The triangle area calculator computes the area of any triangle using base & height, Heron's formula (three sides), or two sides with an included angle (SAS). Supports metric and imperial units.
Triangle Area Calculator
How to Calculate Triangle Area
There are three common methods for finding triangle area, depending on what measurements you have available.
Base and Height (Most Common)
A = ½ × base × height. The height must be perpendicular to the base. For a right triangle with legs 6 and 8: A = ½ × 6 × 8 = 24 sq units. This works for any triangle — identify any side as the base and drop a perpendicular height to it.
Heron's Formula (Three Sides Known)
A = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2. For a 3-4-5 triangle: s=6, A = √[6×3×2×1] = √36 = 6. Same as ½×3×4 = 6. Useful in surveying and construction when you can measure three sides but not the height.
SAS (Two Sides and Included Angle)
A = ½ × a × b × sin(C). For sides 5 and 7 with 60° between them: A = ½ × 5 × 7 × sin(60°) = 17.5 × 0.866 = 15.16. This is useful in trigonometry problems where angles are given instead of heights.
FAQ
What is the formula for triangle area?
A = ½ × base × height (base × height method). A = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2 (Heron's formula, 3 sides). A = ½ × a × b × sin(C) (two sides and included angle). All three give the same result for the same triangle.
What is Heron's formula?
Heron's formula finds the area knowing only the three side lengths: A = √[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2 is the semi-perimeter. For a 3-4-5 triangle: s=6, area = √[6×3×2×1] = √36 = 6. Same as ½×3×4 = 6. Useful when you know sides but not the height.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
How do you find the area of an equilateral triangle?
For equilateral triangle with side a: A = (√3/4) × a². Example: side = 6 cm → A = (1.732/4) × 36 = 0.433 × 36 = 15.59 cm². The height of an equilateral triangle = (√3/2) × a ≈ 0.866a.