Triangle Calculator – Three Sides
Find area, perimeter, angles and triangle type from three sides.
Formula
s=(a+b+c)/2; A=√[s(s−a)(s−b)(s−c)]; cos α=(b²+c²−a²)/(2bc).
Side a: 3 cm · Side b: 4 cm · Side c: 5 cm · Area ≈ (0.0006)×10000 · Perimeter ≈ ((3 cm × 0.01 m/cm)+(4 cm × 0.01 m/cm)+(5 cm × 0.01 m/cm))×100 · Angle α opposite a ≈ (pi÷2-atan(((4 cm × 0.01 m/cm)^2+(5 cm × 0.01 m/cm)^2-(3 cm × 0.01 m/cm)^2)÷(4×(0.0006))))×180÷pi · Angle β opposite b ≈ (pi÷2-atan(((3 cm × 0.01 m/cm)^2+(5 cm × 0.01 m/cm)^2-(4 cm × 0.01 m/cm)^2)÷(4×(0.0006))))×180÷pi · Angle γ opposite c ≈ (pi÷2-atan(((3 cm × 0.01 m/cm)^2+(4 cm × 0.01 m/cm)^2-(5 cm × 0.01 m/cm)^2)÷(4×(0.0006))))×180÷pi · Angle classification ≈ ((0.05)^2-(0.04)^2-(0.03)^2)÷(0.05)^2 · Side classification ≈ floor(min(1,abs((3 cm × 0.01 m/cm)-(4 cm × 0.01 m/cm))÷((0.05)×1e-10)))+floor(min(1,abs((4 cm × 0.01 m/cm)-(5 cm × 0.01 m/cm))÷((0.05)×1e-10)))+floor(min(1,abs((3 cm × 0.01 m/cm)-(5 cm × 0.01 m/cm))÷((0.05)×1e-10)))
How to use
- Enter sides a, b and c.
- Choose the unit for each side.
- Read the area, perimeter and opposite angles.
Examples
- Sides 3, 4 and 5 cm give area 6 cm² and perimeter 12 cm.
Reference table
| Range | Category |
|---|---|
| Below -1 × 10⁻¹⁰ | acute |
| -1 × 10⁻¹⁰ ≤ x < 1 × 10⁻¹⁰ | right |
| 1 × 10⁻¹⁰ and above | obtuse |
Reference table
| Range | Category |
|---|---|
| 0 ≤ x < 1 | equilateral |
| 1 ≤ x < 3 | isosceles |
| 3 and above | scalene |
Frequently asked questions
Which lengths form a triangle?
Each side must be less than the sum of the other two; nearly collinear sides are rejected.
Which angle is α?
α is opposite a; β opposite b; γ opposite c.
Can I mix length units?
Yes. Results use cm, cm² and degrees.
How are triangles classified?
Sides use relative tolerance 10⁻¹⁰. Angles use that tolerance in the normalized squared-side test.
Sources
Updated: