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Geometry Tools
85 tools in this collection. Choose a task below or search the complete FeuTex toolkit.
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Affine Point Transformation
Apply a two-dimensional affine map and inspect its area scale and orientation.
Open tool →GeometryAnnulus Area Calculator
Calculate annulus area with labeled inputs, explicit units and the formula A = π(R² − r²).
Open tool →GeometryArc Length Calculator
Calculate arc length with labeled inputs, explicit units and the formula s = πrθ / 180.
Open tool →GeometryBarycentric Point Location
Express a point as three triangle weights to inspect its location relative to the triangle.
Open tool →GeometryCatenary Sag and Arc Length
Estimate the sag, total arc length and end slope of a symmetric mathematical catenary.
Open tool →GeometryCircle Area Calculator
Calculate circle area with labeled inputs, explicit units and the formula A = πr².
Open tool →GeometryCircle Chord Length Calculator
Calculate circle chord length with labeled inputs, explicit units and the formula c = 2r sin(θ/2).
Open tool →GeometryCircle Circumference Calculator
Calculate circle circumference with labeled inputs, explicit units and the formula C = 2πr.
Open tool →GeometryCircle Overlap Lens
Calculate the shared lens area and common chord where two circles partially overlap.
Open tool →GeometryCircle Sector Area Calculator
Calculate circle sector area with labeled inputs, explicit units and the formula A = πr²θ / 360.
Open tool →GeometryCircle through Three Points
Locate the center and radius of the unique circle passing through three noncollinear points.
Open tool →GeometryCircular Segment Profile
Find a circular segment’s area, chord width and central angle from its radius and height.
Open tool →GeometryClosed Cone Surface Area Calculator
Calculate closed cone surface area with labeled inputs, explicit units and the formula A = πr[r + √(r²+h²)].
Open tool →GeometryClosed Cylinder Surface Area Calculator
Calculate closed cylinder surface area with labeled inputs, explicit units and the formula A = 2πr(r+h).
Open tool →GeometryCommon External Tangent of Two Circles
Find the straight external tangent length between circles for a geometric construction.
Open tool →GeometryCone Frustum Flat Pattern
Calculate the annular-sector radii and sweep for unrolling a cone frustum.
Open tool →GeometryCone Frustum Volume Calculator
Calculate cone frustum volume with labeled inputs, explicit units and the formula V = πh(R²+Rr+r²)/3.
Open tool →GeometryCone Solid Angle and Sphere Fraction
Calculate a cone aperture’s solid angle and the fraction of a sphere it covers.
Open tool →GeometryCone Volume Calculator
Calculate cone volume with labeled inputs, explicit units and the formula V = πr²h/3.
Open tool →GeometryCuboid Space Diagonal Calculator
Calculate cuboid space diagonal with labeled inputs, explicit units and the formula d = √(l²+w²+h²).
Open tool →GeometryCuboid Surface Area Calculator
Calculate cuboid surface area with labeled inputs, explicit units and the formula A = 2(lw + wh + lh).
Open tool →GeometryCuboid Volume Calculator
Calculate cuboid volume with labeled inputs, explicit units and the formula V = length × width × height.
Open tool →GeometryCyclic Quadrilateral from Four Sides
Calculate area and diagonal lengths of a convex cyclic quadrilateral.
Open tool →GeometryCycloid Point and Tangent
Locate a point on a rolling-circle cycloid and evaluate its parametric tangent.
Open tool →GeometryCylinder Volume Calculator
Calculate cylinder volume with labeled inputs, explicit units and the formula V = πr²h.
Open tool →GeometryEllipse Area Calculator
Calculate ellipse area with labeled inputs, explicit units and the formula A = πab.
Open tool →GeometryEllipse Foci and Eccentricity
Find an ellipse’s focal offset, eccentricity and latus rectum from its major and minor semi-axes.
Open tool →GeometryEllipse Local Radius of Curvature
Measure curvature and osculating radius at a location on an elliptical curve.
Open tool →GeometryEllipse Sector Area by Parameter
Measure an ellipse sector swept between two parametric angles.
Open tool →GeometryEllipse Tangent at Parametric Angle
Locate an ellipse point and its tangent line without a vertical-slope singularity.
Open tool →GeometryGreat-Circle Distance
Measure the shortest spherical surface route and straight chord between two latitude-longitude positions.
Open tool →GeometryHelix Path Profile
Measure a circular helix’s length, rise, curvature and torsion from radius, pitch and turns.
Open tool →GeometryHyperbola Foci and Asymptotes
Find focal distance, eccentricity and asymptote slope for a horizontal hyperbola.
Open tool →GeometryInternal Angle Bisector Length
Find the internal angle bisector and how it divides the opposite side.
Open tool →GeometryLattice Polygon Area from Point Counts
Find the area of a simple lattice polygon from its interior and boundary lattice points.
Open tool →GeometryLine and Plane Intersection
Find the parameter and coordinates where a 3D parametric line crosses a plane.
Open tool →GeometryNearest Point on a Line Segment
Find the nearest point on a finite line segment, including endpoint cases.
Open tool →GeometryOblique Cylinder Geometry
Compute perpendicular height and volume from an oblique cylinder axis.
Open tool →GeometryPappus Solid of Revolution
Compute swept volume and surface using a region area, curve length, and centroid distances.
Open tool →GeometryParabola Focus and Directrix
Locate the focus and directrix of a vertical parabola and calculate its focal chord width.
Open tool →GeometryParallelogram Area Calculator
Calculate parallelogram area with labeled inputs, explicit units and the formula A = bh.
Open tool →GeometryPlane Angle and Intersection Direction
Find the acute angle between planes and a direction vector for their intersection line.
Open tool →GeometryPlatonic Solid Comparison
Compare the volumes of four regular Platonic solids sharing one edge length.
Open tool →GeometryPoint Inversion in a Circle
Map a planar point through a geometric inversion circle while preserving its radial direction.
Open tool →GeometryPoint Projection onto a Line
Find the perpendicular distance and closest point from a coordinate to an infinite line.
Open tool →GeometryPoint Projection onto a Plane
Project a three-dimensional point onto a plane and measure its perpendicular distance.
Open tool →GeometryPoint Rotation about a Center
Rotate a planar point counterclockwise around a chosen center.
Open tool →GeometryPyramid Volume Calculator
Calculate pyramid volume with labeled inputs, explicit units and the formula V = base area × height / 3.
Open tool →GeometryQuadratic Bézier Point and Tangent
Evaluate a point and tangent on a quadratic Bézier curve from three control points.
Open tool →GeometryQuadrilateral Coordinate Survey
Calculate signed area and perimeter from four consecutive boundary coordinates.
Open tool →GeometryRectangle Area Calculator
Calculate rectangle area with labeled inputs, explicit units and the formula A = width × height.
Open tool →GeometryRectangle Diagonal Calculator
Calculate rectangle diagonal with labeled inputs, explicit units and the formula d = √(width² + height²).
Open tool →GeometryRectangle Perimeter Calculator
Calculate rectangle perimeter with labeled inputs, explicit units and the formula P = 2(width + height).
Open tool →GeometryReflect a Point across a Plane
Mirror a three-dimensional point across a plane given by its coefficients.
Open tool →GeometryRegular Polygon Area Calculator
Calculate regular polygon area with labeled inputs, explicit units and the formula A = ns² / [4 tan(π/n)].
Open tool →GeometryRegular Polygon Interior Angle Calculator
Calculate regular polygon interior angle with labeled inputs, explicit units and the formula θ = 180(n−2)/n.
Open tool →GeometryRegular Star Polygon Path Length
Measure edge length and total traversal length for a regular star polygon step.
Open tool →GeometryRhombus Area from Diagonals Calculator
Calculate rhombus area from diagonals with labeled inputs, explicit units and the formula A = d₁d₂/2.
Open tool →GeometryRight Triangle Missing Leg Calculator
Calculate right triangle missing leg with labeled inputs, explicit units and the formula b = √(c² − a²).
Open tool →GeometryRounded Rectangle Outline and Area
Calculate area and perimeter for a rectangle with four equal circular corner fillets.
Open tool →GeometryShortest Distance Between Skew Lines
Find separation between two nonparallel 3D lines using their origins and direction vectors.
Open tool →GeometrySphere Cut by a Plane
Find a circular section area and radius for a plane at a given offset from a sphere center.
Open tool →GeometrySphere Intersection Volume
Measure the shared volume and intersection-circle radius of two partially overlapping spheres.
Open tool →GeometrySphere Surface Area Calculator
Calculate sphere surface area with labeled inputs, explicit units and the formula A = 4πr².
Open tool →GeometrySphere Volume Calculator
Calculate sphere volume with labeled inputs, explicit units and the formula V = 4πr³/3.
Open tool →GeometrySpherical Cap Profile
Measure a sphere cap’s volume, curved surface and base radius from cap height.
Open tool →GeometrySpherical Coordinate Position
Convert a spherical position to Cartesian coordinates with explicit polar-angle conventions.
Open tool →GeometrySpherical Triangle Excess and Area
Calculate spherical excess and surface area from three angles on a chosen sphere.
Open tool →GeometrySpherical Zone Surface and Volume
Find the sphere surface band and solid volume between two parallel cut planes.
Open tool →GeometryStadium Shape Area and Boundary
Calculate a capsule-shaped outline formed by a rectangle and two semicircular ends.
Open tool →GeometrySuperellipse Boundary Point
Locate a point on a rounded rectangle or diamond-like superellipse using its exponent.
Open tool →GeometryTetrahedron Volume from Edge Vectors
Compute the volume and orientation of a tetrahedron from its three shared-origin edge vectors.
Open tool →GeometryTorus Volume Calculator
Calculate torus volume with labeled inputs, explicit units and the formula V = 2π²Rr².
Open tool →GeometryTrapezoid Area Calculator
Calculate trapezoid area with labeled inputs, explicit units and the formula A = (a+b)h/2.
Open tool →GeometryTriangle Area Calculator
Calculate triangle area with labeled inputs, explicit units and the formula A = base × perpendicular height / 2.
Open tool →GeometryTriangle Area from Three Sides Calculator
Calculate triangle area from three sides with labeled inputs, explicit units and the formula A = √[s(s−a)(s−b)(s−c)], s = (a+b+c)/2.
Open tool →GeometryTriangle Centroid Coordinates
Locate a triangle’s centroid and measure its first median from three vertex coordinates.
Open tool →GeometryTriangle from Two Sides and Included Angle
Solve a triangle’s remaining side, angles and area from two sides and their included angle.
Open tool →GeometryTriangle Incircle and Circumcircle
Find the inscribed and circumscribed circle radii of a triangle from its three side lengths.
Open tool →GeometryTriangle Median Lengths
Find all three medians to plan centroid bracing or check a triangle construction.
Open tool →GeometryTriangle Orthocenter from Coordinates
Locate the intersection of triangle altitudes from three measured vertices.
Open tool →GeometryTriaxial Ellipsoid Profile
Calculate the volume and three central cross-sections of an ellipsoid with unequal semi-axes.
Open tool →GeometryTwo-Line Intersection
Find the unique intersection of two planar lines expressed in coefficient form.
Open tool →GeometryVector Angle and Projection
Measure the angle between two planar vectors and project the first onto the second.
Open tool →GeometryVector Cross Product
Calculate a three-dimensional cross product and the parallelogram area spanned by two vectors.
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