Triangle Calculator Guide: Sides, Angles, Area & Formulas
A practical guide to solving triangles, finding missing angles and sides, calculating area, and checking whether three lengths can form a triangle.
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What can a triangle calculator find?
A triangle calculator can help determine unknown measurements from known sides and angles. CalculatePilot's triangle calculator accepts three side lengths and returns the area, three angles, and perimeter.
Triangle inequality theorem
Three positive lengths can form a triangle only when the sum of any two sides is greater than the third. For sides a, b, and c: a + b > c, a + c > b, and b + c > a.
How to calculate triangle area
If you know a base and perpendicular height, use:
If all three sides are known, Heron's formula is useful. First calculate the semiperimeter s = (a + b + c) ÷ 2, then:
How to find the angle of a triangle
When all three sides are known, the Law of Cosines can find an angle. For angle A opposite side a:
After calculating the inverse cosine, convert the result to degrees if needed. The three interior angles should total 180°.
How to find a missing side
For a right triangle, the Pythagorean theorem is the standard method: a² + b² = c². For other triangles, the Law of Cosines or Law of Sines may be appropriate depending on which measurements are known.
Worked example: sides 5, 6, and 7
The semiperimeter is 9. Heron's formula gives an area of √216, approximately 14.7 square units. The corresponding angles are approximately 44.4°, 57.1°, and 78.5°.
Types of triangles
- Equilateral: three equal sides and three 60° angles.
- Isosceles: two equal sides and two equal angles.
- Scalene: all sides and angles are different.
- Right: one angle is 90°.
- Acute: all angles are below 90°.
- Obtuse: one angle is above 90°.
Frequently asked questions
How do you find the angle of a triangle?
With three sides known, use the Law of Cosines. If two angles are known, subtract their sum from 180° to find the third angle.
What is the formula for triangle area?
The basic formula is ½ × base × height. With three sides, Heron's formula can be used.
Why is my triangle invalid?
At least one side is greater than or equal to the sum of the other two. Check your measurements and units.
Do triangle angles always add to 180 degrees?
Yes, for a triangle in ordinary Euclidean geometry, the three interior angles sum to 180°.