Triangle Calculator
Calculate triangle area, perimeter, angles, and properties from any combination of sides and angles. Supports SSS, SAS, AAS inputs with triangle diagram. Includes medians, altitudes, and circle radii.
Quick Calculator Get a fast estimate
units
units
units
°
Area (Heron's formula)
14.6969 sq units
Perimeter
18.0000 units
Angle A
44.42°
Angle B
57.12°
Angle C
78.46°
Circumradius R
3.5722 units
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How to Use the Triangle Calculator
Choose your input method: SSS (three sides using Heron's formula), SAS (two sides and the included angle), or Base and Height. All angles and properties compute instantly.
The Extended Calculator adds SVG diagrams and AAS input. The Professional Calculator provides medians, altitudes, angle bisectors, circumradius, and inradius.
Need more detail?
Extended Calculator More options, charts, and scenario comparison
Area (Heron's Formula)
14.6969 sq units
Perimeter
18
Angle A
44.42°
Angle B
57.12°
Angle C
78.46°
Circumradius R
3.5722
Inradius r
1.633
Triangle Area Formulas
Base & Height: A = ½ × base × height
Heron's (SSS): s = (a+b+c)/2
A = √(s(s−a)(s−b)(s−c))
SAS: A = ½ × a × b × sin(C)
Law of Cosines: c² = a² + b² − 2ab·cos(C)
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Triangle Types
| Type | Angle condition | Side condition |
|---|---|---|
| Acute | All angles < 90° | c² < a²+b² |
| Right | One angle = 90° | c² = a²+b² |
| Obtuse | One angle > 90° | c² > a²+b² |
| Equilateral | All 60° | a = b = c |
| Isosceles | Two angles equal | Two sides equal |
Need full precision?
Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown
Triangle sides (SSS)
Triangle: Scalene Acute
Area = 14.6969 sq units
Semi-perimeter s
9
Circumradius R
3.5722
Inradius r
1.633
| Property | From a | From b | From c |
|---|---|---|---|
| Angles | 44.42° | 57.12° | 78.46° |
| Medians | 6.0208 | 5.2915 | 4.272 |
| Altitudes | 5.8788 | 4.899 | 4.1991 |
| Angle bisectors | 5.9822 | 5.1235 | 4.2251 |
Formulas: Circumradius R = abc/(4A) | Inradius r = A/s | Median ma = ½√(2b²+2c²−a²) | Altitude ha = 2A/a | Angle bisector ta = 2bc·cos(A/2)/(b+c)
Frequently Asked Questions
Heron's formula finds triangle area using only the three side lengths. First compute s = (a+b+c)/2 (semi-perimeter), then A = √(s(s−a)(s−b)(s−c)). No angles required.
The sum of any two sides must exceed the third. Example: sides 3, 4, 10 fail because 3+4=7 < 10. The calculator validates this automatically.
Use the Law of Cosines: A = arccos((b²+c²−a²)/(2bc)). Find the largest angle first (opposite the longest side), then use the Law of Sines or subtract from 180° for the remaining angles.
The circumradius R is the radius of the circle passing through all three vertices (circumscribed circle). R = abc/(4A). For a right triangle, R = c/2 (half the hypotenuse).
The inradius r is the radius of the inscribed circle (tangent to all sides). r = Area/s where s is the semi-perimeter. It represents the largest circle that fits inside the triangle.