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Calculate triangle area, perimeter, angles, sides & height instantly. Solve SSS, SAS, ASA & right triangles with step-by-step solutions.
Calculate area, perimeter, angles & sides for any triangle
SSS (Side-Side-Side): Enter all three sides of the triangle
A triangle calculator is a mathematical tool that helps you calculate properties of a triangle including area, perimeter, angles, and sides. Whether you know three sides (SSS), two sides and an angle (SAS), two angles and a side (ASA), or working with a right triangle, this calculator provides accurate results based on established geometric formulas.
About This Calculator: This tool implements standard geometric formulas and theorems taught in mathematics curricula worldwide. All calculations follow established mathematical principles including the Pythagorean theorem, Law of Cosines, Law of Sines, and Heron's formula. Results are computed using precise trigonometric functions to ensure accuracy.
Choose Triangle Type: Select SSS (3 sides), SAS (2 sides + angle), ASA (2 angles + side), or Right Triangle
Enter Known Values: Input the sides and/or angles you know
Calculate: Click the Calculate button to get instant results
View Results: See area, perimeter, all sides, all angles, and step-by-step solution
All three sides are equal (a = b = c). All angles are 60°.
Two sides are equal. Two angles are also equal.
All three sides are different. All angles are different.
One angle is exactly 90°. Pythagorean theorem applies.
All three angles are less than 90°.
One angle is greater than 90°.
When all three sides are known. Use Heron's formula for area and Law of Cosines for angles.
Example: a=5, b=6, c=7
Two sides and the included angle. Use Law of Cosines to find third side, then Law of Sines for angles.
Example: a=5, b=6, C=60°
Two angles and the included side. Find third angle (180° - A - B), then use Law of Sines for sides.
Example: A=50°, B=60°, c=7
One 90° angle. Use Pythagorean theorem (a²+b²=c²) and trigonometric ratios.
Example: base=3, height=4
Triangle area can be calculated using several methods: (1) Base × Height / 2 for any triangle when height is known, (2) Heron's formula: √[s(s-a)(s-b)(s-c)] where s is the semi-perimeter, (3) (1/2) × a × b × sin(C) for triangles where two sides and the included angle are known. This calculator applies the appropriate formula based on your input.
Triangle perimeter = a + b + c, where a, b, and c are the three sides of the triangle. Simply add all three side lengths together to get the perimeter.
To find missing sides, use the Law of Cosines: c² = a² + b² - 2ab·cos(C) when you know two sides and the included angle, or the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) when you know angles and at least one side. For right triangles specifically, the Pythagorean theorem a² + b² = c² applies. This calculator determines and applies the appropriate formula based on the information you provide.
Triangles are classified by sides: Equilateral (all three sides equal), Isosceles (two sides equal), Scalene (all sides different). By angles: Right (one 90° angle), Acute (all angles less than 90°), Obtuse (one angle greater than 90°). This calculator identifies the triangle type based on the calculated measurements.
Triangle angles can be calculated using the Law of Cosines: A = arccos[(b² + c² - a²)/(2bc)] when all sides are known, or the Law of Sines: A = arcsin[(a × sin(C))/c] when some angles and sides are known. Remember that the sum of all interior angles in any triangle equals 180°. This calculator computes all angles using the appropriate trigonometric formulas.
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Accuracy: This calculator uses standard mathematical formulas and provides results accurate to 4 decimal places. All calculations are based on established geometric principles.
Educational Purpose: This tool is designed for educational and general calculation purposes. For professional engineering, construction, or critical applications, please verify results with appropriate professional standards and methods.
Verification: While we strive for accuracy, users should verify critical calculations independently. The calculator validates triangle inequality and provides error messages for invalid inputs.
Solve SSS, SAS, ASA, and right triangles with one tool
Get area, perimeter, all sides, and all angles instantly
Understand the calculation process with detailed steps
Download or copy calculations for homework or reports
Get accurate results in milliseconds
No registration, no limits, completely free forever
Perfect for students learning geometry, trigonometry, and mathematics
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