Triangle Area Calculator
This triangle area calculator finds the area of any triangle from its three sides, using Heron's formula. Enter the side lengths and the triangle area calculator returns the area, the perimeter, all three angles, and the triangle type. It works for scalene, isosceles, equilateral, acute, right, and obtuse triangles.
Results
The Triangle Area Calculator is part of our Geometry collection. Browse more geometry to size, convert, and check your work alongside this tool.
What the triangle area calculator shows
When you know all three sides of a triangle, you do not need its height to find the area. Heron's formula works from the sides alone. The triangle area calculator applies it, then uses the law of cosines to find each angle, so you get the full picture of the triangle from three measurements.
Heron's formula calculator steps
s is the semi-perimeter. The angles come from the law of cosines: cos A = (b² + c² − a²) ÷ 2bc. Three lengths form a triangle only if each side is shorter than the sum of the other two.
Area of triangle with 3 sides: example
Sides of 5, 6, and 7:
The perimeter is 18 and the angles are 44.42°, 57.12°, and 78.46°, a scalene acute triangle. Sides of 3, 4, and 5 give an area of 6 and a right angle.
How to use the triangle area finder
Enter sides a, b, and c in the same unit. The triangle area finder returns the area in square units, the perimeter, the three angles in degrees, and whether the triangle is scalene, isosceles, or equilateral and acute, right, or obtuse. If the sides cannot form a triangle, it says so.
Reading the triangle perimeter and area
The area is in square units of whatever length you entered. The angles always add to 180°. If the largest angle is exactly 90° the triangle is right-angled; above 90° it is obtuse. Very thin triangles have a small area even with long sides.
When to find the area of a triangle
- Measuring a triangular plot or garden bed from its sides
- Finding roof gable or sail area
- Checking a survey with the triangle area finder
- Geometry homework with three known sides
Common triangle area calculator mistakes
- Mixing units across sides.
- Using a slanted side as the height.
- Entering impossible side lengths.
Tips for accurate results
- Measure each side to the same precision.
- Check that the angles add to 180°.
- Use square units for the answer.
Compute area of triangle from coordinates
When the corners are points on a graph, the shoelace formula gives the area directly: half the absolute value of x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2). You can also find each side with the distance formula and then use Heron's formula here. For round shapes rather than straight sides, the circle calculator handles area from the radius, diameter, or circumference.
Find the area of a triangle: base and height vs three sides
The classic formula, half the base times the height, needs a height measured at right angles to the base, which is often hard to measure on real objects. Three side lengths are usually easier, which is why Heron's formula is so practical.
Triangle area calculator reference
| Sides | Area | Type |
|---|---|---|
| 3, 4, 5 | 6 | Scalene, right |
| 5, 6, 7 | 14.6969 | Scalene, acute |
| 5, 5, 5 | 10.8253 | Equilateral, acute |
| 5, 5, 8 | 12 | Isosceles, obtuse |
Triangle Area Calculator FAQ
How do I find the area of a triangle with 3 sides?
Use Heron's formula: Area = √(s(s−a)(s−b)(s−c)), where s is half the perimeter.
What if I know the base and height?
Area = ½ × base × height. Heron's formula is for when you know all three sides.
Why does the calculator say the sides cannot form a triangle?
Each side must be shorter than the sum of the other two.
How are the angles found?
With the law of cosines from the three sides.