Triangle Calculator
Calculate the area, perimeter, and circumradius of a triangle using three sides (SSS) or two sides and the included angle (SAS).
About this Calculator
Calculate the area, perimeter, and circumradius of a triangle using three sides (SSS) or two sides and the included angle (SAS).
Formula & Calculations
Formula
SSS (Heron): A = √(s(s-a)(s-b)(s-c)), s = (a+b+c)/2; SAS: A = ½ab·sin(C); P = a+b+c; R = abc/(4A)Where:
- a, b, c=Side lengths of the triangle
- C=Included angle between sides a and b (for SAS mode)
- s=Semiperimeter: half of the perimeter (a+b+c)/2
- A=Area of the triangle
- P=Perimeter of the triangle (a+b+c)
- R=Circumradius (radius of the circumscribed circle)
Assumptions
- For SSS mode, the three sides must satisfy the triangle inequality: a + b > c, a + c > b, b + c > a.
- For SAS mode, the angle C must be entered in degrees.
- Heron's formula is used for SSS calculations.
Calculation Examples
Example 1
Inputs:SSS mode, a = 3, b = 4, c = 5
Result:Area = 6, Perimeter = 12, Circumradius = 2.5
s = (3+4+5)/2 = 6. A = √(6(6-3)(6-4)(6-5)) = √(6×3×2×1) = √36 = 6.
Example 2
Inputs:SAS mode, a = 5, b = 7, C = 30°
Result:Area = 8.75, Perimeter = 12 + c (c ≈ 3.75), Circumradius ≈ 3.39
A = ½ × 5 × 7 × sin(30°) = ½ × 35 × 0.5 = 8.75.
Frequently Asked Questions
What is the difference between SSS and SAS modes?
SSS (Side-Side-Side) uses all three side lengths and applies Heron's formula. SAS (Side-Angle-Side) uses two sides and the angle between them, using the formula A = ½ab·sin(C).
What is the circumradius and why is it useful?
The circumradius (R) is the radius of the circle that passes through all three vertices of the triangle. It is given by R = abc/(4A) and is useful in geometry, construction, and engineering applications.