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.
Tetrahedron inradius calculator
Find the radius of the largest ball that fits inside a regular tetrahedron and touches all four faces: an edge of 2 gives √6/6, about 0.408248290464.
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Tetrahedron midradius calculator
Get the midradius of a regular tetrahedron, the radius of the sphere that grazes each of its six edges at the midpoint: an edge of 2 gives √2/2, about…
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Tetrahedron surface area calculator
Get only the outer skin of a regular tetrahedron, the area you paint, plate, wrap or cut as a paper net: an edge of 2 gives a total surface of 6.9282032303…
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Trapezoid diagonal calculator
Get both diagonals of a trapezoid from its two bases, two legs and height. Bases 6 and 12 with legs of 5 and a height of 4 give two diagonals of 9.848857801796…
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Trapezoid height from area calculator
Work backwards from a trapezoid's area to its perpendicular height: an area of 60 with bases 8 and 12 gives a height of 6, with a midsegment of 10 to check the…
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Trapezoid perimeter calculator
Add up all four sides of a trapezoid to get the distance around it: bases 8 and 12 with legs of 5 and 5 give a perimeter of 30, the length of fence, trim or…
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Triakis tetrahedron calculator
Get the volume and surface of a triakis tetrahedron, the twelve-faced solid made by raising a small pyramid on each face of a tetrahedron: a shorter edge of 1…
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Triangle altitude lengths calculator
Get all three heights of a triangle from its sides alone: for sides 3, 4 and 5 the area is 6 and the heights are 4, 3 and 2.4.
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Triangle angle bisector lengths
Get the three internal angle bisector lengths from the sides alone: a 3-4-5 triangle has bisectors of 4.216370213558, 3.35410196625 and 2.424366106925.
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Triangle inequality checker
Check in one step whether three lengths can close into a triangle: 3, 4 and 5 can, while 1, 2 and 3 cannot, because 1 plus 2 only equals 3.
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Triangle inradius calculator
A 3-4-5 triangle has room for an inscribed circle of radius 1: the calculator divides the area, 6, by half the perimeter, also 6.
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Triangle semiperimeter calculator
Add the three sides and halve the total: for 3, 4 and 5 the perimeter is 12 and the semiperimeter 6.
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Triangle type by angles
Enter three interior angles and see whether the triangle is acute, right or obtuse: 60°, 60° and 60° is acute, 90°, 45° and 45° is right, and 120°, 30° and 30°…
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Triangular pyramid calculator
Get the volume and surface area of a regular triangular pyramid from just two measurements: a base edge of 2 and a height of 3 give a volume of 1.732050807569…
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Truncated cube calculator
Enter one edge length and get the volume and surface area of a truncated cube: an edge of 1 gives a volume of 13.599663291074 and a surface of 32.434664363615.
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Truncated dodecahedron calculator
A truncated dodecahedron with an edge of 1 encloses a volume of 85.039664559371 and has a surface of 100.990760153102, shared by twelve regular decagons and…
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Truncated icosidodecahedron
With one edge length you get the volume and surface of a truncated icosidodecahedron: an edge of 1 gives a volume of 206.803398874989 and a surface of…
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Truncated octahedron calculator
From one edge length you get the volume and surface area of a truncated octahedron: an edge of 1 means a volume of 11.313708498985 and a surface of…
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Truncated tetrahedron calculator
Find the volume and surface of a truncated tetrahedron from the length of one edge; an edge of 1 gives 2.710575994548 in volume and 12.124355652982 in surface…
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Direction angle of a vector calculator
Get the direction of a 2D vector from its components: the vector (3, 4) points at 53.130102354156° from the positive x-axis, or 0.927295218002 radians, with a…
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Collatz sequence calculator
Start from any positive whole number and watch the Collatz rule run to 1: from 6 the path is 6, 3, 10, 5, 16, 8, 4, 2, 1, taking 8 steps and peaking at 16.
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GCD and LCM of multiple numbers free
For twelve, eighteen and twenty-four, the greatest common divisor is 6 and the least common multiple is 72, both from one list.
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a+bi form converter
Enter 3 and 4 and you get 3+4i, a modulus of 5 and an argument of 53.130102 degrees, or 0.927295 radians.
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AAS triangle calculator
With angles of 50 and 60 degrees and a side of 8 opposite the first, the third angle is 70 degrees and the whole triangle is fixed.
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ABC triangle solver
Sides of 3, 4 and 5 come back as a right triangle, with a 90° angle opposite the longest side. Enter whatever three values you know and the solver picks the…
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Absolute change calculator
The absolute change between 128.5 and 95.25 is 33.25, whichever value you type first. Enter two numbers to see how far apart they are, without the sign, for…
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Absolute value equation solver
The equation |2x − 4| = 10 splits into two linear equations whose solutions are −3 and 7. Enter a, b and c of |ax + b| = c to see every real solution, including…
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Absolute value inequality solver
|2x − 4| < 10 holds for every x strictly between −3 and 7. Enter a, b, c and the comparison sign to get the interval, or the two outer rays for greater-than…
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Acute triangle calculator
Sides of 4, 5 and 6 form an acute triangle, because 6 squared, 36, is less than 41, the sum of the other two squares.
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Add or subtract polynomials
(2x² − 5) + (x + 3) gives 2x² + x − 2. Type each polynomial's coefficients from the highest power down to the constant; polynomials of different degree are…
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Adding and subtracting fractions
3/4 + 2/5 gives 23/20, or 1 3/20 as a mixed number. Choose plus or minus, enter two fractions and get the exact result in lowest terms, with a negative answer…
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Adding fractions
1/2 + 1/3 is exactly 5/6, with 0.833333 shown alongside only as a display decimal. Enter two fractions and get their sum reduced to lowest terms, plus the…
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Addition calculator
Add 0.1 and 0.2 and get exactly 0.3, not 0.30000000000000004, and total a column of invoices without opening a spreadsheet.
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Adjoint matrix calculator
For the matrix with rows (2, 1) and (1, 3), the adjoint has rows (3, −1) and (−1, 2) and the determinant is 5.
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Logical AND calculator
True AND true is true; true AND false, false AND true and false AND false are all false. Combine two conditions, such as accepted the terms and confirmed the…
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Angle of a right triangle from two sides, in degrees
With an opposite side of 3 and an adjacent side of 4, the angle is 36.8698976458 degrees. Name the two sides you know by their role and the right inverse…
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Antilog calculator
The antilog of 2 in base 10 is 100, and the antilog of 3 in base 2 is 8. Enter the value and any positive base to turn a logarithm back into the real quantity.
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Arccos calculator
The inverse cosine of 0.5 is 60 degrees, or 1.047197551197 radians. Enter any value from -1 to 1 and get the one angle between 0 and 180 degrees with that…
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Arcsin calculator
The inverse sine of 0.5 is 30 degrees, or 0.523598775598 radians. Enter any value from -1 to 1 and get the one angle between -90 and 90 degrees with that sine…
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Arctangent calculator
Enter the ratio 1 and get its arctangent: 0.785398163397 radians, which is 45 degrees. Any finite number works, however extreme, and the angle always stays…
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Arcus tangent calculator
The arcus tangent of 1 is 45 degrees, and of −1 it is −45 degrees. Unlike the inverse sine or cosine, it accepts any finite number, and you choose whether the…
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Area calculator
A circle with a radius of 2 covers 12.566371 square units, and a 5-by-3 rectangle covers 15. Pick a square, rectangle, triangle or circle, enter only the…
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Oblique triangle area calculator
Two sides of 5 and 8 with a 60-degree angle between them enclose about 17.320508 square units. Enter the two sides and the angle they form, and get the area of…
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Obtuse triangle area calculator
A base of 10 with a height of 4 gives an area of 20. Enter a base and its height, or the three sides, and from sides the calculator first proves the triangle is…
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Area of a circle calculator
A circle with a radius of 5 has an area of 78.539816, computed with the full value of π, 3.141592653589793, never a rounded 3.14.
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Area of a trapezoid calculator
Bases of 10 and 6 with a height of 4 give an area of 32: add the two parallel sides, halve the sum and multiply by the height.
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Calculate percentage change
Measure how much something moved against where it started: going from 80 to 100 is a rise of 20, a 25% increase, labeled as such so the direction is never in…
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Calculate percentage of an amount
Get the share itself in one step: 18% of 250 is 45, and the reverse question works too, since 45 out of 180 is 25%.
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Simplify and scale a ratio
Simplify a ratio and share out a total in one go: 18:24 reduces to 3:4, and with a total of 140 each of the seven parts is worth 20, so the first term receives…
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Convert ratio to percentage
See what share of the whole each part of a ratio is: 3:7 becomes 30 % and 70 %, and 30:70 gives exactly the same.
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Rule of three calculator
Find the missing value of a proportion: if 4 notebooks cost 10, then 6 notebooks cost 15. Choose direct when both quantities rise together, or inverse when one…
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Calculate screen diagonal from dimensions
Measure the visible panel and get its size corner to corner, so a screen 3 inches wide and 4 inches tall has a 5-inch diagonal.
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Bitwise calculator
60 AND 13 is 12, 60 OR 13 is 61 and 60 XOR 13 is 49. Combine two 32-bit integers with AND, OR, XOR or a shift and get exactly what C, Java or JavaScript would…
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Box method calculator
(2 + 3x) times (4 + 5x) fills four boxes with 8, 10x, 12x and 15x², and the two middle boxes combine into the x term of the product.
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Cartesian to polar converter
Turn x and y into polar form: the point (3, 4) sits 5 units from the origin at an angle of 0.927295218002 radians.
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Catenary curve height calculator
Find how high a hanging cable sits at any distance from its lowest point: with a curve parameter of 10, the height 5 units out is 11.27626.
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Ceiling function calculator
Round any number up to the next whole number: 4.2 becomes 5, −4.2 becomes −4 and 7 stays 7. You also see whether the value was already an integer, so negative…
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Center of an ellipse
Get the center of an ellipse straight from its general equation: 4x² + 9y² − 8x − 36y + 4 = 0 is centered at (1, 2).
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Center of mass calculator
Find where a set of point masses balances: masses of 2, 4 and 3 at (0, 0), (6, 0) and (0, 6) balance at (2.6666666667, 2), with a total mass of 9.
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Central angle calculator
Turn an arc length and a radius into the angle at the center: an arc of 15.708 on a circle of radius 10 spans 90.00021045915 degrees, or 1.5708 radians.
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