Triangle Area Calculator
Find a triangle's area from base and height.
Results update as you type.
How it works
The area of a triangle is the amount of flat space enclosed by its three sides, and the simplest way to find it is with the base and the height. This triangle area calculator takes those two measurements and returns the area using the formula one-half times base times height. The base can be any of the three sides you choose, and the height is the perpendicular distance from that base straight up to the opposite corner, the vertex. It is important that the height is measured at a right angle to the base, not along a slanting edge, because the perpendicular height is what actually determines how much area the triangle covers. The reason for the one-half factor is elegant: any triangle is exactly half of a parallelogram with the same base and height, so taking half of base times height gives the triangle's area. For a triangle with a base of 10 and a height of 4, the area is one-half times 10 times 4, which is 20 square units. This method works for every triangle, whether it is right-angled, acute, or obtuse, as long as you use the perpendicular height. Students learning geometry, builders estimating material, and designers laying out triangular shapes all rely on this quick calculation. Because both the base and the height are lengths, this calculator requires them to be zero or positive.
area = ½ × base × height
The area of a triangle is half the base times the height because any triangle is exactly half of a rectangle or parallelogram built on the same base and height. The base is any chosen side, and the height is the perpendicular distance from that base to the opposite vertex, measured at a right angle rather than along a slanted side. Multiplying base by height would give the area of the surrounding parallelogram, so halving it isolates the triangle's share.
Source:Euclidean geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter base and height.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Area updates instantly as you type — no button to press.
Frequently asked questions
What is the base and height of a triangle?
The base is any one of the three sides you choose to measure from, and the height is the perpendicular distance from that base to the opposite vertex. The height must form a right angle with the base, so it is the straight-up distance, not the length of a slanted side. You can pick any side as the base, as long as you pair it with the matching perpendicular height to that side.
Why is the area half of base times height?
Any triangle fits exactly inside a parallelogram that has the same base and the same height, and it takes up precisely half of that parallelogram's area. Since a parallelogram's area is base times height, the triangle's area is half of that. You can see this by duplicating the triangle, rotating the copy, and joining the two together to form the full parallelogram, confirming the one-half factor.
Does this work for all types of triangles?
Yes, the one-half base times height formula works for every triangle, whether it is right-angled, acute, or obtuse. The only requirement is that you use the perpendicular height matching your chosen base. For obtuse triangles the height may fall outside the triangle, but the formula still holds. If you do not know the height, other methods like Heron's formula use the three side lengths instead.
What if I only know the three side lengths?
If you know all three sides but not the height, you can use Heron's formula, which finds the area from the side lengths alone. It first computes the semi-perimeter, half the sum of the sides, then takes the square root of that value times its difference from each side. This calculator uses the base-and-height method instead, so you would need to determine the height first to use it.
What units is the area in?
The area comes out in square units matching whatever units you used for the base and height. If you measured in centimetres, the area is in square centimetres; if in metres, it is in square metres. Always keep the base and height in the same unit before calculating, because mixing units, such as one in metres and one in centimetres, would give a meaningless result. Convert to a common unit first.