The calculation, without hidden assumptions
Three valid side lengths determine a triangle. This calculator first checks the triangle inequality, then uses Heron’s formula for the area and the law of cosines for all three angles, so you can see the perimeter, semi-perimeter, angle sum and whether the triangle is equilateral, isosceles or scalene and acute, right or obtuse.
How to use this calculator
Enter all three side lengths in the same unit.
Review the area, perimeter and semi-perimeter.
Check the three angles, their sum and the triangle-type label.
Where people use it
- •Survey and land-parcel geometry
- •Checking a roof truss or gusset layout
- •Homework and exam answer checks
Example: 5, 5, 6
The semi-perimeter is 8 and Heron’s formula gives √(8 × 3 × 3 × 2) = 12. The triangle is isosceles and acute, with angles of about 53.13°, 53.13° and 73.74°.
What the result does not assume
- •All sides must use the same unit, and the area is reported in that unit squared.
- •Sides that fail the triangle inequality (any two must sum to more than the third) have no real triangle and are rejected rather than approximated.
Frequently asked questions
What is the triangle inequality?+
The sum of any two sides must exceed the third. If it does not, the three lengths cannot close into a triangle.
When should I use the Pythagorean calculator instead?+
Use it when you already know the triangle has a right angle and one side is missing. This calculator is for three known sides of any triangle.
How is a right triangle detected?+
The triangle is labelled right when the squares of the two shorter sides add up to the square of the longest side, within a tiny numerical tolerance.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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MAXScanner keeps the formula and assumptions beside the result so you can verify the number before using it in a drawing, estimate, specification, worksheet or document. Where a supplier, manufacturer, drawing or applicable standard owns a requirement, that source remains authoritative.