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 area and the law of cosines for all three angles. Showing both the geometry and the validity check makes it harder to mistake an impossible set of lengths for a calculation error.
How to use this calculator
Enter all three side lengths in the same unit.
The calculator checks that every pair of sides is longer than the remaining side.
Review area, perimeter, semi-perimeter, angles and whether the triangle is acute, right or obtuse.
Where people use it
- •Survey and layout geometry
- •Math and trigonometry checks
- •Checking three measured sides before drafting
Example: 5, 5, 6 triangle
The semi-perimeter is 8. Heron’s formula gives area √(8×3×3×2) = 12 square units, and the equal sides produce equal base angles.
What the result does not assume
- •All three values must describe one planar triangle and use the same length unit.
- •Measured side uncertainty can noticeably change small angles in nearly degenerate triangles.
Frequently asked questions
What is the triangle inequality?+
The sum of any two side lengths must be greater than the third side.
How are the angles found?+
The calculator applies the law of cosines to each side-angle pair.
What does semi-perimeter mean?+
It is half the perimeter and is used directly in Heron’s area formula.
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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Keep the result connected to the real job
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.