Triangle Calculator
Pythagorean theorem, sides, angles and area
What You Know
Result
c = 5
a = 3 · b = 4
AnglesA 36.87° · B 53.13° · C 90°
Sidesa 3 · b 4 · c 5
Area6
Perimeter12
Height to side c2.4
TypeRight · scalene
Side a is opposite angle A, and so on. In a right triangle, C is the right angle and c is the hypotenuse.
Pythagorean Triples
| a | b | c (hypotenuse) | Check |
|---|---|---|---|
| 3 | 4 | 5 | 9 + 16 = 25 |
| 5 | 12 | 13 | 25 + 144 = 169 |
| 8 | 15 | 17 | 64 + 225 = 289 |
| 7 | 24 | 25 | 49 + 576 = 625 |
| 20 | 21 | 29 | 400 + 441 = 841 |
| 9 | 40 | 41 | 81 + 1600 = 1681 |
| 6 | 8 | 10 | 36 + 64 = 100 |
| 12 | 16 | 20 | 144 + 256 = 400 |
Special Right Triangles
| Special triangle | Side ratio |
|---|---|
| 30° · 60° · 90° | 1 : √3 : 2 (1 : 1.732 : 2) |
| 45° · 45° · 90° | 1 : 1 : √2 (1 : 1 : 1.414) |
| Equilateral | Area = √3 ÷ 4 × side² |
Triangle Formulas
| Formula | Expression |
|---|---|
| Pythagorean theorem | a² + b² = c² |
| Area (base, height) | ½ × b × h |
| Area (Heron) | √(s(s−a)(s−b)(s−c)), s = (a+b+c) ÷ 2 |
| Area (SAS) | ½ × a × b × sin C |
| Law of cosines | c² = a² + b² − 2ab cos C |
| Law of sines | a ÷ sin A = b ÷ sin B = c ÷ sin C |
Formulas & Sources
- Right triangles: Pythagorean theorem · others: law of cosines and law of sines
- Area by Heron's formula; results shown to 4 decimals (angles to 2)
Last reviewed: 2026-10-19
FAQ
How do I find the hypotenuse?
c = √(a² + b²). With legs 3 and 4, the hypotenuse is √(9 + 16) = 5.
How do I find a missing leg?
Leg = √(c² − other leg²). With a hypotenuse of 13 and a leg of 5, the other leg is √(169 − 25) = 12.
How do I find the area from three sides?
Use Heron's formula: s = (a + b + c) ÷ 2, area = √(s(s−a)(s−b)(s−c)). Sides 5, 6 and 7 give about 14.7.
When can three lengths not form a triangle?
If the longest side is equal to or longer than the other two combined, e.g. 2, 3 and 6.
What are the side ratios of a 30-60-90 triangle?
1 : √3 : 2. A 45-45-90 triangle is 1 : 1 : √2.