Scalene Triangle Calculator — Area, Angles & Properties
Enter the three side lengths of any triangle — scalene, isosceles or equilateral — and get the area (Heron's formula), all three angles (law of cosines), perimeter, inradius and circumradius.
Scalene triangle (all sides different)
- 1
Semi-perimeter s = (a + b + c) ÷ 2
(7 + 5 + 4) ÷ 2 = 8 - 2
Product s(s−a)(s−b)(s−c)
8 × 1 × 3 × 4 = 96Heron's formula — the area is the square root of this product. - 3
Area = √(product)
√(96) = 9.7980
How does this calculator work?
Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2 (Heron's formula). Angles come from A = arccos((b²+c²−a²)/(2bc)) and similarly for B and C. Enter three sides to get area, perimeter, all angles, inradius and circumradius. The triangle inequality must hold: each side < sum of the other two.
Formula
How this is calculated
Heron's formula computes the area of any triangle from its three side lengths without needing a height. The semi-perimeter s = (a+b+c)/2 is computed first, then the area is √(s(s−a)(s−b)(s−c)). The formula is numerically exact for any valid triangle, including obtuse ones.
The three interior angles follow from the law of cosines: angle A opposite side a is arccos((b²+c²−a²)/(2bc)), and similarly for B and C. Because angles B and C are derived independently (not as 180°−A−B), small floating-point errors are distributed evenly rather than accumulated into one angle. The three angles always sum to 180°.
The inradius r = Area / s is the radius of the largest circle that fits inside the triangle (inscribed circle). The circumradius R = abc / (4·Area) is the radius of the circle passing through all three vertices (circumscribed circle). Both are zero only for degenerate triangles. The triangle inequality — each side must be strictly less than the sum of the other two — is enforced; invalid inputs return no result.
Frequently asked questions
A scalene triangle has all three sides of different lengths, which means all three angles are also different. The calculator works for any valid triangle regardless of type — it reports whether the triangle is scalene, isosceles (two equal sides), or equilateral (all sides equal).
If any side equals or exceeds the sum of the other two, the three segments cannot close to form a triangle. For example, sides 1, 2 and 5 fail because 1+2 = 3 < 5. The calculator checks this and hides results for invalid inputs.
The inradius is the radius of the inscribed circle (the largest circle that fits inside the triangle). The circumradius is the radius of the circumscribed circle (passing through all three vertices). Both depend only on the side lengths and are related to the area via r = Area/s and R = abc/(4·Area).
TG we-Calculate Editorial Team. (2026). Scalene Triangle Calculator — Area, Angles & Properties [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/scalene-triangle-calculator
TG we-Calculate Editorial Team. "Scalene Triangle Calculator — Area, Angles & Properties." TG we-Calculate. 2026. https://we-calculate.com/calculator/scalene-triangle-calculator.
TG we-Calculate Editorial Team, "Scalene Triangle Calculator — Area, Angles & Properties," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/scalene-triangle-calculator
@misc{wecalculate_scalene_triangle_calculator, title = {Scalene Triangle Calculator — Area, Angles & Properties}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/scalene-triangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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