Free Triangle Calculator Online
Solve any triangle — sides, angles, area, perimeter (SSS, SAS, ASA, AAS)
The Triangle Calculator solves any triangle given sufficient information — three sides (SSS), two sides and an included angle (SAS), two angles and a side (ASA or AAS). It computes all missing sides and angles using the Law of Sines and Law of Cosines, plus area and perimeter. Surveyors, architects, physics students, and anyone working with oblique triangles use this regularly.
Frequently Asked Questions
About the Triangle Calculator
Triangles are the simplest polygon and appear throughout mathematics, engineering, and physical science. Unlike right triangles (which can be solved with the Pythagorean theorem), oblique triangles (without a 90° angle) require the Law of Sines or Law of Cosines. This calculator handles all cases: SSS (all three sides known), SAS (two sides and included angle), ASA (two angles and included side), and AAS (two angles and a non-included side).
The Law of Cosines generalizes the Pythagorean theorem to any triangle: c² = a² + b² − 2ab·cos(C). When C = 90°, cos(90°) = 0 and it reduces exactly to a² + b² = c². The Law of Sines states that the ratio of each side to the sine of its opposite angle is constant for a given triangle.
Applications include surveying land boundaries, calculating roof pitch in construction, navigation and triangulation, physics problems involving force vectors, and computer graphics where triangles are the basic rendering primitive.
When Should You Use This?
The Triangle Calculator is ideally suited for students, teachers, engineers, and scientists who need to perform quick, accurate calculations related to general calculations. Use this tool when you need to verify figures, compare different scenarios, or get a precise answer without manual computation errors.
What Does The Result Mean?
The calculated output provides an instant, accurate resolution to your input parameters. You can use these results directly for your planning, assignments, or professional tasks, knowing they are based on standardized formulas.
Example Calculation
Solving a triangle with sides a=7, b=10, and included angle C=42°
📥 Inputs
- Side a = 7
- Side b = 10
- Angle C = 42° (SAS case)
🔢 Calculation Steps
- 1Find side c using the Law of Cosines: c² = a² + b² − 2ab·cos(C)
- 2c² = 49 + 100 − 2(7)(10)·cos(42°)
- 3c² = 149 − 140 × 0.7431 = 149 − 104.03 = 44.97
- 4c = √44.97 ≈ 6.71
- 5Find angle A using Law of Sines: sin(A)/a = sin(C)/c
- 6sin(A) = 7 × sin(42°) / 6.71 = 7 × 0.6691 / 6.71 ≈ 0.6984
- 7A = arcsin(0.6984) ≈ 44.3°
- 8Angle B = 180° − 42° − 44.3° = 93.7°
- 9Area = ½ × a × b × sin(C) = ½ × 7 × 10 × sin(42°) = 23.4 units²
Limitations of this Calculator
- Results are based purely on the mathematical relationship of the inputs provided.
- Does not account for edge cases or extreme outlier values that fall outside standard formula constraints.
- Calculated outputs should be double-checked against your specific real-world requirements before finalizing important decisions.
How to Use the Triangle Calculator
- 1Enter your values into the Triangle Calculator input fields above.
- 2Review the input labels to ensure you are using the correct units.
- 3Click the "Calculate" button to get your instant result.
- 4Use the step-by-step breakdown to understand how the result was calculated.
- 5Export or copy your result to use in reports or share with others.
Tips & Best Practices
- Double-check your input units before calculating — using the wrong unit is the most common source of errors.
- Bookmark this Triangle Calculator for quick access next time you need it.
- Use the share button to send your results to a colleague or save them for later reference.
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