Struggling to find a triangle's area? Our Triangle Area Calculator is your ultimate geometry assistant. Whether you know the base and height, all three sides, or two sides with the included angle, this tool adapts to your available data and delivers an accurate result instantly. Stop searching for missing heights—let the calculator handle the complex math for you.
The Universal Triangle Area Formulas
The formula you remember from school is just the beginning. Depending on what you know about your triangle, different formulas come into play.
| Known Values | Formula | When to Use It |
| Base (b) and Height (h) | Area = ½ × b × h | The classic, straightforward method when you have a perpendicular height. |
| Three Sides (SSS: a, b, c) | Area = √[ s(s-a)(s-b)(s-c) ] where s = (a+b+c)/2 | Heron's formula—perfect when you only have side lengths. |
| Two Sides and Included Angle (SAS: a, b, γ) | Area = ½ × a × b × sin(γ) | Ideal for triangles defined by two sides and the angle between them. |
| Two Angles and a Side (ASA: β, γ, a) | Area = a² × sin(β) × sin(γ) / [ 2 × sin(β+γ) ] | Useful in trigonometric applications and when heights are unknown. |
How to Use Our Triangle Area Calculator: A Quick Walkthrough
Let's calculate the area of a triangle where we know two sides and the angle between them (SAS):
- Enter the first side length (e.g., 9 inches).
- Input the known angle between the sides (e.g., 30°).
- Provide the second side length (e.g., 5 inches).
The calculator instantly computes the area—in this example, 11.25 square inches. It’s that simple. The tool automatically selects the correct formula based on your inputs.
Special Case: Area of an Equilateral Triangle
For an equilateral triangle (all sides equal and all angles 60°), the area formula simplifies beautifully:
Area = (side² × √3) / 4
Since √3/4 ≈ 0.433, you can quickly estimate the area by squaring the side length and multiplying by 0.433. For a side length of 10 units, the exact area is 25√3 ≈ 43.3 square units.
You can compute this in our calculator using the "three sides (SSS)" mode, as all sides are equal.
Frequently Asked Questions (FAQ)
How do I find a triangle's area using only the three side lengths?
Use Heron's Formula. Follow these steps:
- Compute the semi-perimeter: s = (a + b + c) / 2.
- Calculate the differences: (s - a), (s - b), (s - c).
- Multiply all four values: s × (s-a) × (s-b) × (s-c).
- Take the square root of the product. The result is the area.
Can I calculate the area if I only know the three angles?
No. Knowing only the angles is insufficient to determine area. Triangles with the same angles can be scaled to different sizes (they are similar), so you need at least one side length (or equivalent measure like a height) to fix the scale and compute the area.
What’s the formula for the area of a right triangle?
It’s the simplest case. Multiply the lengths of the two legs (the sides forming the right angle) and divide by 2.
Area = (leg₁ × leg₂) / 2
For legs of 3 inches and 4 inches, the area is (3 × 4) / 2 = 6 in².
What is the area of an equilateral triangle with a side length of 10?
The exact area is 25√3 square units, which is approximately 43.3 square units.
Area = (10² × √3) / 4 = (100 × √3) / 4 = 25√3 ≈ 43.3.