Triangle Area Calculator (Base×Height and Heron)
Every triangle’s area is half of base times height when you know a side and the perpendicular height to it. When you only know the three side lengths, Heron’s formula uses the semiperimeter. This page does both. Sides that fail the triangle inequality produce no area.
Area20
Perimeter (Heron mode)—
Semiperimeter s—
How this calculation works
Base/height mode: area = ½ × base × height. The height must be perpendicular to the side you called the base.
Heron mode: s = (a+b+c)/2, area = √(s(s−a)(s−b)(s−c)). The 3-4-5 triangle gives s = 6 and area 6.
Triangle inequality: each side shorter than the sum of the other two. 1, 2, 9 is not a triangle; area is omitted.
Units stay consistent: if sides are in cm, area is cm². The calculator does not convert units.
Worked example
Base 10 and height 4 → area 20. Sides 3, 4, 5 → area 6, perimeter 12. Sides 5, 5, 6 → area 12.
Frequently asked questions
Do I need a right triangle for ½bh?
No. Any triangle has a base and a perpendicular height to that base. The height might fall outside an obtuse triangle.
Why is Heron useful?
Surveying and CAD often give three sides and no height. Heron avoids dropping an altitude by hand.
Can sides be zero?
No. All lengths must be positive. Degenerate “flat” triangles are rejected.
Is this the same as SAS ½ab sin C?
Different given data. If you have two sides and the included angle, use ½ab sin C on paper; this tool wants base/height or three sides.
Perimeter in base/height mode?
Not computed — you only entered two numbers. Switch to Heron for a perimeter.
Are inputs stored?
No. Browser only.
This tool is provided for general information only. Verify important figures independently. · Last reviewed: August 25, 2026