Triangle Calculator
Calculate area, perimeter, angles, and all properties of any triangle from known values.
Triangle inputs
Updates as you typePresets
Load a canonical triangle ?
Solve mode
Solve by ?
Length unit
Sides
Side a ?
—
cm
Side b ?
—
cm
Side c ?
—
cm
Display (optional)
Angle unit
Precision
Shape preview
Drawn to scaleExamples
How It Works
A triangle is a polygon with three sides and three angles. The sum of all interior angles is always 180°. This calculator supports multiple input combinations — enter any three or more known values (sides a, b, c; angles A, B, C; or height) and it will compute all remaining properties.
Key formulas used: Area via ½ × base × height, Heron's formula (√[s(s−a)(s−b)(s−c)] where s is the semi-perimeter), the law of cosines (c² = a² + b² − 2ab·cos C) for finding angles from sides, and the law of sines (a/sin A = b/sin B = c/sin C) for mixed side-angle problems.
The calculator also computes the inradius (radius of the inscribed circle) and circumradius (radius of the circumscribed circle) using the formulas r = Area / s and R = a / (2 sin A).
Key formulas used: Area via ½ × base × height, Heron's formula (√[s(s−a)(s−b)(s−c)] where s is the semi-perimeter), the law of cosines (c² = a² + b² − 2ab·cos C) for finding angles from sides, and the law of sines (a/sin A = b/sin B = c/sin C) for mixed side-angle problems.
The calculator also computes the inradius (radius of the inscribed circle) and circumradius (radius of the circumscribed circle) using the formulas r = Area / s and R = a / (2 sin A).
Tips & Best Practices
The sum of any two sides must be greater than the third side (triangle inequality).
All three angles must add up to exactly 180°.
Heron's formula lets you find the area from three sides alone — no height needed.
For a right triangle, use the specialized Right Triangle Calculator for additional trig ratios.
Frequently Asked Questions
What is Heron's formula?
Heron's formula calculates the area of a triangle from three sides: A = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 is the semi-perimeter. It works for any triangle, no height required.
How do I find angles from three sides?
Use the law of cosines: cos C = (a² + b² − c²) / (2ab). Take the inverse cosine to get angle C in degrees. Repeat for the other angles.
What is the inradius?
The inradius is the radius of the largest circle that fits inside the triangle (the inscribed circle). It equals Area / semi-perimeter.
What is the circumradius?
The circumradius is the radius of the circle that passes through all three vertices. It equals a / (2 sin A) for any side a and its opposite angle A.