Triangle Calculator guide
Triangle Calculator: Solve Any Triangle
Use our triangle calculator to find all sides, angles, the area and perimeter of a triangle from three sides, two sides and an angle, or two angles and a side.
By the AllCalculator editorial teamUpdated 16 October 20262 min read
If you know three things about a triangle, including at least one side, you can work out everything else. Our Triangle Calculator does it with the sine and cosine rules.
How to use the calculator (Triangle Calculator)
- Choose what you know: three sides (SSS), two sides and the angle between them (SAS), or two angles and the side between them (ASA).
- Enter the values. Side a is opposite angle A, and so on.
You'll see all three sides and angles, the area, perimeter, heights, and what type of triangle it is.
The rules
- Cosine rule: a² = b² + c² − 2bc cos A. Used to find a side from two sides and the angle between them, or an angle from three sides.
- Sine rule: a ÷ sin A = b ÷ sin B = c ÷ sin C. Used when you know two angles.
- Angles: the three angles always add up to 180°.
- Heron's formula for the area: A = √(s(s − a)(s − b)(s − c)), where s is half the perimeter.
A worked example
With the calculator's default settings, a triangle with sides 5, 6 and 7:
- Angles: A = 44.42°, B = 57.12°, C = 78.46°
- Area: 14.70
- Perimeter: 18
- Type: scalene and acute
Types of triangle
| Type | Sides or angles |
|---|---|
| Equilateral | All sides equal, all angles 60° |
| Isosceles | Two sides equal |
| Scalene | No sides equal |
| Right-angled | One angle is 90° |
| Obtuse | One angle is more than 90° |
Frequently asked questions
Can any three lengths make a triangle?
No. Each side must be shorter than the other two added together. 2, 3 and 6 can't make a triangle.
What about a right-angled triangle?
Why isn't two sides and a non-included angle an option?
That case (SSA) can give two different triangles, or none, so it's ambiguous.
Sources and further reading
- GOV.UK: National curriculum in England – mathematicsgov.uk
- Wolfram MathWorld: Trianglemathworld.wolfram.com
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.