Math
Triangle Calculator
Enter three side lengths to confirm the triangle is valid, then instantly view its area, angles, and classification.
Enter all three sides; get type, area, and precise internal angles.
Heron’s formula & law of cosines
Area = √[s(s − a)(s − b)(s − c)]
The calculator first uses Heron’s formula to get area from the semi-perimeter s = (a + b + c)/2. Internal angles come from the law of cosines: cos(A) = (b² + c² − a²) ÷ (2bc), and so on.
How to use
- Enter the three side lengths; units can be any consistent measure.
- Confirm the triangle is valid—if not, adjust the sides until the triangle inequality is satisfied.
- Read the perimeter, area, angle sizes, and detected triangle type.
Example
Input: Sides = 7, 8, 9
Output: Area ≈ 26.83 square units, Angles ≈ 48.19°, 58.41°, 73.40°, Type = Scalene
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Triangle Calculator: triangle calculator, triangle area calculator, triangle solver, triangle side calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Triangle Calculator: Solve triangle perimeter, area, and internal angles from three sides. It's built around geometry, triangle, angles, so you can go from a raw question to a checked answer without switching tools.
The math behind it: The calculator first uses Heron’s formula to get area from the semi-perimeter s = (a + b + c)/2. Internal angles come from the law of cosines: cos(A) = (b² + c² − a²) ÷ (2bc), and so on. The core relationship is Area = √[s(s − a)(s − b)(s − c)], shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter the three side lengths; units can be any consistent measure. (2) Confirm the triangle is valid—if not, adjust the sides until the triangle inequality is satisfied. (3) Read the perimeter, area, angle sizes, and detected triangle type. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering Sides = 7, 8, 9 returns Area ≈ 26.83 square units, Angles ≈ 48.19°, 58.41°, 73.40°, Type = Scalene. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Why do I get an invalid triangle warning?
A triangle must satisfy the inequality that any two sides summed together exceed the third. If that rule is broken, adjust the inputs until it holds.
Can I use this for right triangles?
Yes. If the inputs form a right triangle the tool labels it accordingly and still reports angles and area.
What formula does the Triangle Calculator use?
The calculator first uses Heron’s formula to get area from the semi-perimeter s = (a + b + c)/2. Internal angles come from the law of cosines: cos(A) = (b² + c² − a²) ÷ (2bc), and so on.
How do I use the Triangle Calculator?
Enter the three side lengths; units can be any consistent measure. Confirm the triangle is valid—if not, adjust the sides until the triangle inequality is satisfied. Read the perimeter, area, angle sizes, and detected triangle type.