × base × height. Three sides (Heron): s = (a+b+c) ÷ 2, area = √(s(s−a)(s−b)(s−c)). Two sides and angle: ½ · a · b · sin(C).
Worked example
A triangle with base 10 and height 6 has area ½ × 10 × 6 = 30. A 3-4-5 triangle has area 6 by Heron's formula.
How to use this tool
- Choose what you know about the triangle.
- Enter the base and height, the three sides, or two sides and the angle.
- Read the area and the worked steps.
Common mistakes to avoid
- Using a slanted side as the height — it must be perpendicular to the base.
- Entering sides that break the triangle inequality.
- Using an angle that is not the one between the two sides given.
About the Triangle Area Calculator
The Triangle Area Calculator finds the area of any triangle from whatever you know: base and height, all three sides (Heron's formula), or two sides and the angle between them. It shows the working too.
Who should use this tool
Students, teachers, builders, surveyors and DIY planners.
Benefits
- Three input methods for different known values.
- Heron's formula with the semi-perimeter shown.
- Checks the triangle inequality and angle range.
- Private — calculated entirely in your browser.
Practical use cases
- Working out the area of a triangular plot or sail.
- Solving geometry homework with any given values.
- Estimating material for a triangular surface.
Frequently asked questions
What is Heron's formula?
It finds a triangle's area from its three sides: compute s = (a+b+c) ÷ 2, then area = √(s(s−a)(s−b)(s−c)).
Which method should I use?
Use base and height if you have a perpendicular height, three sides if you only know the sides, or two sides and the included angle otherwise.
What units is the area in?
Square units of whatever length unit you enter — for example, metres give square metres.