What Is a Triangle Calculator?
A triangle calculator is a free online tool that solves any triangle completely — finding all unknown sides, angles, area, perimeter, and heights from the values you provide. Our solve triangle calculator uses the Law of Sines, Law of Cosines, Heron's Formula, and the Pythagorean Theorem depending on which values you enter, and shows every calculation step clearly.
Whether you need to find the missing side of a triangle, calculate the area, or verify that three measurements form a valid triangle, this free tool handles all five standard input combinations: SSS, SAS, ASA, AAS, and right triangle.
Free triangle calculator — find missing sides, angles, area & height using SSS, SAS, ASA, AAS, right triangle
Triangle Calculator FAQs
How to find the missing side of a triangle?
The method depends on what you know. For the find missing side of triangle calculator:
- Right triangle (90°): Use Pythagoras — c² = a² + b². Enter the two known sides in Right Triangle mode.
- Two sides + included angle (SAS): Use Law of Cosines — c² = a² + b² − 2ab·cos(C).
- One side + two angles (ASA/AAS): Use Law of Sines — a/sin(A) = b/sin(B) = c/sin(C).
📘 Example — Find the missing side: a=5, b=7, C=60°
Using Law of Cosines (SAS mode):
c² = 5² + 7² − 2(5)(7)·cos(60°)
c² = 25 + 49 − 70 × 0.5 = 74 − 35 = 39
c = √39 ≈ 6.245
What is the third side of a triangle?
The third side of a triangle can always be found using the Law of Cosines when two sides and the angle between them are known. The calculator returns all three sides — labelled a, b, and c — where c is opposite to angle C, b opposite to B, and a opposite to A.
How to calculate the area of a triangle?
Our area of a triangle calculator automatically shows the area using the most appropriate formula:
- Heron's Formula (from 3 sides): Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2
- Base × Height: Area = ½ × base × height
- Two sides + angle: Area = ½ × a × b × sin(C)
📘 Example — Area of triangle with sides 5, 7, 8 (Heron's Formula)
s = (5+7+8)/2 = 10
Area = √(10 × (10−5) × (10−7) × (10−8))
Area = √(10 × 5 × 3 × 2) = √300 ≈ 17.32 square units
How to find the height of a triangle?
Once the area is known, all three heights can be found:
h_a = 2 × Area / a h_b = 2 × Area / b h_c = 2 × Area / c
Our triangle calculator automatically shows all three heights in the result. For an equilateral triangle with side a, the height = (a × √3) / 2. For an isosceles triangle, use the Pythagorean theorem with the base halved.
Can three sides form a triangle?
Three sides can form a triangle if and only if the sum of any two sides is greater than the third side. This is called the Triangle Inequality Theorem:
- a + b > c
- a + c > b
- b + c > a
For example: sides 3, 4, 5 form a valid triangle (3+4=7>5 ✓). But sides 1, 2, 10 do NOT (1+2=3, which is not >10 ✗). Our calculator checks this automatically and shows an error if the sides are invalid.
Solve triangle calculator — isosceles, equilateral, right triangle, scalene with all missing values found
How to find the value of x in a triangle?
Finding x depends on what is given:
- Angle sum: If two angles are given, x = 180° − A − B (angles must sum to 180°)
- Missing side: Use the Law of Cosines or Law of Sines depending on the given values
- Right triangle: Use Pythagorean theorem if x is a side, or inverse trig (arcsin, arccos, arctan) if x is an angle
Enter your known values into the matching mode of our solve the triangle calculator and it finds x — along with all other unknowns — automatically.
Triangle Types Quick Reference: Equilateral = all sides equal, all angles 60°. Isosceles = two sides equal, two angles equal. Scalene = all sides different, all angles different. Right = one angle exactly 90°. Our calculator handles all of these — just enter what you know.
