Triangle Calculator
Use this triangle calculator to find the area, perimeter, angles, inradius and circumradius from three side lengths.
What Is a Triangle Calculator?
A triangle calculator finds the properties of a triangle when you know its three sides. Enter sides a, b and c to get the area, perimeter, all three angles, the triangle type, the inradius and the circumradius. It is useful for geometry homework, construction, woodworking and design.
How to Calculate the Area of a Triangle
When you know all three sides, use Heron's formula. First find the semi-perimeter s = (a + b + c) / 2. Then area = square root of s(s - a)(s - b)(s - c). For a triangle with sides 3, 4 and 5, s is 6 and the area is the square root of 36, which is 6.
How to Find the Angles
The calculator uses the law of cosines. For angle A opposite side a, cos(A) = (b squared + c squared - a squared) / (2bc). The other two angles use the same pattern. The three angles of every triangle add up to 180 degrees.
The Triangle Inequality
Three lengths form a triangle only if the sum of any two sides is greater than the third. For example, 2, 3 and 10 cannot make a triangle. The calculator checks this rule for you.
Types of Triangles
- By sides: equilateral (all equal), isosceles (two equal) or scalene (all different).
- By angles: acute (all angles under 90), right (one angle of 90) or obtuse (one angle over 90).
The 3-4-5 triangle is a classic right triangle, and builders use it to check square corners.
Inradius and Circumradius
The inradius is the radius of the largest circle that fits inside the triangle, equal to area divided by the semi-perimeter. The circumradius is the radius of the circle passing through all three corners, equal to abc divided by four times the area.
Frequently Asked Questions
What is the perimeter of a triangle?
It is the sum of the three sides: a + b + c.
How do I know if a triangle is a right triangle?
Check whether a squared plus b squared equals c squared for the longest side c.
Can I use any unit?
Yes. Use the same unit for all three sides, and the area will be in square units of that measure.
Results are rounded for display.