Triangle Calculator
Adjust the inputs below. Results update as you type.
How it works
Law of sines: a/sin(A) = b/sin(B) = c/sin(C). Law of cosines: c² = a² + b² − 2ab×cos(C). Area = ½ab×sin(C) or Heron's formula: √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. Three angles only: triangle is not uniquely determined (infinite similar triangles). SSA (two sides, non-included angle) may have 0, 1, or 2 solutions (ambiguous case).
Input guidance
- Check units and decimal placement before running calculations.
- For percentage and ratio tasks, define the baseline value clearly.
- Use rounded output carefully and keep full precision for intermediate steps.
The formula
Area = ½ × base × height, or Heron's formula with all three sides: √(s(s−a)(s−b)(s−c)), where s is half the perimeter. Angles follow the law of sines and cosines.
Worked example
A triangle with sides 3, 4, 5 has s = 6, so area = √(6×3×2×1) = √36 = 6 square units — a right triangle.
More examples to test
- Baseline example: solve with clean numbers first to verify formula direction.
- Edge-case example: test near-zero or boundary values to avoid interpretation errors.
How to interpret results
Use outputs as quick checks, then verify with step-by-step work for graded or high-stakes use.
When this can be inaccurate
Errors usually come from unit mismatch, wrong baseline assumptions, or rounding too early in multistep problems.
Change history
- July 2026: Published triangle solver with ambiguous SSA case notes.
Site-wide corrections also appear on the corrections log.
Build math and logic skills with guided lessons
Educational platform recommendation.
Frequently asked questions
How do I find a triangle's area without the height?+
Use Heron's formula if you know all three sides, or ½·a·b·sin(C) if you know two sides and the included angle.
What is the law of cosines?+
c² = a² + b² − 2ab·cos(C). It finds a missing side or angle in any triangle, generalizing the Pythagorean theorem.
Do the angles always add to 180°?+
In flat (Euclidean) geometry, yes — the three interior angles of any triangle always sum to 180 degrees.
Why do my classroom and calculator results differ?+
Differences usually come from rounding conventions, order-of-operations handling, or different baseline assumptions.
What is the safest way to validate an answer?+
Recompute with units shown and check against a second method or manual arithmetic for critical problems.