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.
Line equation from two points
Give two points and get the line through them: (0, 0) and (2, 4) give y equals 2x, which is 2x minus y equals 0 in standard form, with slope and intercept…
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Midpoint calculator
The midpoint of the segment from (0, 0) to (4, 6) is (2, 3): the average of the two x values and of the two y values.
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Oblique prism volume
An oblique prism with a base area of 12 and a perpendicular height of 5 holds 60 cubic units, just like an upright prism with the same base and height.
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Octahedron calculator
One edge length fixes every measure of a regular octahedron: with an edge of 2 the circumradius is 1.4142135624 and the volume 3.7712361663.
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Parabola calculator
For y = x², the vertex sits at the origin, the focus 0.25 above it and the directrix 0.25 below. Enter a, b and c to get the vertex, focus, directrix, axis of…
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Paraboloid volume calculator
A paraboloid with base radius 3 and height 4 holds 56.5486677646 cubic units, exactly half of the 113.0973355292 in the cylinder around it.
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Parallel or perpendicular lines
Slopes 2 and −0.5 multiply to −1, so the two lines are perpendicular and meet at 90 degrees. Enter two slopes, or mark one line as vertical, to learn whether…
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Pentagonal prism calculator
A regular pentagonal prism 5 units tall on a pentagon of side 2 holds 34.409548011779 cubic units, with 50 square units of rectangular walls.
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Point to line distance
The origin lies exactly 1 unit from the line 3x + 4y − 5 = 0. Enter the line's three coefficients and a point to get the shortest distance, its sign and whether…
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Polygon diagonals calculator
Enter the number of sides and get how many diagonals the polygon has: a hexagon has 9, a pentagon 5, a quadrilateral 2 and a triangle none, all from the formula…
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Polygon perimeter from coordinates
Enter the corners of a polygon in order and get the length of its boundary: the rectangle (0, 0), (3, 0), (3, 4), (0, 4) has a perimeter of 14, closing edge…
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Quadrilateral area calculator
Type the four corners of a quadrilateral in boundary order and get the area it encloses: (0, 0), (4, 0), (4, 3), (0, 3) give 12, with a perimeter of 14 and…
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Rectangular prism calculator
Enter the length, width and height of a box and get three answers at once: edges of 3, 4 and 5 give a volume of 60, a surface area of 94 and the…
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Regular polygon calculator
Enter the number of sides and the side length of a regular polygon and get all its measures at once: a hexagon with sides of 2 has a perimeter of 12, interior…
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Right triangle calculator
Give any two sides of a right triangle and get the rest: legs of 3 and 4 return a hypotenuse of 5, an area of 6 and both acute angles in degrees.
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Section formula calculator
Locate the point that splits a segment in a given ratio: from A (2, 3) to B (8, 7) at 1:2, it sits a third of the way along, at x of 4 and y of 4 and a third.
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Circular sector area and perimeter
Give the radius and central angle of a pie-slice sector and get its area: a quarter circle of radius 5 at 90 degrees covers 25π/4, with an arc of 5π/2 and a…
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Circular segment area
Get the area between a chord and its arc from the radius and central angle: with a radius of 10 at 90 degrees, the segment is the quarter sector minus a…
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Sphere volume calculator
Enter either the radius or the diameter of a sphere and get the rest: a radius of 3 gives a diameter of 6, a volume of four-thirds π times 3 cubed, and the…
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Spherical cap calculator
Get the volume and the curved dome area of a spherical cap together from two numbers, the sphere radius and the cap height, with the volume given by (1/3)πh²(3R…
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Spherical sector calculator
Solve the cone-plus-cap solid cut from a sphere in one step: a sphere of radius 5 with a cap 2 high gives a rim radius of 4, plus the volume and the total…
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Tank volume calculator
Turn a dipstick or level reading into liquid volume for a horizontal or vertical cylindrical tank: a horizontal tank of radius 1 and length 10 filled to depth 1…
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Tetrahedron volume calculator
Enter one edge and get every main measure of a regular tetrahedron at once: an edge of 2 gives a volume of 0.942809041582 and a surface of 6.928203230276, plus…
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Trapezoid area calculator
Find the area of a trapezoid from its two parallel sides and its height, together with the midsegment: bases 8 and 12 with a height of 5 give a midsegment of 10…
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30-60-90 triangle calculator
Solve a 30-60-90 triangle from a single side. A short leg of 5 gives a long leg of 8.660254037844, a hypotenuse of 10 and an area of 21.650635094611.
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AAS triangle calculator
Solve an angle-angle-side triangle in one step: with angles of 40° and 60° and a side of 7 opposite the first, the third angle is 80° and the other sides are…
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Triangle area from coordinates
Get the area of a triangle straight from its three corner points: (0, 0), (4, 0) and (0, 3) enclose an area of 6.
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ASA triangle calculator
Two angles and the side between them fix a triangle completely: from 40°, 60° and an included side of 10 you get a third angle of 80° and sides of…
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Triangle centroid calculator
Find the center of a triangle by averaging its corners: the vertices (0, 0), (6, 0) and (0, 6) give a centroid at (2, 2).
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Triangle orthocenter from coordinates
Find where the three altitudes of a triangle cross from its corner coordinates: for (0, 0), (4, 0) and (0, 3) the orthocenter sits on the right angle at (0, 0).
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SAS triangle calculator
Two sides and the angle between them give you the whole triangle: sides 3 and 4 with 90° between them close with a third side of 5, an area of 6 and angles of…
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Triangular prism calculator
Enter the three sides of the triangular base and the length to get volume and surface: a 3-4-5 base stretched to a length of 10 holds a volume of 60 with a…
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Two circles intersection
Find where two circles cross from their centers and radii: circles of radius 5 centered at (0, 0) and (8, 0) meet at (4, 3) and (4, -3).
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Wedge volume calculator
Work out the volume of a ramp-shaped solid from its base and two end heights: a 10 by 4 base sloping from a height of 6 down to 2 holds 160.
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Arithmetic sequence calculator
Start at 2 and add 3 each time: the fifth term is 14, and the first five terms add up to 40. Enter the first term, the common difference and a position to get…
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Arithmetic series sum calculator
The numbers from 1 to 10 add up to 55, and the even numbers from 2 to 20 add up to 110. Enter the first term, the last term and how many terms there are, and…
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Catalan number calculator
Get the exact n-th Catalan number: C(5) is 42 and C(10) is 16796, written out digit for digit with no rounding, even for very large n.
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Double factorial calculator
7!! is 7 × 5 × 3 × 1, which makes 105, and 6!! is 6 × 4 × 2, which makes 48: the double factorial multiplies only the numbers that share the parity of n.
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Factorial calculator
5! is 120 and 10! is 3628800. Enter a whole number from 0 to 5000 and get its exact factorial with every digit, never a rounded or approximate value, ready for…
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Fibonacci number calculator
The 10th Fibonacci number is 55, counting F1 and F2 as 1. Enter a position up to 10000 and get the exact term, even when it runs to hundreds of digits, or ask…
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Sum of Fibonacci series
The first 10 Fibonacci numbers add up to 143, which is F(12) minus 1. Enter how many terms to add, up to 1000, and get the exact sum and the list of terms…
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Infinite geometric series sum
Enter the first term and the common ratio to get the total of an infinite geometric series: a first term of 1 with a ratio of 0.5 adds up to 2.
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Hexagonal number calculator
The 5th hexagonal number is 45. Enter a position to get its exact hexagonal number, every digit kept even for huge results, or enter any whole number to learn…
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Look-and-say sequence
Read a string of digits aloud in runs and write down what you hear: starting from 1, the fifth term is 111221.
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Padovan sequence calculator
P(10) is 12: each Padovan number adds the terms two and three places back, starting from three ones, so the list runs 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12.
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Pentagonal number calculator
The 5th pentagonal number is 35, from n(3n − 1)/2. Enter an index to get its pentagonal number, or enter any whole number to find out whether it belongs to the…
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Polygonal number calculator
Choose the number of sides and the position in the sequence to get any polygonal number exactly: the fifth pentagonal number is 35 and the tenth square is 100.
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Primorial calculator
Multiply every prime up to n and get the exact result: 10# is 2 × 3 × 5 × 7, which is 210, along with the list of primes and how many there are.
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Square pyramidal number
Get the n-th square pyramidal number, the count of balls stacked in a square-based pyramid: for n of 5 it is 55, the sum of the first five squares.
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Stern diatomic / Stern-Brocot sequence
Get any term of Stern's diatomic sequence from its index: s(10) is 3, worked out in whole-number steps that halve the index each time, so even large indices…
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Sum of first n even numbers
Add 2 + 4 + … + 2n in one step with the formula n(n + 1): with n of 5 the total is 30, and the result stays an exact whole number for any n up to ten million.
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Sum of first n odd numbers
Add the first n odd numbers in one step, because they always total n squared: the first 10 odd numbers add up to 100 and the first 100 add up to 10000.
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Sum of first n squares
Add the first n squares in one step with n(n + 1)(2n + 1)/6: 1² + 2² + 3² + 4² + 5² is 55, and every n from 0 to ten million gives an exact whole number.
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Sylvester sequence calculator
Each term of Sylvester's sequence is 1 plus the product of all the terms before it: 2, 3, 7, 43, 1807, and the term at position 5 is 3263443.
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Aliquot sum calculator
The proper divisors of 12 add up to 16, which is more than 12, so 12 is abundant; 6 gives exactly 6 and is perfect.
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Amicable numbers checker
220 and 284 are amicable: the proper divisors of 220 add up to 284, and those of 284 add up to 220.
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Armstrong number checker
153 is an Armstrong number: it has three digits, and 1 + 125 + 27, the cubes of 1, 5 and 3, add back up to 153.
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Automorphic number checker
25 is automorphic because 25 squared is 625, which ends in 25. Enter any non-negative whole number to see its exact square, its digit count and whether the…
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Digit sum calculator
The digits of 12345 add up to 15. Enter any integer, choose a base from 2 to 36 when you need one other than ten, and see every digit together with their total.
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Digital root calculator
9875 becomes 29, then 11, then 2: its digital root is 2, reached in 3 steps. Enter any non-negative whole number, even one with up to 1000 digits, and see the…
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