šŸ“ Triangle Area: Calculator

Find a triangle's area from base and height, or three sides using Heron's Formula.

units
units
TRIANGLE AREA
0
square units
Semi-Perimeter (s)
ā€”
Validity
ā€”
Area = 0.5 Ɨ base Ɨ height

How the Triangle Area Calculator Works

This calculator finds the area of a triangle using either of the two most common methods: the simple base-and-height formula, or Heron's Formula, which works when you only know the lengths of all three sides and don't have a height measurement. Switch between the two modes using the toggle above depending on which measurements you have available.

Base & Height: Area = 0.5 Ɨ base Ɨ height
Heron's Formula (sides a, b, c): s = (a + b + c) / 2    Area = āˆš( s(sāˆ’a)(sāˆ’b)(sāˆ’c) )

When to Use Heron's Formula

Heron's Formula, named after the ancient Greek mathematician Heron of Alexandria, is especially useful when you know the lengths of all three sides of a triangle but have no easy way to measure its height — for example, when working from a land survey, a set of GPS coordinates, or a triangle that isn't drawn with a convenient right angle. It first computes the semi-perimeter (s), half the triangle's total perimeter, then combines it with each side in a single formula that always produces the correct area for any valid triangle, regardless of its shape.

Why Some Side Lengths Don't Form a Valid Triangle

Not every combination of three lengths can actually form a triangle. The triangle inequality theorem states that the sum of the lengths of any two sides must always be strictly greater than the length of the remaining side. For example, sides of 1, 1, and 10 units cannot form a triangle — the two short sides combined (2 units) can't even reach across the 10-unit side. When you enter side lengths that violate this rule, this calculator detects it and clearly reports "Not a valid triangle" rather than showing a meaningless or broken result.

šŸ“Ž Related Tools: Perimeter Calculator Root Calculator Quadratic Formula Calculator Percentage Calculator

ā“ Frequently Asked Questions

What is the basic formula for the area of a triangle?
The most common formula is Area = 0.5 Ɨ base Ɨ height, where the height is measured as the perpendicular distance from the base to the opposite vertex, not along one of the slanted sides.
What is Heron's Formula and when should I use it?
Heron's Formula calculates a triangle's area from the lengths of all three sides (a, b, c) without needing a height measurement: Area = āˆš(s(sāˆ’a)(sāˆ’b)(sāˆ’c)), where s is the semi-perimeter, (a+b+c)/2. Use it whenever you know all three side lengths but not the height.
Why did my calculator say 'Not a valid triangle'?
This happens when your three side lengths violate the triangle inequality theorem ā€” the sum of any two sides must be greater than the third side. If, for example, two short sides combined are shorter than the longest side, those three lengths physically cannot form a closed triangle.
Do the base-and-height and Heron's Formula methods give the same answer for the same triangle?
Yes, for any triangle, both methods give the mathematically identical area when applied to consistent measurements of that triangle ā€” they're just two different ways of calculating the same value.
Does the height in the base-and-height formula have to be one of the triangle's sides?
No. The height must be measured perpendicular (at a 90Ā° angle) to the chosen base, from the base up to the opposite vertex. In an obtuse triangle, this perpendicular line may even fall outside the triangle itself, but the formula still applies correctly.

šŸ† About This Tool ā€” Accuracy & Trust

šŸ”’ Data Privacy: All calculations run entirely within your browser using JavaScript. Nothing you enter here is ever transmitted to our servers, stored, sold, or shared.

šŸ“ Accuracy Note: This tool uses standard, widely published formulas and guidelines. Results are estimates for informational purposes; for financial, medical, or engineering decisions, consult a licensed professional.

šŸ“… Last Updated: September 2026.