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Calculators/Maths/Geometry

Geometry calculators

Area, perimeter, volume and surface area for flat shapes and solids, plus coordinate geometry, triangles and the constructions built on them.

CircleArea, circumference and diameter from any one measure.Circle sector & arcA wedge of a circle: arc length, area and chord.Triangle from three sidesArea, angles and centres via Heron’s formula.Right triangle / PythagorasThird side, angles and area of a right-angled triangle.Rectangle & squareArea, perimeter and diagonal.TrapezoidArea and perimeter of a four-sided figure with parallel sides.Parallelogram & rhombusArea from base and height, or from sides and angle.EllipseArea, perimeter (Ramanujan) and eccentricity.Regular polygonArea, angles and radii of an n-sided regular shape.SphereVolume and surface area from the radius.CylinderVolume, surface area and capacity of a tube or tank.ConeVolume, slant height and surface area.Rectangular prism & cubeVolume, surface area and space diagonal of a box.PyramidVolume and surface area of a rectangular-based pyramid.Torus (ring)Volume and surface of a doughnut shape.Distance, midpoint & slopeEverything about the line between two points.Area & volume unit scalingHow area and volume change when a shape is scaled.Perimeter of a SectorPerimeter of a circle sector from its radius and central angle: two radii plus the arc.Square Pyramid VolumeVolume of a square-based pyramid from its base side and height, with slant height shown.Surface Area of a Square PyramidTotal and lateral surface area of a square-based pyramid from its base side and height.Heptagon CalculatorArea and perimeter of a regular heptagon from its side length, apothem or circumradius.Area of a KiteArea of a kite from the lengths of its two diagonals.Volume of a CubeVolume, surface area and space diagonal of a cube from its side length.Area of Semicircle CalculatorArea, perimeter and arc length of a semicircle from its radius or diameter.Volume of a HemisphereVolume and surface area of a hemisphere (half a sphere) from its radius or diameter.Dodecagon CalculatorArea and perimeter of a regular 12-sided dodecagon from its side length, apothem or circumradius.Cross-Sectional AreaArea of a slice cut across a circular, rectangular or pipe-shaped object.Vertex Form CalculatorRewrites a quadratic from standard form into vertex form a(x-h)²+k, with the vertex shown.Diameter to Radius CalculatorConverts a circle’s diameter to its radius, or a radius to its diameter, both directions.Height of a TriangleSolves for a triangle’s height from its area and base, or the height of an equilateral triangle from its side.Hexagonal PyramidVolume and surface area of a right pyramid with a regular hexagonal base, from the base edge length and height.Rectangular Pyramid VolumeVolume of a pyramid with a rectangular base, from its length, width and height.Volume of Rectangle (Rectangular Box)Volume of a rectangular box (cuboid) from its length, width and height.Diagonal of a RectangleThe diagonal length of a rectangle from its two side lengths, using the Pythagorean theorem.Trapezium Prism VolumeVolume of a prism with a trapezium cross-section, from its two parallel sides, height and prism length.Area of QuadrilateralArea of any four-sided shape from the (x,y) coordinates of its four corners, using the shoelace formula.Complementary AngleThe complement (90° minus the angle) and supplement (180° minus the angle) of a given angle.Pixel Circle GeneratorWhich grid squares to fill to draw a circle of a given pixel diameter, row by row.Area of common shapesArea of a circle, square, rectangle or triangle from one shared calculator.Length and WidthSolves for the missing side of a rectangle from its area or perimeter and one known side.Euclidean DistanceStraight-line distance between two points in 2D or 3D from their coordinates.Volume in LitresVolume in litres of a box, tank or container from its length, width and height.Surface Area to Volume RatioSurface area, volume and the resulting surface-area-to-volume ratio for a cube, sphere or cylinder.Angle Between Two VectorsAngle between two 2D or 3D vectors from their components, using the dot product.Degrees in a TriangleThe fixed 180° angle sum of any triangle, plus a mini calculator for the third angle from two known ones.Aquarium VolumeVolume of a rectangular aquarium in litres and gallons, from its length, width and height.Triangle Centroid CalculatorThe centroid of a triangle, the balance point, from the coordinates of its three vertices.30-60-90 Triangle CalculatorAll three sides and the area of a 30-60-90 right triangle from any one known side.Isosceles Right Triangle CalculatorThe sides, hypotenuse and area of a 45-45-90 isosceles right triangle from any one known side.Decagon CalculatorArea and perimeter of a regular decagon from its side length, apothem or circumradius.Truncated Cone CalculatorVolume, slant height and surface area of a truncated cone (frustum) from its two radii and height.Lateral & Surface Area of a Trapezoidal PrismLateral and total surface area of a trapezoidal prism from its cross-section and length.Isosceles Trapezium CalculatorArea, perimeter and base angles of an isosceles trapezium from its two parallel sides and equal leg length.Second Moment of Area CalculatorSecond moment of area (and polar second moment) for a rectangle, solid circle or hollow tube cross-section.Volume of a Parallelepiped CalculatorVolume of a parallelepiped from three edge vectors sharing a common vertex, using the scalar triple product.Triangular Pyramid Surface AreaTotal surface area of a regular tetrahedron (all four faces equilateral) from its edge length.Vertical Exaggeration CalculatorHow much a cross-section or map profile stretches vertical relief compared with its horizontal scale.Hollow Cylinder Volume CalculatorVolume, wall thickness and surface area of a pipe or tube from its outer and inner radius.Diameter of a Cylinder CalculatorVolume and surface area of a cylinder from its diameter and height, without converting to radius first.Pot Volume CalculatorVolume in litres of a cylindrical pot, bucket or planter from its radius or diameter and height.Degrees Decimal Minutes (DDM) ConverterConverts a coordinate between decimal degrees and degrees decimal minutes (D° M.mmm′) format.Square in a Circle CalculatorThe largest square that fits inside a circle, or the smallest circle that fits around a square.Base of a TriangleFinds the base of a triangle from its area and height, by rearranging the area formula.Height of a Cone (from Slant Height)Finds the vertical height of a cone from its base radius and slant height, using Pythagoras.Minecraft Arch GeneratorBlock-by-block column heights for a symmetric semicircular arch of a given width in Minecraft.Hexadecagon (16-Sided Shape) CalculatorArea, perimeter and interior angle of a regular 16-sided polygon (hexadecagon) from its side length.Triangle Vertices CalculatorArea and perimeter of a triangle from the (x, y) coordinates of its three vertices, using the shoelace formula.Radius of a CylinderSolve for the radius of a cylinder from its volume and height, or from its curved surface area and height.Centroid of Rectangle CalculatorCentroid (geometric centre) of a rectangle from its width and height.Triangular Prism Surface Area CalculatorSurface area and volume of a right triangular prism from its right-angle leg lengths and prism length.Slant Height CalculatorFinds the slant height of a cone or a square pyramid from its vertical height and base measurement.Latus Rectum CalculatorFinds the latus rectum of a parabola, ellipse or hyperbola from its defining parameters.Radius of Curvature CalculatorFinds the radius of a circular arc from its chord width and its height at the middle (the sagitta).Circles around a circleHow many circles of a given radius fit around a central circle while each touches it, and how much angular slack is left over.Unit circle pointCoordinates, quadrant, reference angle and sin/cos/tan for a point on the unit circle.Perimeter of common shapesPerimeter or circumference of a rectangle, square, circle, triangle or regular polygon, from one shared calculator.Triangular prismVolume and surface area of a triangular prism from its base sides and length.CircumferenceCircumference of a circle from its radius or diameter, with area shown alongside.DiameterDiameter of a circle from its radius, area or circumference.Area of a CircleArea of a circle from its radius, diameter or circumference, plus the circumference itself.Volume of a CylinderVolume of a cylinder from its radius and height, with capacity in litres.Surface Area of a CylinderTotal and curved surface area of a cylinder from its radius and height.Triangle AreaArea of a triangle from base and height, three sides, or two sides and the included angle.Pythagoras Theorem HypotenuseSolve the Pythagorean theorem for the hypotenuse, or for a missing leg.Area of TrapeziumArea of a trapezium from the two parallel sides and the height between them.HexagonArea and perimeter of a regular hexagon from its side length, across-flats or across-corners measure.Isosceles TriangleArea, perimeter and angles of an isosceles triangle from its equal sides and base.Cone VolumeVolume of a cone from its base radius and height.Scalene TriangleArea, perimeter and angles from three sides, with a check that the triangle is scalene.Minecraft Circle GeneratorBlock-by-block grid for building a circle of a given diameter in Minecraft.RadiusRadius of a circle from its diameter, circumference or area.Sector AreaArea of a circle sector from its radius and central angle, with arc length shown alongside.Surface Area of a Triangular PrismTotal surface area of a triangular prism from its base sides and length.Triangle CalculatorSolve a triangle for its area, sides and angles from three common known-value combinations.Area of a RectangleArea of a rectangle from its length and width, with perimeter and diagonal shown alongside.Sphere VolumeVolume of a sphere from its radius, with surface area and litre capacity shown alongside.Angle of a Right TriangleFind an unknown angle of a right-angled triangle from two known sides.Circumference to DiameterConvert a circle’s circumference to its diameter, or a diameter to its circumference.Rhombus AreaArea of a rhombus from its two diagonals, or from a side length and interior angle.Diameter of a CircleRadius, circumference and area of a circle worked out from its diameter.Parallelogram AreaArea of a parallelogram from base and height, or from two sides and the included angle.Distance Formula (2D & 3D Points)Straight-line distance between two coordinate points, in a plane or in 3D space.Triangular Pyramid VolumeVolume of a triangular pyramid (tetrahedron) from its base sides and height.Pentagon ShapeArea, perimeter and angles of a regular pentagon from its side length, apothem or circumradius.Equilateral TriangleArea, perimeter, height and angles of an equilateral triangle from its single side length.OctagonArea, perimeter and angles of a regular octagon from its side length, across-flats or across-corners measure.Square Metre CalculationWork out the square metreage of a room in square metres, including an L-shaped room with an alcove.Area of a SphereSurface area of a sphere from its radius, with diameter and volume shown alongside.DiagonalDiagonal length of a rectangle, square or cube from its side lengths.

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