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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
Perpendicular bisector calculator
For the segment from (0, 0) to (4, 6), the perpendicular bisector passes through the midpoint (2, 3) and is the line 2x + 3y − 13 = 0.
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➗ MathFree
Point in triangle checker
The point (1, 1) lies inside the triangle with corners (0, 0), (4, 0) and (0, 3), whose area is 6.
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➗ MathFree
Point to plane distance calculator
The point (1, 1, 1) sits four thirds of a unit, 1.333333333333, from the plane 2x + y + 2z − 9 = 0.
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➗ MathFree
Point-slope form calculator
Enter a point and a slope and get the line's equation two ways: the point (1, 2) with slope 3 gives y − 2 = 3(x − 1), and the same line crosses the y-axis at…
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➗ MathFree
Number of sides from interior angle calculator
Enter one interior angle of a regular polygon and get its number of sides: 108° gives 5 sides, a pentagon, with an exterior angle of 72°.
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➗ MathFree
Sum of interior angles calculator
Enter the number of sides and get the total of all interior angles of any simple polygon: a pentagon adds up to 540°, regular or not, because it splits into…
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➗ MathFree
Prism volume calculator
Enter the area of the base and the height of a right prism and get its volume: a base of 12 and a height of 5 hold 60 cubic units, whatever the shape of the…
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➗ MathFree
Prolate spheroid calculator
Enter the equatorial and polar radii of a stretched sphere, such as a rugby ball or an elongated tank end, and get its exact volume, four thirds of π times a²…
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➗ MathFree
Pyramid lateral surface area
Enter the base perimeter and the slant height of a regular pyramid and get the area of its triangular faces: a perimeter of 40 and a slant height of 12 give…
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➗ MathFree
Quadrilateral area from diagonals calculator
Enter the two diagonals of a quadrilateral and the angle between them and get its area: diagonals of 6 and 8 crossing at 90° enclose 24, half their product…
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➗ MathFree
Quarter circle area calculator
Enter a radius and get the area of a quarter circle and the length of its curved edge: a radius of 2 gives an area of exactly π and an arc of the same length.
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➗ MathFree
Rectangle area calculator
Enter the length and width of a rectangle and get its area: a length of 8 and a width of 5 give 40, the figure you need for a floor, a patio slab or a garden…
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➗ MathFree
Rectangle sides from area and ratio
Give the area of a rectangle and how many times longer it is than wide, and get both sides: an area of 48 with a ratio of 3 gives a length of 12 and a width of…
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➗ MathFree
Rectangle perimeter calculator
Enter the length and width of a rectangle and get the distance around it: 10 and 5 give a perimeter of 30, twice their sum, ready for fencing, trim or…
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➗ MathFree
Reflect a point over the x-axis calculator
Enter a point and get its mirror image across the x-axis: (3, 5) becomes (3, −5), because only the vertical coordinate changes sign.
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➗ MathFree
Reflect a point over the y-axis calculator
Enter a point and get its mirror image across the y-axis: (3, 4) becomes (−3, 4), since the horizontal coordinate changes sign and the height stays the same.
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➗ MathFree
Reflect a point over y=x calculator
Enter a point and get its mirror image across the diagonal line y = x: (3, 7) becomes (7, 3), because the two coordinates simply trade places.
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➗ MathFree
Regular polygon central angle calculator
Enter the number of sides of a regular polygon and get the angle at its center between two neighbouring corners: a regular pentagon has a central angle of 72°…
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➗ MathFree
Regular polygon diagonal lengths
Enter the number of sides and the circumradius of a regular polygon and get each distinct diagonal length: a hexagon with a radius of 1 has 6 short diagonals of…
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➗ MathFree
Rhombic triacontahedron calculator
Enter the edge length of a rhombic triacontahedron, the 30-face Catalan solid behind many zomes and decorative shells, and get its volume and surface area: an…
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➗ MathFree
Rhombicosidodecahedron calculator
Enter the edge length of a rhombicosidodecahedron and get its exact volume and total surface area: an edge of 1 gives a volume of about 41.6153237825 and a…
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➗ MathFree
Rhombicuboctahedron calculator
Enter the edge length of a rhombicuboctahedron, the solid of 8 triangles and 18 squares, and get its volume and surface area: an edge of 1 gives about…
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➗ MathFree
Rhombus area from diagonals calculator
Enter the two diagonals of a rhombus and get its area as half their product: diagonals of 6 and 8 give an area of 24, with no side length or angle needed.
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