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Choose what you know
Select three sides, two sides with the included angle, one side with two angles, or a right triangle.
Free geometry solver with steps
Free Triangle Calculator
A triangle calculator finds missing sides, angles, perimeter, and area from a valid set of measurements. Choose SSS, SAS, ASA/AAS, or right-triangle mode to see a labeled diagram and formulas you can check.
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Triangle solver
Choose what you know
Side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C.
Enter sides a, b, and c.
Calculations stay in your browser. Use one consistent unit for all side lengths; area is reported in the matching square unit.
Triangle calculator result
scalene right triangle
Solved: scalene right triangle.
Side a
3
Side b
4
Side c
5
Perimeter
12
Angle A
36.869898°
Angle B
53.130102°
Angle C
90°
Area
6
Step-by-step solution
- 1. Use the Law of Cosines to solve each angle from the three known sides.
- 2. A = cos⁻¹((b² + c² − a²) ÷ 2bc) = 36.869898°.
- 3. B = cos⁻¹((a² + c² − b²) ÷ 2ac) = 53.130102°.
- 4. C = 180° − A − B = 90°.
- 5. Perimeter = a + b + c = 12.
- 6. Area = √(s(s − a)(s − b)(s − c)) = 6, where s = 6.
How to Use the Triangle Calculator
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Enter valid measurements
Use one length unit for sides and degrees for angles. In right mode, leave one side blank.
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Check the complete triangle
Review the diagram, all six measurements, classification, perimeter, area, and formula steps.
Triangle Calculator FAQ
What is a triangle calculator?
A triangle calculator uses known sides and angles to find the triangle's missing sides, angles, perimeter, area, and classification.
What measurements are enough to solve a triangle?
A triangle has one unique solution from three valid sides (SSS), two sides and their included angle (SAS), or one side and two angles (ASA or AAS).
How do you solve a right triangle?
Enter any two side lengths and leave the unknown blank. The calculator uses a² + b² = c², then trigonometry to find the two acute angles.
Why do some side lengths not make a triangle?
The triangle inequality says any two sides must add to more than the third side. If that rule fails, the sides cannot meet to enclose an area.
Which units does the triangle calculator use?
Use any one length unit consistently. The perimeter uses that unit and the area uses its square, such as centimeters and square centimeters.