Find the area of any triangle using whichever measurements you have. Choose a method — base and height, two sides and the angle between them, all three sides, or two angles and the side between them — enter the values, and the calculator returns the area with the formula it used. Angles are in degrees.
The triangle area calculator finds the area of any triangle from whatever measurements you happen to have. Not every problem gives you a neat base and height — sometimes you know two sides and the angle between them, sometimes all three sides, and sometimes two angles and a side. This calculator handles all four of those situations with dedicated methods, so you never have to force your numbers into a formula that does not fit. Pick the tab that matches your known values, type them in, and the area appears along with the exact formula used to get it.
Triangles are the most fundamental shape in geometry — every polygon can be split into triangles — so being able to find their area quickly is useful far beyond the classroom. Builders, designers, surveyors, and students all reach for these formulas, and this tool puts every one of them in a single place.
Each tab corresponds to a classic way of measuring a triangle. Here is what each one needs and the formula behind it.
The most familiar formula. If you know the length of one side (the base, b) and the perpendicular distance from that side to the opposite vertex (the height, h), the area is:
area = ½ × b × h
This works for every triangle — right, acute, or obtuse — as long as the height is measured at a right angle to the base. For example, a triangle with a base of 10 and a height of 8 has an area of ½ × 10 × 8 = 40 square units.
When you know two sides and the angle between them, you do not need the height. The area is half the product of the two sides times the sine of the included angle:
area = ½ × a × b × sin(γ)
Here γ is the angle formed where sides a and b meet. For instance, two sides of 9 and 5 with a 30° angle between them give an area of ½ × 9 × 5 × sin(30°) = ½ × 45 × 0.5 = 11.25 square units. This method is a favorite in surveying and navigation, where angles are easy to measure.
If you know all three side lengths but no angles or height, Heron's formula gives the area directly. This calculator uses the numerically stable form:
area = ¼ × √( (a+b+c)(−a+b+c)(a−b+c)(a+b−c) )
which is mathematically identical to the classic version using the semi-perimeter s = (a + b + c) / 2, area = √(s(s−a)(s−b)(s−c)). A 3-4-5 triangle, for example, has an area of exactly 6 square units. Heron's formula only works if the three sides can actually form a triangle — each side must be shorter than the sum of the other two — and the calculator checks this for you.
When you know two angles and the side between them, the area is:
area = a² × sin(β) × sin(γ) / (2 × sin(β + γ))
where a is the known side and β and γ are the two angles at its ends. Since the three angles of a triangle add up to 180°, the two you enter must sum to less than 180°. For example, a side of 10 between two 45° angles gives an area of 10² × sin(45°) × sin(45°) / (2 × sin(90°)) = 100 × 0.5 / 2 = 25 square units.
The area of a triangle is the amount of two-dimensional space it covers, measured in square units. The classic definition — half the base times the height — comes from a neat piece of reasoning: any triangle is exactly half of a parallelogram (or rectangle) with the same base and height. Copy a triangle, rotate the copy 180°, and the two together tile a parallelogram whose area is base times height; the single triangle is therefore half of that. Every other area formula, including the ones on this page, can be derived from this basic idea combined with trigonometry. No matter which method you use, the answer is the same area for the same triangle.
If you have different measurements for the same triangle, try more than one method — you should get the same area every time, which is a good way to check your work.
The best method is simply the one that matches your data, but a few pointers help:
Some triangles have area shortcuts worth knowing. An equilateral triangle, where all three sides equal a, has an area of a² × √3 / 4, which is about 0.433 × a² — so a side of 10 gives roughly 43.3 square units. A right triangle is especially easy: the two legs are perpendicular, so they serve directly as base and height, and the area is simply half their product. An isosceles triangle can be split down its axis of symmetry into two identical right triangles, which is often the quickest route to its height. All of these are just special cases of the four general methods above, and you can compute any of them here by entering the appropriate values.
Area is always expressed in square units — square inches, square feet, square meters, square centimeters, and so on — because it measures a two-dimensional region. Whatever unit you use for the side lengths, the area comes out in that unit squared: enter sides in meters and the area is in square meters; enter them in feet and it is in square feet. Just be sure every length in a single calculation uses the same unit. If your measurements are mixed — say, some in feet and some in inches — convert them to a common unit before entering them, or the area will be wrong. Angles, by contrast, are unit-independent in the sense that a 30° angle is the same wherever it appears; this calculator expects them in degrees.
The four methods on this page cover almost every everyday situation, but a few other formulas are worth knowing for special cases. When you know the coordinates of the three corners, the shoelace formula gives the area directly: area = ½ × |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. It is a favorite in computer graphics and surveying because it works straight from map or screen coordinates. When you know all three sides and want the area in one keystroke, Heron's formula (the "3 Sides" tab) is the tool. And if you know a side and its opposite angle along with another angle, the law of sines lets you find a second side and then apply the SAS method. Every one of these routes leads to the same area for the same triangle — they simply start from different known quantities. Whenever you have a choice, pick the method that uses the measurements you are most confident about, since the accuracy of your inputs matters more than which formula you choose.
To see the calculator in action, here is the same job done four different ways on four different triangles:
Type any of these into the matching tab to confirm the result and see the full working. Trying several examples is the fastest way to get comfortable with which method fits which set of measurements.
The best-known formula is area = ½ × base × height. When you do not have the height, you can use two sides and the included angle (½ × a × b × sinγ), all three sides (Heron's formula), or two angles and a side (ASA).
Use Heron's formula: area = ¼ × √((a+b+c)(−a+b+c)(a−b+c)(a+b−c)). Select the "3 Sides" tab and enter the lengths; the calculator applies it automatically.
If the angle is between the two sides, the area is ½ × a × b × sin(γ). Use the "2 Sides & Angle" tab and enter the two side lengths and the included angle in degrees.
For a side length a, the area is a² × √3 / 4, roughly 0.433 × a². A side of 10 gives about 43.3 square units. You can also get this by entering all three sides as equal in the "3 Sides" tab.
Degrees. If your angle is given in radians, multiply it by 180/π (about 57.2958) to convert to degrees before entering it.
The three lengths must satisfy the triangle inequality — each side shorter than the sum of the other two. If they do not, no triangle can be formed and the area is undefined, so the calculator asks you to check the values.
This Triangle Area Calculator is provided for educational and general informational purposes. Results are rounded for display. For construction, surveying, or other precision work, verify measurements and calculations independently.