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➗ MathFree
Cube space diagonal calculator
Find the longest straight line inside a cube, from one corner to the opposite one: it is the edge times √3, so an edge of 2 gives about 3.464.
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➗ MathFree
Cube surface area from volume calculator
Turn a cube's volume into its outer surface area: a volume of 8 gives an edge of 2 and a surface of 24, since the edge is the cube root and the surface is six…
S
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➗ MathFree
Cuboid space diagonal calculator
Find the longest straight line inside a box, from one corner to the opposite one: a box of 2 by 3 by 6 has a space diagonal of exactly 7.
A
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➗ MathFree
Cuboid surface area calculator
Get the total outer area of a rectangular box from its three edges: a box of 3 by 4 by 5 has faces of 12, 15 and 20 and a total surface of 94.
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➗ MathFree
Brahmagupta formula calculator
Enter the four sides of a quadrilateral inscribed in a circle and get its area: sides 3, 4, 3 and 4 give a semiperimeter of 7 and an area of 12.
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➗ MathFree
Ptolemy theorem calculator
Ptolemy's theorem from four sides: for a cyclic quadrilateral with sides 3, 4, 3 and 4, the diagonals multiply to 25, shown as 9 plus 16 from the opposite pairs…
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➗ MathFree
Cycloid arc length and area calculator
Give the radius of the rolling circle and get one full cycloid arch: a radius of 1 gives an arch length of 8 and an area of 3π, three times the area of the…
A
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➗ MathFree
Cylinder height from volume calculator
Get the missing height of a right cylinder from its volume and the radius of its base: with radius 3, a volume equal to ten times the base area means a height…
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➗ MathFree
Cylinder lateral surface area
Get the area of a cylinder's curved wall alone: radius 3 and height 5 give 30π, the label or insulation you would wrap around it, without the two ends.
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➗ MathFree
Decagon area calculator
Enter one side of a regular ten-sided figure and get its area: a side of 5 gives about 192.355, with a perimeter of 50 plus the apothem and outer radius for the…
A
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➗ MathFree
Decagon area from apothem
Turn the apothem of a regular decagon into its area: an apothem of 1 gives ten times tan(π/10) square units, and any other apothem scales that by its square.
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➗ MathFree
Decagon circumradius calculator
Get the radius of the circle through all ten corners of a regular decagon from its side length, so a side of 2 gives a circumradius of about 3.2360679775.
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➗ MathFree
Decagon perimeter calculator
Multiply one side by ten and you have the full boundary of a regular decagon: a side of 6 gives a perimeter of 60, the trim, rope or fence you need to go all…
A
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➗ MathFree
Decagonal prism calculator
Enter the base side and height of a regular decagonal prism and get its capacity and surfaces: side 2 and height 5 give a base perimeter of 20 and a wall area…
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➗ MathFree
Distance between two points in 3D
Give two points in space and get the straight line between them: from (0, 0, 0) to (3, 4, 12) is exactly 13, with the differences along x, y and z listed so no…
A
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➗ MathFree
Dodecagon area calculator
Give the side of a regular dodecagon and get the area it encloses: a side of 1 covers about 11.196 square units, three times (2 + √3) the side squared, with…
A
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➗ MathFree
Dodecagon area from apothem
Measure from the centre of a regular twelve-sided shape to the middle of one side, and that apothem gives the area: for an apothem of 1 it is twelve times…
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➗ MathFree
Dodecagon circumradius calculator
Enter the side of a regular dodecagon and get the radius of the circle through its twelve corners: a side of 5 gives about 9.65926, and a side of 1 about…
A
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➗ MathFree
Dodecagon perimeter calculator
Twelve equal sides make the sum easy: a regular dodecagon with a side of 6 has a perimeter of 72, the length of frame, trim or rope that goes once round it.
A
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➗ MathFree
Dodecahedron inradius calculator
Enter the edge of a regular dodecahedron and get the radius of the largest sphere that fits inside it: an edge of 2 gives an inradius of about 2.2270327288…
A
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➗ MathFree
Dodecahedron midradius calculator
Enter the edge of a regular dodecahedron and get the radius of the sphere that touches every edge at its midpoint: an edge of 2 gives a midradius of about…
P
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➗ MathFree
Dodecahedron surface area calculator
Enter the edge of a regular dodecahedron and get the area of its whole outer skin: an edge of 2 gives twelve faces of about 6.881909602356 each, about…
P
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➗ MathFree
Ellipse area calculator
Multiply pi by the two semi-axes and you have the area of an ellipse: semi-axes of 5 and 3 enclose about 47.123889803847 square units.
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➗ MathFree
Ellipse directrix calculator
Enter the two semi-axes of an ellipse and get the distance from the centre to each directrix line: semi-axes of 5 and 3 give a focus at 4, an eccentricity of…
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➗ MathFree
Ellipse foci calculator
Enter the semi-major and semi-minor axes of an ellipse and get its two foci: axes of 5 and 3 put them at (4, 0) and (−4, 0), 8 apart, with an eccentricity of…
A
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➗ MathFree
Ellipse latus rectum calculator
Enter the two semi-axes of an ellipse and get the chord through a focus: semi-axes of 5 and 3 give a semi-latus rectum of 1.8 and a full latus rectum of 3.6…
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➗ MathFree
Ellipse perimeter calculator
Get the distance around an ellipse from its two semi-axes with Ramanujan's first approximation: semi-axes of 5 and 3 give about 25.526986393759, using one…
A
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➗ MathFree
Ellipse circumference
Give the two semi-axes of an ellipse and get its circumference from Ramanujan's second formula: semi-axes of 5 and 3 give about 25.53, with a shape value h of…
P
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➗ MathFree
Ellipse segment area calculator
Enter the two semi-axes of an ellipse and where a vertical line cuts it, and get the smaller piece: semi-axes of 5 and 3 cut 2 from the centre leave a segment…
A
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➗ MathFree
Ellipse general to standard form calculator
Enter the six coefficients of a general second-degree equation and get the ellipse in standard form: x² + 4y² − 4 = 0 becomes an ellipse centred at the origin…
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➗ MathFree
Ellipsoid semi-axis from volume calculator
Recover the missing semi-axis of an ellipsoid from its volume — a volume of 8π with semi-axes 3 and 2 leaves a third semi-axis of 1.
A
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➗ MathFree
Ellipsoid surface area calculator
Get the skin area of an ellipsoid from its three semi-axes: 3, 2 and 1 give close to 49 square units, while three equal semi-axes of 5 give exactly 100π.
A
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➗ MathFree
Equilateral triangle area from side calculator
Enter one side and get the equilateral triangle's area, height and perimeter at once: side 6 gives an area of 9√3, about 15.5885, a height of about 5.1961 and a…
S
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➗ MathFree
External tangent length calculator
Get the length of the outer common tangent between two separate circles: radii 5 and 3 with centres 10 apart give 4√6, just under 10.
S
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➗ MathFree
Foot of perpendicular calculator
Find the point on a line closest to a given point: a perpendicular dropped from the origin onto the line 3x + 4y − 5 = 0 lands at (0.6, 0.8), at distance 1.
S
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➗ MathFree
Conical frustum slant height calculator
Get the slant height of a truncated cone from its two radii and height, so radii 3 and 4 with a height of 5 give √26, about 5.099.
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➗ MathFree
Hendecagon apothem calculator
Turn the measured side of a regular 11-sided polygon into its apothem, the distance from the centre to the middle of each edge, so side 1 gives 1 ÷…
P
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➗ MathFree
Hendecagon area calculator
Get the area of a regular 11-sided polygon from its side length, so side 5 gives about 234.141 square units and a perimeter of 55.
A
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➗ MathFree
Hendecagon area from apothem
Get the area of a regular 11-sided polygon from its apothem, the distance from the centre to a side: apothem 1 gives 11·tan(π/11).
P
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➗ MathFree
Heptagon area calculator
A regular heptagon with side 5 covers about 90.848 square units and has a perimeter of 35. Enter any side and the seven-sided area arrives with the apothem and…
A
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➗ MathFree
Heptagon area from apothem calculator
Get a regular heptagon's area straight from its apothem, the centre-to-side distance, so apothem 5 gives 7 × 5² × tan(π/7).
A
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➗ MathFree
Heptagon circumradius calculator
Get the radius of the circle that passes through every corner of a regular heptagon from its side, so side 4 gives about 4.60953 and a perimeter of 28.
A
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➗ MathFree
Heptagon perimeter calculator
The outline of a regular heptagon is seven equal sides long, so a side of 5 gives a perimeter of 35.
P
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➗ MathFree
Hexagon apothem calculator
Turn a hexagon's edge length into its inner radius, so a side of 2 gives an apothem of √3, about 1.732050807569.
S
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➗ MathFree
Hexagon area calculator
Get the area of a regular hexagon from one edge length, so side 6 gives 54√3, about 93.531, with a perimeter of 36 and a long diagonal of 12.
A
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➗ MathFree
Hexagon area from apothem
Get the area of a regular hexagon from its apothem, the distance from the centre to a flat side, so apothem 1 gives 2√3 square units.
P
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➗ MathFree
Hexagonal antiprism calculator
Enter one edge length and get the volume, total surface and height of a uniform hexagonal antiprism: edge 1 gives a surface of exactly 6√3.
A
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➗ MathFree
Hexagonal bipyramid calculator
Get the volume and surface of a regular hexagonal bipyramid from its equator side and half-height: side 2 with half-height 3 gives a volume of 12√3 and a…
A
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➗ MathFree
Hollow cylinder volume calculator
Get the volume of material in a tube wall from its outer radius, inner radius and height, so 5, 3 and 10 give 160π, the gap between an outer 250π and an inner…
A
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➗ MathFree
Homothety dilation calculator
Find where a point lands under a homothety: the point (4, 2) scaled by 2 about the origin goes to (8, 4).
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➗ MathFree
Hyperbola asymptotes calculator
Get both asymptotes of a hyperbola from its semi-axes: semi-axes 3 and 4 give slopes of ±4/3, so the guide lines are 4x − 3y = 0 and 4x + 3y = 0.
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➗ MathFree
Hyperbola latus rectum calculator
Get the full width of a hyperbola through its focus from the two semi-axes: 3 and 4 give a latus rectum of 2 × 4² ÷ 3, a little over 10.
A
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➗ MathFree
Hyperbola vertices and directrix calculator
Enter the semi-axes 3 and 4 and the hyperbola gets vertices at (3, 0) and (−3, 0) and directrices at x = ±1.8, shown with c of 5 and eccentricity 5/3.
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➗ MathFree
Icosahedron circumradius calculator
An icosahedron with an edge of 2 fits inside a sphere of radius about 1.9021 that touches all 12 vertices.
A
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➗ MathFree
Icosahedron midradius calculator
An icosahedron with an edge of 2 has a midradius of about 1.618: that is the radius of the sphere touching all thirty edges at their midpoints.
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➗ MathFree
Icosahedron surface area calculator
An icosahedron with an edge of 2 has 20 faces of √3 each, so its outer skin is 20√3 square units. Enter any edge and get the total surface plus one face, ready…
A
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➗ MathFree
Icosidodecahedron calculator
An icosidodecahedron with an edge of 1 has a surface of about 29.306 square units and a volume of (45 + 17√5)/6 cubic units.
P
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➗ MathFree
Internal tangent length calculator
Two circles with radii 3 and 2 whose centers are 10 apart have an internal common tangent of 5√3, measured between the two touch points of the crossed line.
A
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➗ MathFree
Kite area calculator
A kite with diagonals 6 and 8 covers an area of 24, half the product of the two. Enter both diagonals in the same unit and get the area in square units, with…
A
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➗ MathFree
Kite perimeter calculator
A kite with sides 5 and 8 has a perimeter of 26, because its outline holds two sides of each length: 2 × (5 + 8).
P
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