Triangle Area Calculator
Three Ways to Measure a Triangle
A triangle's area can be pinned down from whatever information happens to be on hand — a base and a height, all three side lengths, or the coordinates of its corners. Each situation calls for a different formula, and this calculator covers all three so you never have to rearrange a diagram just to get the numbers you actually have into the right shape.
The Formulas
Base & Height: Area = ½ × Base × Height
Heron's Formula: s = (a+b+c)/2, Area = √(s(s−a)(s−b)(s−c))
Shoelace Formula: Area = |x1(y2−y3) + x2(y3−y1) + x3(y1−y2)| / 2
Heron's Formula: s = (a+b+c)/2, Area = √(s(s−a)(s−b)(s−c))
Shoelace Formula: Area = |x1(y2−y3) + x2(y3−y1) + x3(y1−y2)| / 2
Worked Examples
| Mode | Given | Area |
|---|---|---|
| Base & Height | base = 10, height = 6 | 30 |
| Heron's (sides) | a = 5, b = 6, c = 7 | 14.6969 |
| Coordinates | (0,0), (4,0), (0,3) | 6 |
The Heron's example uses s = (5+6+7)/2 = 9, giving √(9×4×3×2) = √216 ≈ 14.6969.
Where This Matters
- Land surveying — irregular plots are often split into triangles and measured from corner coordinates using the shoelace method.
- Materials estimation — roofers and fabricators use base-and-height to work out triangular panel or gusset areas.
- Navigation and trigonometry — Heron's formula gives area straight from three measured distances, with no angles needed.
How to Use This Calculator
- Choose the mode: Base and Height, Three Sides (Heron's Formula), or Three Vertices (X, Y).
- For base and height, enter Base and Height.
- For Heron's formula, enter Side A, Side B, and Side C.
- For coordinates, enter Vertex 1, 2, and 3 X/Y values.
- Select Calculate to get the triangle's area.
Related Calculations
Need the sides or angles instead of just the area? Try the Triangle Solver or the Cosine Rule Calculator.