Geometry
Areas, perimeters, volumes and angles for flat and solid shapes, from the triangle to the torus. 69 tools, including 3D Distance Calculator, Angle Bisector Calculator (triangle), Annulus (ring) area calculator and Aquarium volume calculator. All free, with no account and nothing to install.
3D Distance CalculatorCompute the distance between two points in space, with an isometric view, the Δx / Δy / Δz components and the midpoint.Angle Bisector Calculator (triangle)Enter the three sides or the three vertices and get the length of each internal angle bisector, the incenter, the inradius, and the exact point where every bisector cuts the opposite side. The angle bisector theorem is the heart of it: the bisector splits the opposite side in the ratio of the two adjacent sides. The triangle inequality is checked before anything is computed, and the triangle is drawn with its three bisectors.Annulus (ring) area calculatorCompute the area of a ring from its outer and inner radius.Aquarium volume calculatorCompute the water volume of a rectangular aquarium in litres and gallons.Area calculatorCompute the area of a rectangle, square, circle or triangle.Circle calculatorCompute the area, circumference and diameter of a circle from its radius.Circle sector area calculatorCompute the area and arc length of a circle sector from its radius and angle.Circumscribed Circle CalculatorCircumradius R = abc/4K, circumcentre and circumcircle of a triangle, from three sides or three vertices, with the figure drawn.Cone flat pattern generatorUnroll a cone or a truncated cone (frustum) into the flat sheet you cut out to build it. From the radii and height it computes the slant height, the exact sector angle and radii, the lateral area and the base arc length, and draws the pattern to scale — for sheet metal, paper craft or a lampshade.Cone surface area calculatorCompute the total surface area and slant height of a cone from its radius and height.Cone volume calculatorCompute the volume, surface area and slant height of a cone, drawn to scale.Cylinder volume calculatorCompute the volume and surface area of a cylinder from its radius and height.Distance between two pointsCompute the straight-line distance between two points on a plane.Distance Formula CalculatorFind the distance between two points on an interactive coordinate plane, with the Pythagorean working, the midpoint, the slope and the direction angle.Ellipse area calculatorCompute the area of an ellipse from its semi-major and semi-minor axes.Ellipse perimeter calculatorEstimate the perimeter of an ellipse from its two semi-axes (Ramanujan's formula).Equilateral triangle calculatorCompute the area, height and perimeter of an equilateral triangle from its side.Frustum CalculatorVolume, lateral and total surface area, and slant height of a conical frustum.General Triangle SolverSolve any triangle from 3 known values (SSS, SAS, ASA/AAS, SSA) with the laws of sines and cosines: all sides and angles, area, perimeter and type, handling the ambiguous SSA case (0, 1 or 2 triangles).Golden Rectangle CalculatorFrom the long side, short side, diagonal, area or perimeter, derive the whole golden rectangle — and see it drawn with its golden-spiral subdivision.Great Circle Distance CalculatorGreat-circle distance between two latitude/longitude points by the haversine formula, with initial and final bearing, the midpoint and a globe view.Triangle area calculator (Heron's formula)Compute a triangle's area from the length of its three sides.Hexagon area calculatorCompute the area of a regular hexagon from its side length.Inscribed Circle CalculatorInradius r = K/s, incentre, tangent points and incircle of a triangle, from three sides or three vertices, with the figure drawn.Irregular polygon area calculatorThe area of any polygon — regular or not, convex or concave — from its corner coordinates. Enter the vertices in order and the shoelace formula returns the exact area, plus the perimeter, the centroid and whether the points run clockwise or counter-clockwise, with a drawing of the shape. Ideal for land plots and CAD sketches.Julia set generatorRender Julia sets in your browser by iterating z → z² + c for a fixed complex parameter c. Each pixel is a starting point coloured by how fast it escapes to infinity. Try famous values — the Douady rabbit, San Marco dragon, dendrite — tune the iterations and palette, and zoom in.L-system fractal generatorGrow fractals from a Lindenmayer system: an axiom string rewritten by production rules, then drawn as turtle graphics. Type your own axiom, rules and angle, or load presets for the Koch snowflake, Heighway dragon, fractal plants and trees — each one blossoms from a handful of symbols.Magic square generatorGenerate a magic square of any order from 3 to 20 — a grid of the numbers 1…N² where every row, column and diagonal adds to the same magic constant. It picks the right construction automatically: the Siamese method for odd orders, diagonal complements for multiples of four, and the Strachey method otherwise.Mandelbrot set explorerExplore the Mandelbrot set, the most famous fractal, rendered live in your browser. Each pixel is a complex number c; it iterates z → z² + c from zero and is coloured by how fast it escapes — black where it stays bounded. Pan by editing the centre, zoom in for the infinite detail of its boundary.Midpoint calculatorFind the midpoint between two points on a plane.Parallel and Perpendicular Line CalculatorThe line parallel and the line perpendicular to a given line through a chosen point.Parallelogram area calculatorCompute the area of a parallelogram from its base and height.Parametric curve grapherPlot a curve defined by x(t) and y(t) as the parameter t sweeps an interval — the natural way to draw circles, Lissajous figures, spirals and roses that no single y=f(x) can. Pick a preset or type your own expressions; it samples the pair, auto-scales, and draws the curve in your browser.Pentagon area calculatorCompute the area of a regular pentagon from its side length.Perimeter calculatorCompute the perimeter of a rectangle, square, circle or triangle.Point-Slope Form CalculatorWrite y − y1 = m(x − x1) from a point and slope or two points, with the other line forms.Point to Plane Distance CalculatorDistance from a point to the plane Ax + By + Cz + D = 0, with a live equation preview, the foot of the perpendicular and which side of the plane the point is on.Polygon diagonals calculatorHow many diagonals a polygon has, from its number of sides: n·(n−3)/2 — because each vertex connects to all others except itself and its two neighbours. It also names the polygon and gives the number of triangles it splits into and the sum of its interior angles.Pyramid volume calculatorCompute the volume of a square-based pyramid from its base and height.Pythagorean theorem calculatorFind any side of a right triangle — hypotenuse or leg — from the two you know, with the three squares drawn.Rectangle calculatorEvery property of a rectangle from any two you know. Pick what you have — length & width, area & a side, perimeter & a side, or diagonal & a side — and it returns the length, width, area, perimeter and diagonal, using A = l·w, P = 2(l+w) and d = √(l²+w²).Rectangle diagonal calculatorCompute the diagonal, area and perimeter of a rectangle.Regular polygon area calculatorCompute the area of a regular polygon from its number of sides and side length.Regular polygon calculatorEvery measure of a regular polygon from the number of sides and the side length: the area, perimeter, interior and exterior angles, the sum of interior angles, the apothem (inradius), the circumradius and the number of diagonals. One entry, the full geometry — for triangles through many-sided polygons.Regular polygon perimeter calculatorCompute the perimeter of a regular polygon from its number of sides and side length.Rhombus area calculatorCompute the area of a rhombus from its two diagonals.Shoelace formula calculatorCompute a polygon's area with the shoelace formula (Gauss's area formula): sum the cross-products of consecutive vertex coordinates, halve, and take the absolute value — A = ½·|Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|. It also gives the signed area, whose sign tells you the winding direction, plus the perimeter and centroid.Sierpinski triangle generatorGenerate the Sierpinski triangle two ways: by recursive subdivision, which removes the central triangle at every level, or by the chaos game, where thousands of random midpoint jumps make the fractal emerge from pure randomness. Choose the depth or iteration count and a colour palette.Slope calculatorFind the slope and y-intercept of the line through two points.Slope-Intercept Form CalculatorReduce any line — from two points, a point and slope, or standard form — to y = mx + b.Speed, distance & time calculatorCompute average speed from a distance and a time, plus the pace per km.Sphere volume calculatorCompute the volume and surface area of a sphere from its radius.Spirograph generatorDraw hypnotic spirograph curves — the hypotrochoids and epitrochoids traced by a point on a circle rolling inside or outside a fixed one. Slide the fixed radius, rolling radius and pen offset and watch endless rosettes and stars redraw live, in a palette of your choice.Square calculatorAll four measures of a square from any one. Give the side, the area, the perimeter or the diagonal and it returns the rest — side s, area s², perimeter 4s and diagonal s√2 — instantly.Square diagonal calculatorCompute the diagonal and area of a square from its side length.Sum of Squares CalculatorCompute the sum of squares for the first N integers, a range n₁..n₂ or a custom list, using the n(n+1)(2n+1)/6 formula with exact big-integer arithmetic.Surface Area CalculatorTotal surface area of a sphere, cylinder, cone, cuboid, prism, pyramid or tetrahedron.Surface gravity calculatorCompute the surface gravity of a planet or moon from its mass and radius.Surface of Revolution CalculatorS = 2π∫ f·√(1+f′²) dx about the x-axis, with the radius and the arc-length element both rederived for the other axes. The sphere case √(1−x²) on [−1, 1] returns exactly 4π despite the integrand blowing up at both endpoints.Torus CalculatorVolume and surface area of a torus (doughnut) from its major and minor radii.Trapezoid area calculatorCompute the area of a trapezoid from its two parallel sides and height.Trapezoidal Rule CalculatorApproximates an integral from a function or from raw measured points, and unevenly spaced points are supported — real data rarely arrives on a regular grid. Draws the trapezoids, gives the error bound and compares to the exact value when one is obtainable.Triangle area calculatorArea of a triangle from base and height, three sides, or two sides and the angle between them.Triangle Centroid CalculatorFind the centroid of a triangle from its three vertices, with the medians, side midpoints, median lengths and the 2:1 ratio, plus a diagram.Triangle Orthocenter CalculatorFind the orthocenter of a triangle (the intersection of its altitudes) from the three vertices, with the altitude equations and a diagram — note it can lie outside an obtuse triangle.Triangular prism volume calculatorCompute the volume of a triangular prism from its base, height and length.Volume calculatorCompute the volume of a box, cube, sphere, cylinder or cone.Volume of an ellipsoid calculatorThe volume of an ellipsoid from its three semi-axes: V = 4⁄3·π·a·b·c. It also reports the surface area (Thomsen's approximation) — set all three axes equal and it becomes a sphere. Useful for eggs, tanks, planets and any squashed sphere.Volume of Revolution CalculatorDisk, washer and shell methods about the x-axis, the y-axis, or any line y = k or x = k. The integral is set up on screen before it is evaluated, and shifting the axis changes the radius to |f(x) − k| — the step most calculators get wrong.