Triangle Calculator
From three sides, two sides and the included angle, or one side and two angles, the tool works out all sides and angles plus the area and perimeter.
Enter at least three values (e.g. three sides or two sides and one angle).
Results
Side a
5.0000
Angle Alpha
43.90°
Side b
7.0000
Angle Beta
76.10°
Side c
6.2450
Angle Gamma
60.00°
Area
15.1554
Perimeter
18.2450
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.
Which values does the calculator need to solve a triangle?
The calculator handles three cases: three sides (SSS), two sides with the included angle (SAS, e.g. a, b and γ) and one side with two angles (ASA/AAS). Two sides with a non-included angle (SSA) or three angles alone are not enough; with three sides, each side must be shorter than the sum of the other two. Leave all other fields empty. Example: a = 3, b = 4 and c = 5 give angles of 36.87°, 53.13° and 90°, an area of 6 and a perimeter of 12.
Guide
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. Result: the calculator shows all three sides and angles plus area and perimeter. The heights follow as h_a = 2 x area / a, the inradius as r = area / s. 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
Official sources
Calculations are based on applicable German laws and official data:
Full methodology at Methodology.
Reviewed by Konstantin Iakovlev · Last updated:
Mathematics
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