Understanding your result
Each angle is opposite the side with the matching letter. Area uses squared length units. The table gives the altitude measured perpendicular to each side or its extended line.
When your triangle is right-angled and only two sides are known, use the Pythagorean Theorem Calculator .
The formula
Heron’s formula determines area without needing an entered angle. The calculation uses an equivalent rearrangement to reduce cancellation for narrow triangles. Angles follow the same geometry as the law of cosines, with a two-argument arctangent preserving the correct acute or obtuse angle.
Worked example
Sides of 3, 4, and 5 units give a semiperimeter of 6 and area √(6 × 3 × 2 × 1) = 6 square units. The perimeter is 12, and the angle opposite side 5 is 90°. The height to side 5 is 2.4 units.
How to use this calculator
- Measure or obtain all three side lengths in the same unit.
- Enter each side using its letter in your drawing.
- Read the angles opposite those sides and expand the table for altitudes.
The triangle inequality
The longest side must be strictly shorter than the sum of the other two. Equal values create a straight line, not a triangle with positive area. Measurement rounding can create this problem for a very narrow real shape. Recheck the original measurements rather than forcing a zero-area line through a triangle formula.
Using area in a practical estimate
If the sides are metres, the area is square metres; if they are feet, it is square feet. A material order may require waste, overlaps, thickness, or packaging increments after the area is known. For an obtuse triangle an altitude can meet the extended base outside the triangle, so it should not automatically be interpreted as an internal clearance.
Assumptions & limitations
What this calculation assumes
- The inputs are straight sides of a flat, nondegenerate Euclidean triangle.
What to keep in mind
- Three-side solving only; no ambiguous two-side/angle cases, spherical geometry, or measurement uncertainty propagation.
Common questions
Can the same three sides give two different triangles?
They determine one size and shape up to rotation and reflection. Reflecting the drawing does not change its area or angles.
Why do displayed angles sometimes not add to exactly 180?
Each angle is rounded separately for display. The underlying geometry sums to 180 degrees, but the displayed decimal values can differ slightly after rounding.