Triangle Calculator
Calculate area, perimeter and angles of a triangle. With side lengths or angles. Online calculator with solution path and worked examples.
Enter at least three values (e.g. three sides or two sides and one angle).
Result
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Note: These calculations are for informational purposes only and do not replace professional tax or financial advice. All information without guarantee.
FAQ
Frequently Asked Questions
How do I calculate the area of a triangle?
Area equals base times height divided by 2. Alternatively, use Heron's formula with three sides: Area equals the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter.
What is the Pythagorean theorem?
In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a squared plus b squared equals c squared. Only valid for right triangles.
Does the calculator show the working steps?
Yes. In addition to the final result the calculator displays the intermediate steps so you can follow the solution — ideal for school, university or homework.
Guide
Quick Answer
The triangle calculator computes sides, angles, area, perimeter and heights of a triangle from the given values.
What is the Triangle Calculator?
The triangle calculator computes sides, angles, area, perimeter and heights of a triangle from the given values.
How does the Triangle Calculator work?
Enter at least three values (e.g. 3 sides or 2 sides + 1 angle). The calculator computes all missing values using the sine rule, cosine rule and area formulas. For right triangles the Pythagorean theorem is applied.
Key Data and Facts
Area formula: A = 0.5 * base * height. Pythagoras: a squared + b squared = c squared. Sum of interior angles: always 180 degrees. Cosine rule: c squared = a squared + b squared - 2ab * cos(C).
Step-by-Step Guide
How to solve a triangle step by step: 1. Enter the known values: At least 3 values (sides and/or angles) are required. Possible combinations: SSS (3 sides), SAS (2 sides + included angle), ASA (2 angles + included side), SSA (2 sides + opposite angle). 2. Calculate the missing sides: Law of cosines: c2 = a2 + b2 - 2ab x cos(C). Law of sines: a/sin(A) = b/sin(B) = c/sin(C). 3. Missing angles: Sum of angles = 180 degrees. Single angle: cos(C) = (a2 + b2 - c2) / (2ab). 4. Calculate the area: A = 0.5 x base x height. Or Heron's formula: A = sqrt(s(s-a)(s-b)(s-c)) with s = (a+b+c)/2. 5. Perimeter: P = a + b + c. 6. Heights, medians and the inradius are also displayed. For right-angled triangles the Pythagorean theorem applies: a2 + b2 = c2.
Calculation Example
Triangle with a = 5 cm, b = 7 cm, C = 60 degrees: c2 = 25 + 49 - 2 x 5 x 7 x cos(60) = 74 - 35 = 39, c ≈ 6.24 cm. Area = 0.5 x 5 x 7 x sin(60) ≈ 15.16 cm2.
Sources · E-E-A-T
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Mathematics
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