Geometry Tools
Browse all available geometry tools.
Available tools
- 2D, 3D & Geographic Distance Calculator Calculate distance between points in 2D, 3D, or geographic coordinates.
- 3D Euclidean Distance Calculator Compute Euclidean distance between two 3D points.
- 3D Shape Surface Area Calculator Calculate the total surface area of common three-dimensional shapes.
- Annulus Area Calculator Calculate the area of an annulus from its outer and inner radii as π(R²−r²).
- Annulus Area Practice Create reproducible practice for Annulus Area Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Bounding Box Calculator Compute the axis-aligned bounding box of a set of two-dimensional points.
- Chebyshev Distance Calculator Find the greatest coordinate difference between two equal-length points or vectors.
- Chord Apothem Sign Branch Tool Return the selected signed circle chord apothem branch without choosing a geometric side.
- Chord Length Calculator Compute the chord length subtended by a central angle in a circle.
- Chord Length Practice Create reproducible practice for Chord Length Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Chord Sagitta Curvature Sensitivity Tool Circular curvature and its derivative with respect to supplied sagitta at fixed chord length.
- Chord Sagitta Residual Tool Compare supplied minor-segment sagitta to a circular chord using a cancellation-resistant expression.
- Circle Arc Length Calculator Compute the arc length of a circular segment from its central angle and radius.
- Circle Arc Length Practice Create reproducible practice for Circle Arc Length Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Circle Calculator Calculate a circle's radius, diameter, circumference, and area.
- Circle Chord Sagitta Difference Calculate a stable minor sagitta and the major-minus-minor sagitta for explicit circle radius and half-chord.
- Circle Circumference Calculator Compute circumference of a circle as 2*pi*r.
- Circle Common Chord Midpoint Offset Tool Calculate circle common chord midpoint offset from explicit caller-supplied inputs.
- Circle External Tangent Length Squared Gap Tool Calculate circle external tangent length squared gap from explicit caller-supplied inputs.
- Circle Radical Axis Signed Residual Tool Compute circle radical axis signed residual from explicit bounded inputs.
- Circle Sector Area Calculator Compute the area of a circular sector from its central angle and radius.
- Circle Sector Area Practice Create reproducible practice for Circle Sector Area Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Circle Tangent Chord Angle Tool Calculate circle tangent chord angle from explicit caller-supplied inputs.
- Circular Annulus Area Bisecting Radius Tool Calculate circular annulus area bisecting radius from explicit caller-supplied inputs.
- Circular Sector Centroid Radial Factor Tool Compute circular sector centroid radial factor from explicit bounded inputs.
- Circular Segment Area Calculator Calculate the area of a circular segment as (r²/2)·(θ−sin θ) for a central angle in radians.
- Circular Segment Area Practice Create reproducible practice for Circular Segment Area Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Circular Segment Centroid Height Factor Tool Calculate circular segment centroid height factor from explicit caller-supplied inputs.
- Cone Apex Angle Radius Height Tool Calculate cone apex angle radius height from explicit caller-supplied inputs.
- Cone Base To Slant Angle Calculate the explicit right-cone slant angle above its base and slant length from radius and height.
- Cone Normal Cross Section Angle Term Tool Compute cone normal cross section angle term from explicit bounded inputs.
- Cone Volume Calculator Compute the volume of a cone from its base radius and height.
- Cone Volume Practice Create reproducible practice for Cone Volume Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Cuboid Space Diagonal Direction Cosine Tool Calculate cuboid space diagonal direction cosine from explicit caller-supplied inputs.
- Cuboid Volume Calculator Compute volume of a cuboid as length*width*height.
- Cylinder Annulus Cross Section Thickness Tool Describe a concentric cylindrical annulus by radial thickness and cross-sectional area in consistent length units.
- Cylinder Oblique Section Area Factor Tool Compute cylinder oblique section area factor from explicit bounded inputs.
- Cylinder Volume Calculator Compute the volume of a cylinder from its radius and height.
- Ellipse Area Calculator Compute the area of an ellipse from its semi-major and semi-minor axes.
- Ellipse Eccentric Angle Focal Distance Tool Calculate ellipse eccentric angle focal distance from explicit caller-supplied inputs.
- Ellipse Focal Distance Residual Tool Calculate ellipse focal distance residual from explicit caller-supplied inputs.
- Ellipse Focal Radius Derivative Tool Derivative of center-to-focus distance with the other semiaxis fixed; circular singularity is flagged.
- Ellipse Normal Tangent Orthogonality Residual Tool Calculate ellipse normal tangent orthogonality residual from explicit caller-supplied inputs.
- Ellipse Parametric Normal Unit Vector Tool Compute ellipse parametric normal unit vector from explicit bounded inputs.
- Ellipsoid Volume Calculator Calculate the volume of an ellipsoid from its three semi-axes as (4/3)π·a·b·c.
- Ellipsoid Volume Practice Create reproducible practice for Ellipsoid Volume Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Euclidean Distance Calculator Calculate straight-line distance between two equal-length points or vectors.
- Frustum Slant Height From Generators Tool Calculate frustum slant height from generators from explicit caller-supplied inputs.
- Frustum Volume Calculator Calculate the volume of a conical frustum as (π·h/3)·(R²+R·r+r²).
- Frustum Volume Practice Create reproducible practice for Frustum Volume Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Geometry: Circle Radial Offset Curvature Tool Return radius and unsigned curvature of an ideal concentric circle offset, rejecting zero/negative offset radius; no curve-offset topology engine.
- Geometry: Circle Tangent Radius Dot Check Tool Check planar radius/tangent perpendicularity using a normalized dot product under supplied tolerance; neither vector may be zero.
- Geometry: Cone Generatrix Angle From Radii Tool Compute a right cone/frustum generatrix angle relative to its axis and slant length from explicit nonnegative radii and positive axial height.
- Geometry: Ellipse Focus Directrix Gap Tool Evaluate the right-focus/right-directrix ellipse distance residual for an axis-aligned noncircular ellipse; no fitting, closest-point solver or approximate membership tolerance.
- Geometry: Ellipse Parametric Tangent Direction Tool Evaluate the parameter derivative and oriented unit tangent of x=a*cos(t), y=b*sin(t), with positive axes; parameter is not the polar angle.
- Geometry: Line Angle Halfturn Canonical Form Tool Canonicalize an unoriented planar line angle modulo a half-turn into [0,180), retaining the distinction from an oriented bearing.
- Geometry: Planar Line Normal Form Coefficients Tool Normalize ax+by+c=0 to a unit normal, either preserving its orientation or making the first nonzero normal coefficient positive.
- Geometry: Prism Oblique Edge Height Component Tool Compute the perpendicular height component of a prism lateral edge from its explicit angle above the base plane, not volume or a general oblique solid model.
- Geometry: Rectangle Corner Sign Label Tool Label one rectangle corner from explicit +/-1 axis signs in a Cartesian y-up frame, not screen-coordinate inference.
- Geometry: Triangle Angle Bisector Foot Tool Return the internal angle-bisector foot on BC using opposite-side division in a nondegenerate planar triangle; no external bisector or symbolic solver.
- Hyperbola Asymptote Direction Slope Tool Calculate hyperbola asymptote direction slope from explicit caller-supplied inputs.
- Kite Area Calculator Calculate the area of a kite from the lengths of its two perpendicular diagonals.
- Kite Area Practice Create reproducible practice for Kite Area Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Parabola Focus Directrix Distance Residual Tool Compute parabola focus directrix distance residual from explicit bounded inputs.
- Parabola Latus Rectum Halfwidth Tool For y²=4*p*x return the positive focal chord halfwidth and full latus rectum width.
- Parabola Parametric Tangent Normal Pair Tool Return perpendicular tangent and left normal for the parabola (a*t²,2*a*t).
- Parallelogram Signed Height From Cross Product Calculate signed parallelogram height from explicit planar vectors, using left of the directed base as positive.
- Point In Polygon Tester Even-odd ray-casting test of whether a point lies inside a simple polygon given as parallel vertex coordinate lists, with exact boundary detection.
- Point Segment Clamped Nearest Point Find the clamped nearest point on a nondegenerate planar segment and its Euclidean distance; finite number arithmetic, not a spatial index.
- Point Segment Projection Parameter Project a point onto the infinite supporting segment line and return the unclamped parameter; a degenerate segment is rejected.
- Point to Line Distance Calculator Compute the shortest distance from a point to an infinite line defined by two points.
- Polygon Area Calculator Compute the area of a simple polygon from parallel vertex coordinate lists using the shoelace formula.
- Polygon Boundary Turn Sum Tool Sum explicitly supplied signed exterior turns; this does not validate a polygon or round winding to an integer.
- Polygon Edge Orientation Table Report directed polygon edge displacements and radian orientations; zero edges have null direction, and the cycle is implicitly closed.
- Polygon Half Plane Clip Clip an ordered polygon against the closed half-plane nx*x+ny*y<=maximum; no self-intersection validation or geographic geometry.
- Polygon Rectangle Clip Clip an ordered planar polygon against four rectangle half-planes, preserving algorithm order; floating boundary arithmetic, no polygon topology repair.
- Polygon Repeated Vertex Audit Audit exact repeated polygon coordinates with an explicit allowance for one repeated closure point; interior repetition remains observable.
- Polygon Signed Area Centroid Compute algebraic signed polygon area and shoelace centroid, returning null for zero algebraic area; caller supplies a simple ordered polygon, no topology validation.
- Polygon Signed Area Edge Term Tool Return one directed edge’s shoelace signed-area contribution without validating or summing a polygon.
- Polygon Turn Cross Product Sign Tool Classify the directed turn at a polygon vertex using the exact floating-point cross-product sign; no tolerance is inferred.
- Polygon Zero Length Edge Audit Identify exactly zero-length edges in an implicitly closed polygon coordinate cycle; explicit repeated closure creates a zero closing edge.
- Polyline Length Calculator Sum the Euclidean distances between consecutive points of a polyline given as parallel coordinate lists.
- Polyline Rectangle Clip Clip each polyline segment independently, retaining source-segment indexes and boundary point intersections instead of inventing path continuity.
- Prism Dihedral Normal Dot Term Tool Calculate prism dihedral normal dot term from explicit caller-supplied inputs.
- Pythagorean Theorem Calculator Calculate a missing side of a right triangle from two known sides.
- Rectangle Area Calculator Compute the area of a rectangle.
- Rectangle Center Anchor Transform Position a rectangle around a supplied fractional anchor, with nonnegative dimensions and arbitrary explicit fractions; no CSS writing-mode interpretation.
- Rectangle Diagonal Unit Direction Normalize an explicit nonzero signed rectangle diagonal into a Euclidean unit direction.
- Rectangle Minimum Separation Vector For disjoint rectangles return the shortest translation closing both axis gaps; for overlapping rectangles return a minimum axis escape translation, ties left/right/down/up in that order.
- Rectangle Perimeter Calculator Compute perimeter of a rectangle as 2*(width+height).
- Rectangle Point Clamp Clamp a finite planar point to a closed axis-aligned rectangle, allowing degenerate rectangle axes; no polygon or geographic containment.
- Rectangle Signed Axis Gaps Return signed rectangle axis gaps: positive separation, zero contact, negative overlap depth on each axis; no Euclidean distance inferred.
- Regular Hexagon Area Calculator Calculate the area of a regular hexagon from its side length as (3√3/2)·s².
- Regular Hexagon Area Practice Create reproducible practice for Regular Hexagon Area Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Regular Hexagon Perimeter Calculator Calculate the perimeter of a regular hexagon as six times its side length.
- Regular Hexagon Perimeter Practice Create reproducible practice for Regular Hexagon Perimeter Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Regular Octahedron Volume Calculator Calculate the volume of a regular octahedron from its edge length as (√2/3)·a³.
- Regular Octahedron Volume Practice Create reproducible practice for Regular Octahedron Volume Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Regular Polygon Apothem Radius Ratio Tool Compute regular polygon apothem radius ratio from explicit bounded inputs.
- Regular Polygon Area Calculator Compute the area of a regular polygon from its side length and number of sides.
- Regular Polygon Central Angle Halfangle Pair Tool Calculate regular polygon central angle halfangle pair from explicit caller-supplied inputs.
- Regular Polygon Side Sagitta Tool Calculate regular polygon side sagitta from explicit caller-supplied inputs.
- Regular Tetrahedron Volume Calculator Calculate the volume of a regular tetrahedron from its edge length as a³/(6√2).
- Rhombus Area Calculator Compute the area of a rhombus from its two diagonals.
- Rhombus Area Practice Create reproducible practice for Rhombus Area Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Rhombus Inscribed Circle Radius Tool Calculate rhombus inscribed circle radius from explicit caller-supplied inputs.
- Right Triangle Calculator Calculate a right triangle’s hypotenuse, area, and perimeter.
- Scale Factor Area Calculator Compute the new area when a shape's linear dimensions are scaled by a factor.
- Segment Axis Bounding Overlap Audit inclusive axis-envelope overlap of two planar segments; overlapping envelopes alone do not prove segment intersection.
- Segment Intersection Witness Return planar closed-segment intersection witnesses, including degenerate-point and collinear overlap cases; exact floating comparisons, no robust geometry guarantee.
- Segment Rectangle Clip Clip one closed planar segment to an inclusive axis-aligned rectangle using parameter bounds; null means no intersection.
- Sphere Cap Base Radius Ratio Tool Calculate sphere cap base radius ratio from explicit caller-supplied inputs.
- Sphere Chord Midpoint Depth Tool Return the minor spherical-cap depth from the surface to a chord midpoint, using a cancellation-resistant sagitta expression. The minor cap ranges from zero to the radius.
- Sphere Inversion Radial Coordinate Tool Calculate sphere inversion radial coordinate from explicit caller-supplied inputs.
- Sphere Section Circle Radius Gap Tool Calculate sphere section circle radius gap from explicit caller-supplied inputs.
- Sphere Surface Area Calculator Compute surface area of a sphere as 4*pi*r^2.
- Sphere Tangent Plane Offset Point Tool Compute sphere tangent plane offset point from explicit bounded inputs.
- Sphere Volume Calculator Compute the volume of a sphere from its radius.
- Spherical Cap Centroid Axis Offset Tool Return the volume centroid axial coordinate of a solid spherical cap measured from the sphere center toward the cap.
- Square Pyramid Volume Calculator Calculate the volume of a right square pyramid from its base edge and perpendicular height as (a²·h)/3.
- Square Pyramid Volume Practice Create reproducible practice for Square Pyramid Volume Calculator from supplied scenarios, returning validated questions and computed answers under the source tool's assumptions and limits.
- Stadium Shape Hydraulic Diameter Tool Calculate stadium shape hydraulic diameter from explicit caller-supplied inputs.
- Tetrahedron Face Altitude Volume Term Tool Calculate tetrahedron face altitude volume term from explicit caller-supplied inputs.
- Tetrahedron Face Normal Orientation Tool Orient the supplied triangular face away from the opposite vertex using a scalar triple-product sign.
- Tetrahedron Oriented Volume Single Term Tool Calculate tetrahedron oriented volume single term from explicit caller-supplied inputs.
- Three Point Orientation Orient three finite planar points by exact floating arithmetic cross-product sign; no adaptive numerical robustness, geographic coordinates or tolerance inference.
- Torus Inner Outer Radius Crosswalk Tool Calculate torus inner outer radius crosswalk from explicit caller-supplied inputs.
- Torus Tube Wall Thickness Gap Tool Tube wall gap and central-hole clearance for supplied concentric torus tube radii.
- Trapezoid Area Calculator Compute the area of a trapezoid from its parallel sides and height.
- Triangle Altitude Foot Parameter Tool Project a supplied triangle vertex onto the opposite side’s infinite line; parameters outside [0,1] are retained.
- Triangle Area Calculator Compute the area of a triangle from base and height.
- Triangle Barycentric Membership Audit supplied three-coordinate barycentric closed-triangle membership with an explicit nonnegative absolute tolerance; does not validate a triangle’s geometry.
- Triangle Barycentric Point Map three supplied barycentric weights summing to one to a planar triangle point; weights may be negative, no inside-triangle claim.
- Triangle Circumcenter Power At Point Tool Compute triangle circumcenter power at point from explicit bounded inputs.
- Triangle Excentral Angle From Internal Tool Compute triangle excentral angle from internal from explicit bounded inputs.
- Triangle Exradius From Area Semiperimeter Tool Calculate triangle exradius from area semiperimeter from explicit caller-supplied inputs.
- Triangle Incenter Weighted Coordinate Term Tool Calculate triangle incenter weighted coordinate term from explicit caller-supplied inputs.
- Triangle Isogonal Cevian Ratio Tool Calculate triangle isogonal cevian ratio from explicit caller-supplied inputs.
- Triangle Median Ratio Tool Compare supplied collinear median segments to the centroid’s two-to-one division.
- Triangle Mid Segment Endpoint Tool Return one triangle midsegment endpoint as the midpoint of its specified side.
- Triangle Oriented Double Area Sign Calculate the explicit planar triangle cross product and orientation sign under binary64 arithmetic.
- Triangle Perimeter Calculator Sum three side lengths of a triangle.
- Triangle Point Barycentric Coordinates Invert planar barycentric coordinates on a nondegenerate supplied triangle; floating arithmetic and signed exterior weights are retained.