Triangle Area Calculator
Find the area of any triangle using the method that fits your known measurements — side-height, three sides (Heron's formula), or coordinate points. Ideal for geometry homework, land surveying, and construction layouts.
About this calculator
A triangle's area can be computed several ways depending on what you know. The simplest is Area = ½ × base × height. When you know all three sides but no height, Heron's formula applies: first compute the semi-perimeter s = (a + b + c) / 2, then Area = √(s × (s − a) × (s − b) × (s − c)). For triangles defined by coordinate vertices (x₁,y₁), (x₂,y₂), (x₃,y₃), the shoelace formula gives Area = ½ |x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|. All three methods yield the same result when the same triangle is described. Choosing the right method avoids unnecessary trigonometry and reduces rounding errors.
How to use
Suppose you have a triangle with sides a = 5, b = 6, c = 7. Select the "Three Sides" method and enter those values. First calculate the semi-perimeter: s = (5 + 6 + 7) / 2 = 9. Then apply Heron's formula: Area = √(9 × (9−5) × (9−6) × (9−7)) = √(9 × 4 × 3 × 2) = √216 ≈ 14.70 square units. Enter 5, 6, and 7 in the Side A, Side B, and Side C fields and the calculator returns 14.70 instantly.
Frequently asked questions
How do I calculate triangle area when I only know the three side lengths?
Use Heron's formula when no height is given. Start by computing the semi-perimeter s = (a + b + c) / 2. Then the area equals √(s(s−a)(s−b)(s−c)). This works for any triangle — acute, obtuse, or right — as long as the three sides form a valid triangle (each side must be less than the sum of the other two).
What is the difference between base-height and Heron's formula for triangle area?
The base-height method (Area = ½ × base × height) is the simplest but requires you to know a perpendicular height, which isn't always given. Heron's formula uses only the three side lengths, making it practical for surveying or any scenario where measuring a perpendicular height is impractical. Both formulas yield identical results for the same triangle. Heron's formula involves more arithmetic but no need to find or measure an altitude.
When should I use the coordinate method to find triangle area?
The coordinate (shoelace) method is best when your triangle's vertices are defined by (x, y) points on a grid or map — common in GIS, computer graphics, and analytic geometry problems. Instead of measuring physical lengths, you plug the three coordinate pairs into the formula Area = ½ |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|. It handles any orientation automatically and avoids the need to compute side lengths first.