Triangle Perimeter Calculator — Perimeter, Area & Angles
Enter the three side lengths of any triangle to get the perimeter, area, all three interior angles, inradius, circumradius, and the classification of the triangle — instantly.
Total length of all three sides (P = a + b + c)
- 1
Semi-perimeter
(3 + 4 + 5) ÷ 2 = 6Used in Heron's area formula and the inradius. - 2
Perimeter
3 + 4 + 5 = 12
How does this calculator work?
Perimeter = a + b + c. Semi-perimeter s = P/2. Area = √[s(s−a)(s−b)(s−c)] (Heron's formula). Inradius = Area/s. Circumradius = abc/(4·Area). Enter three sides to get all properties of the triangle instantly.
Formula
How this is calculated
The perimeter of a triangle is simply the sum of its three sides: P = a + b + c. The semi-perimeter s = P/2 is a convenient intermediate value used in several related formulas. The area follows from Heron's formula: Area = √[s(s−a)(s−b)(s−c)], which requires no angle input and works for any triangle type.
Once the area and sides are known, the interior angles are found via the Law of Cosines (e.g. A = arccos((b² + c² − a²) / (2bc))), the inradius via r = Area / s (the radius of the largest circle fitting inside the triangle), and the circumradius via R = abc / (4·Area) (the radius of the circle passing through all three vertices).
The calculator also classifies the triangle: equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides different); and acute (all angles < 90°), right (one angle = 90°), or obtuse (one angle > 90°). All three sides must be positive and satisfy the triangle inequality — the sum of any two sides must exceed the third — otherwise no real triangle exists.
Frequently asked questions
The semi-perimeter s = (a + b + c) / 2 appears in Heron's area formula, the inradius formula (r = Area / s), and several other triangle identities. It is a shorthand for half the perimeter and simplifies many calculations.
The inradius r is the radius of the inscribed circle — the largest circle that fits entirely inside the triangle and touches all three sides. It equals Area / s. A larger inradius means the triangle is "more roomy" relative to its perimeter.
Yes — enter the same value for a, b, and c. The perimeter will be 3a, the area will be (√3 / 4) a², and all three angles will be 60°.
Also known as
TG we-Calculate Editorial Team. (2026). Triangle Perimeter Calculator — Perimeter, Area & Angles [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/triangle-perimeter-calculator
TG we-Calculate Editorial Team. "Triangle Perimeter Calculator — Perimeter, Area & Angles." TG we-Calculate. 2026. https://we-calculate.com/calculator/triangle-perimeter-calculator.
TG we-Calculate Editorial Team, "Triangle Perimeter Calculator — Perimeter, Area & Angles," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/triangle-perimeter-calculator
@misc{wecalculate_triangle_perimeter_calculator, title = {Triangle Perimeter Calculator — Perimeter, Area & Angles}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/triangle-perimeter-calculator}}, year = {2026}, note = {TG we-Calculate} }
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