Area of a Triangle Calculator
Whether you need the floor area of a triangular room, the surface of a plot, or a quick geometry answer for homework, a simple slip in mental math can lead to costly mistakes. Instead of re‑checking formulas, use the area of a triangle calculator below. Pick the input method that fits what you already know–base and height, all three sides, or two sides with the angle between them–and get the result in square units, instantly.
How do you calculate the area of a triangle?
The area equals half the product of a base and its corresponding height. That classic rule, ½ × base × height, works for every triangle when you have those two numbers. But real‑world data rarely arrives in such a neat pair. You might be given side lengths only, or a side and an angle from a surveyor’s report. The tool above adapts to three common scenarios.
Base and height
Area = ½ × b × h
If you know the length of one side (the base) and the perpendicular distance from that side to the opposite vertex (the height), simply multiply them and divide by two. This method is the fastest when you can measure both directly, for example on a blueprint where dimensions are clearly marked.
Three sides (SSS – Heron’s formula)
Area = √[s(s‑a)(s‑b)(s‑c)], where s = (a + b + c) / 2
When only the three side lengths are available, the calculator first computes the semiperimeter (s) and then applies Heron’s formula. This approach works for any triangle shape–acute, obtuse, or right–as long as the sides satisfy the triangle inequality.
Two sides and the included angle (SAS)
Area = ½ × a × b × sin C
If you know two sides and the angle between them, multiply the two sides, take the sine of the angle (in degrees), and halve the product. This is especially handy in construction when you have a laser‑measured diagonal and the spread angle.
Which triangle area formula should I use?
The choice depends entirely on the data you already hold. Use the base‑height option when you have a clear perpendicular measurement. Choose Heron when all three sides are known but no angle or height is given–common in land surveying where only boundary lengths are recorded. The side‑angle‑side method is ideal when two walls meet at a known internal corner; you measure the two wall lengths and the angle between them.
If you are unsure, simply enter your numbers into the calculator tabs. The tool checks which inputs are complete and delivers the result for that set, ignoring empty fields. There is no need to convert units or rearrange equations.
What makes the area of a triangle calculator reliable?
The computations follow standard geometric identities that have remained unchanged for centuries. The sine function in the SAS method uses the same trigonometric table as any scientific device. Heron’s formula is numerically stable for typical side lengths, and the tool automatically prevents negative square roots by validating the triangle inequality. You can trust the output whether you are cutting fabric, ordering turf, or checking a student’s answer.
For academic or professional use, always confirm that your measurements are in the same unit. The result will be in square units of that length–if you input meters, the area is in square meters; if you input feet, it’s in square feet. No hidden conversions take place.