THE FEUTEX TOOLKIT
Geometry Tools
Explore Geometry tools with clear inputs, worked examples and downloadable results.
Apply a two-dimensional affine map and inspect its area scale and orientation.
Calculate annulus area with labeled inputs, explicit units and the formula A = π(R² − r²).
Calculate arc length with labeled inputs, explicit units and the formula s = πrθ / 180.
Express a point as three triangle weights to inspect its location relative to the triangle.
Estimate the sag, total arc length and end slope of a symmetric mathematical catenary.
Calculate circle area with labeled inputs, explicit units and the formula A = πr².
Calculate circle chord length with labeled inputs, explicit units and the formula c = 2r sin(θ/2).
Calculate circle circumference with labeled inputs, explicit units and the formula C = 2πr.
Calculate the shared lens area and common chord where two circles partially overlap.
Calculate circle sector area with labeled inputs, explicit units and the formula A = πr²θ / 360.
Locate the center and radius of the unique circle passing through three noncollinear points.
Find a circular segment’s area, chord width and central angle from its radius and height.
Calculate closed cone surface area with labeled inputs, explicit units and the formula A = πr[r + √(r²+h²)].
Calculate closed cylinder surface area with labeled inputs, explicit units and the formula A = 2πr(r+h).
Calculate cone frustum volume with labeled inputs, explicit units and the formula V = πh(R²+Rr+r²)/3.
Calculate a cone aperture’s solid angle and the fraction of a sphere it covers.
Calculate cone volume with labeled inputs, explicit units and the formula V = πr²h/3.
Calculate cuboid space diagonal with labeled inputs, explicit units and the formula d = √(l²+w²+h²).
Calculate cuboid surface area with labeled inputs, explicit units and the formula A = 2(lw + wh + lh).
Calculate cuboid volume with labeled inputs, explicit units and the formula V = length × width × height.
Locate a point on a rolling-circle cycloid and evaluate its parametric tangent.
Calculate cylinder volume with labeled inputs, explicit units and the formula V = πr²h.
Calculate ellipse area with labeled inputs, explicit units and the formula A = πab.
Find an ellipse’s focal offset, eccentricity and latus rectum from its major and minor semi-axes.
Measure the shortest spherical surface route and straight chord between two latitude-longitude positions.
Measure a circular helix’s length, rise, curvature and torsion from radius, pitch and turns.
Find focal distance, eccentricity and asymptote slope for a horizontal hyperbola.
Find the nearest point on a finite line segment, including endpoint cases.
Locate the focus and directrix of a vertical parabola and calculate its focal chord width.
Calculate parallelogram area with labeled inputs, explicit units and the formula A = bh.
Find the acute angle between planes and a direction vector for their intersection line.
Compare the volumes of four regular Platonic solids sharing one edge length.
Map a planar point through a geometric inversion circle while preserving its radial direction.
Find the perpendicular distance and closest point from a coordinate to an infinite line.
Project a three-dimensional point onto a plane and measure its perpendicular distance.
Rotate a planar point counterclockwise around a chosen center.
Calculate pyramid volume with labeled inputs, explicit units and the formula V = base area × height / 3.
Evaluate a point and tangent on a quadratic Bézier curve from three control points.
Calculate signed area and perimeter from four consecutive boundary coordinates.
Calculate rectangle area with labeled inputs, explicit units and the formula A = width × height.
Calculate rectangle diagonal with labeled inputs, explicit units and the formula d = √(width² + height²).
Calculate rectangle perimeter with labeled inputs, explicit units and the formula P = 2(width + height).
Mirror a three-dimensional point across a plane given by its coefficients.
Calculate regular polygon area with labeled inputs, explicit units and the formula A = ns² / [4 tan(π/n)].
Calculate regular polygon interior angle with labeled inputs, explicit units and the formula θ = 180(n−2)/n.
Calculate rhombus area from diagonals with labeled inputs, explicit units and the formula A = d₁d₂/2.
Calculate right triangle missing leg with labeled inputs, explicit units and the formula b = √(c² − a²).
Measure the shared volume and intersection-circle radius of two partially overlapping spheres.
Calculate sphere surface area with labeled inputs, explicit units and the formula A = 4πr².
Calculate sphere volume with labeled inputs, explicit units and the formula V = 4πr³/3.
Measure a sphere cap’s volume, curved surface and base radius from cap height.
Convert a spherical position to Cartesian coordinates with explicit polar-angle conventions.
Calculate spherical excess and surface area from three angles on a chosen sphere.
Calculate torus volume with labeled inputs, explicit units and the formula V = 2π²Rr².
Calculate trapezoid area with labeled inputs, explicit units and the formula A = (a+b)h/2.
Calculate triangle area with labeled inputs, explicit units and the formula A = base × perpendicular height / 2.
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.
Locate a triangle’s centroid and measure its first median from three vertex coordinates.
Find the inscribed and circumscribed circle radii of a triangle from its three side lengths.
Solve a triangle’s remaining side, angles and area from two sides and their included angle.
Calculate the volume and three central cross-sections of an ellipsoid with unequal semi-axes.
Find the unique intersection of two planar lines expressed in coefficient form.
Measure the angle between two planar vectors and project the first onto the second.
Calculate a three-dimensional cross product and the parallelogram area spanned by two vectors.
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