Triangle Area Calculator
Find the area of any triangle using three methods: base × height (½bh), two sides and the included angle (½ab sin C), or all three sides via Heron's formula. Switch method to match your known values.
Method
Area = ½ × base × height
- 1
Multiply base by height
8 × 5 = 40 - 2
Area = ½ × base × height
40 ÷ 2 = 20
How does this calculator work?
A triangle's area can be computed three ways: ½ × base × height (when height is known), ½ × a × b × sin C (two sides + included angle), or √(s(s−a)(s−b)(s−c)) with s = (a+b+c)/2 (Heron's formula from three sides). Select the method matching your inputs and get the area instantly.
Formula
How this is calculated
The most direct way to find a triangle's area is ½ × base × height, where the height is the perpendicular distance from the opposite vertex to the chosen base — not the slant side. If you know any two sides and the angle squeezed between them (the included angle C), the sine formula Area = ½ × a × b × sin C avoids the need to find the height explicitly. The factor sin C acts as the effective fraction of a parallelogram.
When only the three side lengths are available, Heron's formula gives the area without any angle or height measurement. First compute the semi-perimeter s = (a + b + c) / 2, then Area = √(s(s − a)(s − b)(s − c)). This is algebraically equivalent to ½bh but eliminates the need to find a perpendicular height, which is often harder to measure.
For SAS inputs, this calculator also derives the third side using the law of cosines (c = √(a² + b² − 2ab cos C)) so the triangle diagram can be drawn. The triangle inequality (each side < sum of the other two) is checked for the three-sides case; SAS is invalid if the included angle is 0° or 180°. All methods give the same area for the same triangle — choose the one matching your available measurements.
Frequently asked questions
Use base × height (½bh) when you can measure or compute the perpendicular height. Use the SAS formula (½ab sin C) when you have two sides and the angle between them — common in surveying and trigonometry. Use Heron's formula when you only have three side lengths, such as in construction or when angles are not available.
The height (altitude) in ½bh must be the perpendicular distance from a vertex to the opposite base, not just any side length. For a right triangle the two legs serve as base and height directly; for other triangles you must drop a perpendicular from a vertex to the extended line of the base.
If any side equals or exceeds the sum of the other two, no closed triangle can be formed — Heron's formula would try to take the square root of a negative number. The calculator detects this and asks you to re-enter valid side lengths.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Area Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-area-calculator
TG we-Calculate Editorial Team. "Triangle Area Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-area-calculator.
TG we-Calculate Editorial Team, "Triangle Area Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-area-calculator
@misc{wecalculate_triangle_area_calculator, title = {Triangle Area Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-area-calculator}}, year = {2026}, note = {TG we-Calculate} }
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