Triangle Calculator
Solve any triangle from sides or angles using the law of sines and cosines. Enter any three values (SSS, SAS, ASA, AAS, or SSA) and get all remaining sides, angles, and area.
Area
6
Perimeter
12
∠A
36.870°
∠B
53.130°
∠C
90.000°
How to use the triangle calculator
Enter three side lengths. We compute area, perimeter, and the three interior angles.
Formula & explanation
Area: Heron's formula, A = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. Angles: law of cosines, e.g. cos(A) = (b² + c² − a²) / (2bc).
Examples
Sides 3, 4, 5 → area 6, angles 36.87°, 53.13°, 90° (right triangle).
Frequently asked questions
- What is Heron's formula?
- Heron's formula computes a triangle's area from its three side lengths without needing the height: A = √(s(s−a)(s−b)(s−c)), where s is the semi-perimeter (a+b+c)/2.
- How do I know if three sides form a valid triangle?
- The triangle inequality requires that each side must be less than the sum of the other two. If 3, 4, 5 are the sides, all pass: 3+4 > 5, 3+5 > 4, 4+5 > 3.
- How are the angles computed?
- Using the law of cosines: cos(A) = (b² + c² − a²) / (2bc). This works for any triangle, not just right triangles.
- What is a right triangle and how can I spot one here?
- A right triangle has one 90° angle. If one of the computed angles equals exactly 90°, the triangle is a right triangle. The classic 3-4-5 triangle is a well-known example.
Related math tools
- Scientific CalculatorFull scientific calculator with trigonometric functions (sin, cos, tan), logarithms, exponents, factorials, and constants. Supports degree and radian mode.
- Average CalculatorCalculate mean, median, mode, range, sum, min, and max for any list of numbers. Paste in grades, scores, or measurements — results update instantly.
- Ratio CalculatorSimplify ratios to lowest terms, convert a ratio to a decimal, scale to any value, and compare two ratios. For recipes, map scales, and aspect ratios.
- Root CalculatorCalculate square roots, cube roots, and any nth root with high precision. Handles perfect squares and irrational results — shows the decimal approximation and the radical form.
- Permutation & Combination CalculatorCalculate nPr (permutations) and nCr (combinations) with a step-by-step formula breakdown. Enter n and r to see the count, formula expansion, and intermediate values.
- Exponent CalculatorRaise any base to any power — including negative bases, decimal exponents, and fractional powers. Shows the full numeric result with high precision for scientific and engineering work.