Triangle Calculator
Enter any three values, including at least one side, to solve the whole triangle.
Side a is opposite angle A, side b opposite B, and side c opposite C. Leave the unknown boxes empty.
Angles are in degrees. Results are rounded to 4 decimal places.
How to use the triangle calculator
This calculator solves any triangle from three known values. Enter any combination of three sides and angles, including at least one side, and it finds everything else: the missing sides and angles, the area, perimeter and heights. It also draws your triangle to scale.
Sides are labeled a, b and c, and angles A, B and C. Each side is opposite the angle with the same letter, so side a is opposite angle A.
Which three values do you need?
| You know | Short name | Method used |
|---|---|---|
| Three sides | SSS | Law of cosines |
| Two sides and the angle between them | SAS | Law of cosines, then the remaining angles |
| Two angles and the side between them | ASA | Angles add to 180°, then law of sines |
| Two angles and another side | AAS | Angles add to 180°, then law of sines |
| Two sides and an angle not between them | SSA | Law of sines (may have two answers) |
Three angles alone (AAA) aren't enough, because triangles with the same angles can be any size.
Key triangle formulas
Angles
Law of sines
Law of cosines
When angle A is 90°, cos A is 0, and this becomes the Pythagorean theorem: a² = b² + c².
Area (Heron's formula)
Example: a triangle with sides 3, 4 and 5.
- s = (3 + 4 + 5) ÷ 2 = 6
- Area = √(6 × 3 × 2 × 1) = √36 = 6
- Because 3² + 4² = 5², it's a right triangle, with the 90° angle opposite the longest side.
The ambiguous case (SSA)
When you know two sides and an angle that isn't between them, there can be two different triangles that fit. For example, with a = 6, b = 8 and A = 30°, angle B could be about 41.8° or about 138.2°. The calculator shows the first solution and, when a second one exists, describes it in a note below the results. Sometimes no triangle fits at all, and the calculator will tell you.
Types of triangles
- By sides: equilateral (all sides equal), isosceles (two sides equal) or scalene (no sides equal).
- By angles: acute (all angles under 90°), right (one angle exactly 90°) or obtuse (one angle over 90°).
The triangle inequality
For three lengths to form a triangle, any two sides must add up to more than the third. Sides of 1, 2 and 10 can't make a triangle, because 1 + 2 is less than 10. The calculator checks this automatically.
Where triangle calculations are used
- Construction and DIY: roof pitches, ramps, stairs and checking corners are square using the 3-4-5 rule.
- Navigation and surveying: working out distances you can't measure directly.
- School and exams: trigonometry and geometry homework.
- Design and engineering: trusses, frames and supports.
Need sine, cosine or other functions directly? Try the scientific calculator.
Frequently asked questions
How do I find the missing side of a triangle?
For a right triangle, use the Pythagorean theorem. For any triangle, use the law of sines or the law of cosines depending on what you know. Enter your three known values above and the calculator picks the right method.
How do I find the area of a triangle with three sides?
Use Heron's formula: find s = (a + b + c) ÷ 2, then Area = √(s(s − a)(s − b)(s − c)).
Why do I need at least one side?
Angles only fix a triangle's shape, not its size. At least one side length is needed to work out the actual lengths and area.
Why are there sometimes two answers?
With two sides and a non-included angle (SSA), two different triangles can sometimes fit the same values. The calculator shows both when that happens.
Are angles in degrees or radians?
All angles are in degrees. To convert from radians, multiply by 180 and divide by π.