Math
1,470 math calculators: percentages, fractions, equations, geometry, trigonometry, statistics and number theory. Each one shows the method in plain words, so you get the answer and understand how it was reached, free in your browser.
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.
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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).
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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…
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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).
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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.
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Heptagon perimeter calculator
The outline of a regular heptagon is seven equal sides long, so a side of 5 gives a perimeter of 35.
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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.
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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.
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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.
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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.
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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…
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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…
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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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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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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.
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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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Icosahedron circumradius calculator
An icosahedron with an edge of 2 fits inside a sphere of radius about 1.9021 that touches all 12 vertices.
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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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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…
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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.
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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.
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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…
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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).
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Line from intercepts calculator
Intercepts 3 and 2 give the line x/3 + y/2 = 1, which is also 2x + 3y − 6 = 0 and has a slope of −2/3.
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Line plane intersection calculator
A line from the origin heading along (1, 1, 1) hits the horizontal plane at height 1 at the point (1, 1, 1), with t equal to 1.
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Line standard form converter
Slope 2 and intercept 3 become 2x − y = −3 in standard form, ready for a rubric or a distance formula.
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Lune area calculator
Two circles of radii 5 and 4 with centers 5 apart give a lune of 20.7940112152 square units, the sum of the two circular segments on either side of the common…
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Lune of Hippocrates calculator
With a leg of 6, the lune of Hippocrates has an area of 18, exactly the same as the isosceles right triangle it is built on.
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Manhattan distance calculator
From (0, 0) to (3, 4) the Manhattan distance is 7, not the straight-line 5, because you only move along the grid: 3 across plus 4 up.
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Medial triangle calculator
For the triangle (0, 0), (6, 0), (0, 6), the side midpoints are (3, 3), (0, 3) and (3, 0), and the medial triangle they form has area 4.5, a quarter of 18.
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Napkin ring volume calculator
A napkin ring 2 units high holds about 4.1887902048 cubic units, whether it came from a huge sphere with a fat hole or a small one with a thin hole: only the…
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Nine-point circle calculator
For the right triangle (0, 0), (4, 0), (0, 3), the nine-point circle is centered at (1, 0.75) with a radius of 1.25, half the circumradius.
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Nonagon apothem calculator
A regular nonagon with sides of 4 has an apothem of about 5.49495, the distance from its center to the middle of each side.
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Nonagon area from apothem
A regular nonagon whose center sits 1 unit from each side has an area of 9·tan(π/9), about 3.275732108396 square units.
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Nonagon perimeter calculator
A regular nonagon with sides of 5 has a perimeter of 45: nine equal sides added together. Enter one side length and get the full boundary in the same unit…
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Oblique cone volume calculator
An oblique cone with base radius 3 and vertical height 5 holds about 47.1238898038 cubic units, exactly as much as an upright cone of the same size.
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Octagon apothem calculator
A regular octagon with sides of 2 has an apothem of exactly 1 + √2, about 2.414213562373: the distance from its center to the middle of every side.
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Octagon area calculator
A regular octagon with sides of 1 encloses 2(1 + √2), about 4.828427124746 square units, and the area grows with the square of the side.
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Octagon area from apothem
Measure 1 unit from the center of a regular octagon to any side and its area is 8(√2 − 1), about 3.313708498985 square units.
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Octagon circumradius calculator
The circle through all eight corners of a regular octagon with sides of 4 has a radius of about 5.22625.
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Octagonal prism calculator
A regular octagonal prism with base side 2 and height 5 has a base perimeter of 16 and 80 square units of wall.
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Octagonal pyramid calculator
With base side 2 and height 3, a regular octagonal pyramid holds exactly its base area in volume, since a pyramid is a third of base times height.
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Octahedron circumradius calculator
An octahedron with edge 2 has a circumradius of exactly √2, the radius of the sphere touching all six vertices.
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Octahedron inradius calculator
An octahedron with edge 2 has an inradius of 0.8164965809: the edge times √6, divided by six. Enter one edge to get the inscribed sphere for homework…
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Octahedron surface area calculator
An octahedron with edge 2 has 13.8564064606 square units of skin: eight equilateral faces of 1.7320508076 each.
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Parabola arc length calculator
The curve y = x² is 4.646783762433 units long from 0 to 2 along x. Enter the coefficient and the two bounds to get the exact arc length of a parabolic arch…
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Parabola from focus and directrix
A focus at (0, 1) with a directrix one unit below the origin gives the parabola x² = 4y, with its vertex at the origin and a focal length of 1.
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Parabola vertex form calculator
Enter 1, −4 and 3 and y = x² − 4x + 3 becomes y = (x − 2)² − 1, with its vertex at (2, −1). Check a completed-square answer without flipping a sign in the…
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Parabolic segment area calculator
A parabolic segment with base 6 and height 3 has an area of 12: two thirds of base times height, and four thirds of the triangle of area 9 inside it.
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Parallelogram area calculator
A parallelogram with base 10 and height 5 covers 50 square units: base times the perpendicular height, never the slanted side.
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Parallelogram area
Sides 5 and 8 meeting at 60 degrees enclose 34.641016151378 square units. Enter two adjacent sides and the angle between them to get the area of a plot, room or…
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Parallelogram height calculator
A parallelogram with an area of 50 on a base of 10 stands 5 units high: the height is the area divided by the base.
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Parallelogram perimeter calculator
Adjacent sides of 5 and 8 give a parallelogram perimeter of 26: twice their sum, because opposite sides are equal.
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Pentagon area calculator
A regular pentagon with side 1 covers 1.720477400589 square units, and the area grows with the square of the side.
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Pentagon area from apothem
A regular pentagon whose centre sits 1 unit from each side covers 3.632712640027 square units. Enter that centre-to-side distance, the apothem, to get the area…
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Pentagon circumradius calculator
A regular pentagon with side 4 fits inside a circle of radius 3.402603233408, the circle through all five vertices.
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Pentagon perimeter calculator
A regular pentagon with 6-unit sides has a perimeter of 30, because all five sides are equal. Enter one side to get the total frame, trim or fence length around…
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Pentagonal antiprism calculator
A pentagonal antiprism with every edge 1 encloses 1.578689325833 cubic units and has 7.7710818201 square units of surface: two pentagons plus a twisted band of…
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Pentagonal bipyramid calculator
A pentagonal bipyramid with edge 1 holds 0.603005664792 cubic units and has 4.330127018922 square units of surface across its ten equilateral faces.
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Pentagram area calculator
A five-pointed star whose tips sit 1 unit from the centre has a filled area of 1.122569941449 square units, against 2.377641290738 for the pentagon on the same…
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