How to use the triangle area calculator
- Choose your method: Base and height if you know those two measurements, or Three sides if you only have the side lengths.
- Enter the values in the corresponding fields. Leave unused fields empty.
- The triangle area calculator updates automatically as you type, showing the result below.
- For three sides, the tool applies Heron's formula and checks that the sides form a valid triangle.
How the area formulas work
When you know the base and the perpendicular height, the area is simply half their product:
Area = (base x height) / 2
For example, a triangle with a base of 10 units and a height of 5 units has an area of (10 x 5) / 2 = 25 square units.
When you only know the three side lengths, the calculator uses Heron's formula. First it finds the semi-perimeter s = (a + b + c) / 2, then computes Area = sqrt(s x (s - a) x (s - b) x (s - c)). For a 3-4-5 right triangle, s = 6, so the area is sqrt(6 x 3 x 2 x 1) = sqrt(36) = 6.
Common triangle areas reference
This table shows exact areas for frequently encountered triangles. Use it to verify your own calculations.
| Type | Sides | Area |
|---|---|---|
| Equilateral | 1, 1, 1 | 0.433013 |
| Right (3-4-5) | 3, 4, 5 | 6 |
| Right (5-12-13) | 5, 12, 13 | 30 |
| Isosceles | 5, 5, 6 | 12 |
| Equilateral | 10, 10, 10 | 43.301270 |
Validating the triangle inequality
Not every set of three numbers can form a triangle. The triangle inequality theorem states that the sum of any two sides must be strictly greater than the third side. If you enter sides 1, 2, and 3, the sum of the two shorter sides (1 + 2 = 3) equals the longest side rather than exceeding it, so these lengths produce a degenerate line segment with zero area. The calculator rejects such inputs.
This check only applies when using the three-sides method. When using base and height, both values simply need to be positive numbers (or zero).
Practical uses for triangle area
Computing the area of a triangle comes up in construction, landscaping, and design. Roofers calculate gable-end areas to estimate siding or paint. Surveyors break irregular plots into triangles to find total acreage, sometimes converting the result with tools like the acres to square feet converter.
In mathematics and physics, triangular areas appear when computing cross products, integrating over regions, or working out forces on inclined surfaces. If you are dealing with rectangular spaces instead, a rectangle area calculator handles the simpler length-times-width formula.
Units and precision
The triangle area calculator is unit-agnostic. If you enter the base and height in centimeters, the result is in square centimeters. If you use feet, you get square feet. Always ensure all measurements use the same unit before entering them.
Floating-point arithmetic can introduce tiny rounding errors. Results are rounded to 12 significant digits to remove noise while preserving meaningful precision. For most practical applications, four to six decimal places are more than sufficient.
Worked examples
Each result below was produced by the same code the tool runs, so you can check your own numbers against them.
| Example | Input | Result |
|---|---|---|
| Right triangle (base and height) | Method: base-height; Base: 6; Height: 8 | Area: 24 |
| Equilateral triangle (sides) | Method: sides; Side a: 10; Side b: 10; Side c: 10 | Semi-perimeter (s): 15; Area: 43.3012701892 |
| Scalene triangle 3-4-5 | Method: sides; Side a: 3; Side b: 4; Side c: 5 | Semi-perimeter (s): 6; Area: 6 |
| Small decimal triangle | Method: base-height; Base: 2.5; Height: 1.2 | Area: 1.5 |
FAQ
What is the formula for the area of a triangle?
The standard formula is Area = (base x height) / 2. If you only know the three side lengths, use Heron's formula: Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semi-perimeter.
Can I use this triangle area calculator for any type of triangle?
Yes. It works for equilateral, isosceles, scalene, right, acute, and obtuse triangles. Just choose the correct input method based on the measurements you have.
Why does the calculator say my three sides are invalid?
The three sides must satisfy the triangle inequality: the sum of any two sides must be greater than the third. If they do not, no real triangle can be formed.
Do I need to convert units before calculating?
All inputs must be in the same unit. The calculator does not convert between units automatically, so convert your measurements first if they differ.
Is my data sent to a server?
No. All calculations happen locally in your browser. Nothing is uploaded or stored.
How do I find the height if I only know the sides?
You do not need the height if you have all three sides. Select the three-sides method and the calculator will apply Heron's formula directly.