Mathematics · Geometry
Right Triangle & Pythagoras Calculator
Find the missing sides and angles of a right-angled triangle from two legs, a leg and the hypotenuse, or one side and an acute angle — plus its area, perimeter and height to the hypotenuse, with a² + b² = c² worked through.
A ready-made version of the Triangle Calculator — Solve Any Triangle (SSS, SAS, ASA, AAS, SSA).
Your inputs
Quick start — try a typical case
Your result Live
Area
15 cm²
Sides 5, 6, 7.8102497 cm · angles 39.8056°, 50.1944°, 90°
- Sides a, b, c
- 5 cm · 6 cm · 7.8102497 cm
- Angles A, B, C
- 39.8056° · 50.1944° · 90°
- Perimeter
- 18.81025 cm
- Type
- scalene, right
- Heights to a, b, c
- 6 · 5 · 3.8411064 cm
- Inradius · Circumradius
- 1.5948752 · 3.9051248 cm
Pythagoras: a² + b² = c² → 5² + 6² = 7.8102497²
How this is calculated
Law of cosines c² = a² + b² − 2ab·cos C · Law of sines a/sin A = b/sin B = c/sin C · Heron: area = √(s(s−a)(s−b)(s−c)), s = (a+b+c)/2
- a, b, c
- Sides opposite angles A, B, C
Three parts fix a triangle (as long as one is a side). With three sides or two sides and the angle between them, the law of cosines gives the rest; with two angles, the third is 180° minus them and the law of sines gives the sides. Two sides and an angle that isn't between them can fit no triangle, one, or two different triangles — the 'ambiguous case' — and the calculator shows both.
Assumptions & sources
- Angles in degrees; a flat (Euclidean) triangle.
Calculator ID MATH-TRIANGLE-001/right · version 1.0.0
Common questions
How do I find the hypotenuse?
c = √(a² + b²). With legs 3 and 4: √(9 + 16) = 5.
How do I find a missing leg?
b = √(c² − a²). With hypotenuse 13 and leg 5: √(169 − 25) = 12.
Which side is the hypotenuse?
The longest side, opposite the right angle.