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Right Triangle - Geometry Calculator

2D Regular Polygons:
Equilateral Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, Hendecagon, Dodecagon, Hexadecagon, N-gon, Polygon Ring

Other Polygons:
Triangle, Right Triangle, Isosceles Triangle, IR Triangle, 1/2 EL Triangle, Golden Triangle, Quadrilateral, Rectangle, Golden Rectangle, Rhombus, Equidiagonal Rhombus, Parallelogram, Kite, 60-90-120 Kite, Half Square Kite, Right Kite, Trapezoid, Right Trapezoid, Isosceles Trapezoid, Tri-equilateral Trapezoid, Obtuse Trapezoid, Cyclic Quadrilateral, Tangential Quadrilateral, Arrowhead, Concave Quadrilateral, Crossed Rectangle, Antiparallelogram, House-Shape, Symmetric Pentagon, Diagonally Bisected Octagon, Cut Rectangle, Concave Pentagon, Concave Regular Pentagon, Stretched Pentagon, Straight Bisected Octagon, Stretched Hexagon, Symmetric Hexagon, Semi-regular Hexagon, Parallelogon, Concave Hexagon, Arrow-Hexagon, Rectangular Hexagon, L-Shape, Sharp Kink, T-Shape, Square Heptagon, Truncated Square, Stretched Octagon, Frame, Open Frame, Grid, Cross, X-Shape, H-Shape, Threestar, Fourstar, Pentagram, Hexagram, Unicursal Hexagram, Oktagram, Star of Lakshmi, Double Star Polygon, Polygram, The Hat, Polygon

Round Forms:
Circle, Semicircle, Circular Sector, Circular Segment, Circular Layer, Circular Central Segment, Round Corner, Circular Corner, Circle Tangent Arrow, Drop Shape, Crescent, Pointed Oval, Two Circles, Lancet Arch, Knoll, Elongated Semicircle, Annulus, Semi-Annulus, Annulus Sector, Annulus Segment, Cash, Curved Rectangle, Rounded Polygon, Rounded Rectangle, Ellipse, Semi-Ellipse, Elliptical Segment, Elliptical Sector, Elliptical Ring, Stadium, Half Stadium, Stadium Segment, Spiral, Log. Spiral, Reuleaux Triangle, Cycloid, Double Cycloid, Astroid, Hypocycloid, Cardioid, Epicycloid, Parabolic Segment, Heart, Tricorn, Pointed Semicircle, Interarc Triangle, Circular Arc Triangle, Interarc Quadrangle, Intercircle Quadrangle, Circular Arc Quadrangle, Circular Arc Polygon, Claw, Half Yin-Yang, Arbelos, Salinon, Bulge, Lune, Three Circles, Polycircle, Round-Edged Polygon, Rose, Gear, Oval, Egg-Profile, Lemniscate, Squircle, Circular Square, Digon, Spherical Triangle

3D Platonic Solids:
Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron

Archimedean Solids:
Truncated Tetrahedron, Cuboctahedron, Truncated Cube, Truncated Octahedron, Rhombicuboctahedron, Truncated Cuboctahedron, Icosidodecahedron, Truncated Dodecahedron, Truncated Icosahedron, Snub Cube, Rhombicosidodecahedron, Truncated Icosidodecahedron, Snub Dodecahedron

Catalan Solids:
Triakis Tetrahedron, Rhombic Dodecahedron, Triakis Octahedron, Tetrakis Hexahedron, Deltoidal Icositetrahedron, Hexakis Octahedron, Rhombic Triacontahedron, Triakis Icosahedron, Pentakis Dodecahedron, Pentagonal Icositetrahedron, Deltoidal Hexecontahedron, Hexakis Icosahedron, Pentagonal Hexecontahedron

Johnson Solids:
Pyramids, Cupolae, Rotunda, Elongated Pyramids, Gyroelongated Pyramids, Bipyramids, Elongated Bipyramids, Gyroelongated Square Dipyramid, Gyrobifastigium, Disheptahedron, Snub Disphenoid, Sphenocorona, Disphenocingulum

Other Polyhedrons:
Cuboid, Square Pillar, Triangular Pyramid, Square Pyramid, Regular Pyramid, Pyramid, Square Frustum, Regular Frustum, Frustum, Bent Pyramid, Regular Bipyramid, Bipyramid, Bifrustum, Frustum-Pyramid, Ramp, Right Wedge, Wedge, Half Tetrahedron, Rhombohedron, Parallelepiped, Regular Prism, Prism, Oblique Prism, Anticube, Antiprism, Prismatoid, Trapezohedron, Disphenoid, Corner, General Tetrahedron, Wedge-Cuboid, Half Cuboid, Skewed Cuboid, Ingot, Skewed Three-Edged Prism, Cut Cuboid, Truncated Cuboid, Obtuse Edged Cuboid, Elongated Dodecahedron, Truncated Rhombohedron, Obelisk, Bent Cuboid, Hollow Cuboid, Hollow Pyramid, Hollow Frustum, Star Pyramid, Stellated Octahedron, Small Stellated Dodecahedron, Great Stellated Dodecahedron, Great Dodecahedron, Great Icosahedron

Round Forms:
Sphere, Hemisphere, Quarter Sphere, Spherical Corner, Cylinder, Cut Cylinder, Oblique Cylinder, Bent Cylinder, Elliptic Cylinder, Generalized Cylinder, Cone, Truncated Cone, Oblique Circular Cone, Elliptic Cone, Truncated Elliptic Cone, General Cone, General Truncated Cone, Bicone, Truncated Bicone, Pointed Pillar, Rounded Cone, Elongated Hemisphere, Drop, Spheroid, Ellipsoid, Semi-Ellipsoid, Spherical Sector, Spherical Cap, Spherical Segment, Spherical Central Segment, Double Calotte, Rounded Disc, Double Sphere, Spherical Wedge, Half Cylinder, Diagonally Halved Cylinder, Cylindrical Wedge, Cylindrical Sector, Cylindrical Segment, Flat End Cylinder, Half Cone, Conical Sector, Conical Wedge, Spherical Shell, Half Spherical Shell, Spherical Shell Cap, Cylindrical Shell, Cut Cylindrical Shell, Oblique Cylindrical Shell, Hollow Cone, Truncated Hollow Cone, Spherical Ring, Torus, Spindle Torus, Toroid, Torus Sector, Toroid Sector, Arch, Reuleaux-Tetrahedron, Capsule, Half Capsule, Capsule Segment, Double Point, Anticone, Truncated Anticone, Sphere-Cylinder, Lens, Concave Lens, Barrel, Egg Shape, Paraboloid, Hyperboloid, Oloid, Steinmetz Solids, Solid of Revolution

Calculations at a right triangle. A right triangle has one right angle of 90 degrees and two acute angles of less than 90 degrees.
Enter at a, b and c two values and choose the number of decimal places. Then click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units.

Formulas:
a² + b² = c² (Pythagorean theorem)
p = a² / c
q = b² / c
h = √ p * q
Perimeter = a + b + c
A = a * b / 2
α = arccos( (b² + c² - a²) / (2bc) )
β = arccos( (a² + c² - b²) / (2ac) )
γ = π/2 = 90°
r_c = c / 2
r_i = ( a + b - c ) / 2
m_a = √2 * ( b² + c² ) - a² / 2
m_b = √2 * ( c² + a² ) - b² / 2
m_c = √2 * ( a² + b² ) - c² / 2

Catheti (legs), hypotenuse, median lines, heights, perimeter and radius have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

The heights of the legs are identical with each other leg. The centroid of the right triangle is at the intersection of the median lines. The intersection of the bisecting lines is the center of the incircle. The center of the circumcircle is the intersection of the perpendicular bisectors of the legs and the center of the hypotenuse.

Right triangle, perpendicular bisectors and circumcircle
perpendicular bisectors and circumcircle

A right triangle is created when you cut a rectangle in half diagonally. The right triangle forms the basis for the Pythagorean theorem and for trigonometric functions such as sine and cosine. The longest side, the one opposite the right angle, is called the hypotenuse, the other two are called catheti or legs. Regarding one of the acute angles, there is the adjacent angle, which lies against the angle, and the opposite angle, which lies opposite this angle. The Pythagorean theorem states that the square of the hypotenuse is equal to the squares of the legs combined. Since the hypotenuse is also the diagonal of the corresponding rectangle, you can use this to calculate the length of diagonals opposite to a right angle as the root of the sum of the squares of the two sides. The Pythagorean theorem is a fundamental theorem of Euclidean geometry and is of outstanding importance; Pythagoras of Samos is said to have been the first to prove it.