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.
Multiplicative inverse calculator
Get the reciprocal of any non-zero number: 4 inverts to 0.25 and −8 to −0.125. The two are multiplied back next to the answer, so you can see the product is…
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Multiplicative inverse modulo n
Find the number that undoes multiplication by an integer modulo n: the inverse of 3 modulo 11 is 4, because 3 × 4 = 12 leaves remainder 1.
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Multiplying fractions
Multiply two fractions and get the product already in lowest terms: 2/3 times 3/4 is 6/12, which cancels by 6 to 1/2.
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Multiplying radicals calculator
Multiply two roots and get the product in simplest form: √8 times √2 is 4. Roots with different indices are first brought to a common index, then every perfect…
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Natural log calculator
Find the natural logarithm of any positive number: ln 1 is 0, ln e is 1 and ln 10 is about 2.30258509299.
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Oblique triangle calculator
With sides 8 and 6 and a 40° angle between them, the calculator finds the third side and the other two angles and reports an obtuse triangle.
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Obtuse triangle checker
Sides 3, 4 and 6 form an obtuse triangle, because 3² + 4² = 25 is less than 6² = 36. Enter any three side lengths to get a yes or no with that comparison, no…
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Bitwise OR calculator
5 OR 3 gives 7: in binary, 101 and 11 line up from the right and every column holding a 1 keeps it, giving 111.
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Pentagon calculator
A regular pentagon with sides of 2 has a perimeter of 10 and an area of about 6.8819. Enter the side length to get both measures together with the formula…
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Percentage change calculator
From 80 to 100 is a rise of 25 %: the difference of 20 divided by the old value of 80, times 100. Enter an old and a new value to get the signed percent change…
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Percentage difference calculator
10 and 6 differ by 50 %: their gap of 4 is half of their average, 8. Enter two values to get the percentage difference measured against their mean, with neither…
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Percent of time calculator
15 minutes into a 60-minute meeting, 25 % of the time is gone. Enter the time elapsed and the total duration in the same unit to get the share used, the time…
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Percentage of a percentage calculator
20% of 50% is 10%, because (20 × 50) / 100 = 10. Enter two percentages to get the compound rate they form together, for a cut of a discount, a tax on a taxable…
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Perfect square trinomial
x² + 6x + 9 is a perfect square, (x + 3)², because 6² equals 4 × 1 × 9. Enter the three coefficients to learn whether ax² + bx + c is the square of a binomial…
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Rectangle perimeter from area and one side
A rectangle of area 24 with one side of 6 has its other side at 4 and a perimeter of 20. Enter the area and the side you know to get the missing side and the…
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Perimeter of a sector
A sector with radius 5 and a 90° angle has a perimeter of 10 + 5π/2: two radii of 5 plus a quarter-circle arc.
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Triangle perimeter from vertices
The triangle with corners (0, 0), (3, 0) and (0, 4) has sides 3, 5 and 4 and a perimeter of 12. Enter the coordinates of three points to get each side and the…
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Perimeter of a rectangle
A rectangle 8 long and 5 wide has a perimeter of 26, twice the sum of its sides. Enter the length and the width to get the distance all the way round, ready for…
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Phase shift calculator
In y = sin(2x + 1) the graph moves half a unit to the left, because the phase shift is −C/B = −1/2.
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Polar decomposition calculator
The matrix with rows (2, 1) and (0, 3) splits into a rotation U and a symmetric stretch P, so that A = U P.
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Polar form of a complex number
3 + 4i has a magnitude of 5 and an angle of about 0.927 radians, so its polar form is 5∠0.927. Enter the real and imaginary parts to get the magnitude, the…
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Polygon angle
Type the number of sides and get both angles of a regular polygon at once: a pentagon has interior angles of 108° and exterior angles of 72°.
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Polynomial division calculator
Divide one polynomial by another and get the quotient and the remainder: x² − 3x + 2 divided by x − 1 gives x − 2 with a remainder of 0.
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Polynomial graphing calculator
Enter the coefficients and an x-range and get evenly spaced points ready to draw: x² from −2 to 2 with five points gives (−2, 4), (−1, 1), (0, 0), (1, 1) and…
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Power modulo calculator
Get the remainder of a huge power without ever computing the power: 2 to the 10th mod 1000 leaves 24, and 3 to the 5th mod 13 leaves 9.
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Power of a power calculator
Collapse a nested power into a single one: (2^3)^4 is 2 to the 12th, which is 4096, because the two exponents multiply.
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Power-reducing identities calculator
Rewrite sin² or cos² of an angle as a first-power cosine of the double angle and get the number: sin² of 30 degrees is 0.25, because the cosine of 60 degrees is…
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Prisoner's dilemma calculator
Score one round of the prisoner's dilemma: pick cooperate or defect for each player and get both scores.
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Pyramid angle calculator
Give the base side and height of a square pyramid and get the angle its slant edges make with the base: a side of 6 and a height of 4 give just over 43 degrees…
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Pythagorean triples
List every primitive Pythagorean triple up to the hypotenuse you choose: up to 25 there are four, 3-4-5, 5-12-13, 8-15-17 and 7-24-25, each with the legs in…
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QR decomposition
Factor a real matrix into Q with orthonormal columns and an upper-triangular R using Gram-Schmidt: the matrix with rows 3, 1 and 0, 2 is already triangular, so…
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Quarter circle perimeter
Get the full boundary of a quarter circle from its radius, the curved arc plus the two straight radii: a radius of 7 gives a perimeter of 24.995574287564, with…
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Quaternion calculator
Enter the four parts of a quaternion and get its norm and conjugate together: for 1 + 2i + 3j + 4k the conjugate is 1 − 2i − 3j − 4k and the norm is the square…
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Simplify radical
Rewrite a square root in simplest radical form: √12 becomes 2√3 and √50 becomes 5√2, with the number that comes out and the part that stays under the root shown…
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Radius of a circle
Get the radius of a circle from the distance around it: a circumference of 2π gives a radius of 1 and a diameter of 2, and one of 10π gives a radius of 5.
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Sphere radius calculator
Recover the radius of a sphere from its volume, surface area or diameter: a volume of thirty-six π, about 113.097335529233, gives a radius of 3 and a diameter…
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Ratio of 2 numbers calculator
Compare two numbers as a ratio in lowest terms and as a decimal: 8 to 12 reduces to 2:3, with a greatest common divisor of 4 and a quotient of 0.666666666667.
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Rational exponents calculator
Evaluate a power with a fractional exponent: 8 to the 2/3 is 4, because the cube root of 8 is 2 and 2 squared is 4.
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Rationalize denominator calculator
Clear the square root from the bottom of a fraction: 1/√8 becomes √2/4, with the square factor pulled out and the result reduced, and 6/√9 simplifies all the…
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Reciprocal calculator
Get the reciprocal of any non-zero number, one divided by it: the reciprocal of 4 is 0.25, of two thirds is three halves, and of minus four is minus one…
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Rectangle diagonal angle calculator
A 4 by 3 rectangle has a diagonal of 5 that meets the length at arctan(3/4) and the width at arctan(4/3), two angles that always add up to 90°.
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Rectangular prism volume
A box 3 by 4 by 5 holds 60 cubic units. Enter the three edges and get the volume as length times width times height, in the cubic version of your unit.
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Rectangular to polar
The point (3, 4) sits 5 units from the origin at an angle of about 53.13°. Enter any x and y and get the radius and the angle in degrees, in the right quadrant…
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Regular polygon perimeter
A regular hexagon with sides of 2 has a perimeter of 12, because every side is equal and the total is simply the number of sides times their length.
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Relatively prime checker
8 and 15 are relatively prime because their only common divisor is 1, even though neither number is prime.
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Right circular cone
A cone with radius 3 and height 4 has a slant height of exactly 5 and a volume of 37.6991118431 cubic units.
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Right rectangular pyramid
A pyramid with a 6 by 4 base and a height of 3 holds 24 cubic units and has a total surface of 62.603870401261.
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Right trapezoid area calculator
A right trapezoid with bases of 8 and 12 and a height of 5 has an area of 50: the average of the bases times the height.
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Right triangle trigonometry
With legs of 3 and 4 the hypotenuse is 5 and the acute angles are about 36.87° and 53.13°. Give any two sides, or one side and one acute angle, and get the…
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Rise over run calculator
A rise of 3 over a run of 4 is a slope of 3/4, or 0.75. Enter the vertical and the horizontal change and get the slope as a reduced fraction and as a decimal…
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Round to the nearest hundred
247 rounded to the nearest hundred is 200, while 250 goes up to 300. Enter any number, negative or with decimals, and get the closest hundred together with the…
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Round to the nearest penny
An amount of 1.235 rounds to 1.24 and comes back as 124 cents: a half-cent always moves away from zero, the rule most ledgers expect.
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Round to the nearest ten
24 rounds to the nearest ten as 20, while 25 goes up to 30 because halves move away from zero. Enter any whole number, decimal or negative and get the closest…
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Rounding calculator
3.14159 rounded to 2 decimal places is 3.14, and 2.5 rounded to a whole number is 3. Choose how many decimals to keep, from 0 to 15, and get the school half-up…
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Round to the nearest thousandth
3.14159 rounded to the nearest thousandth is 3.142, and 2.3456 becomes 2.346. Enter any number and keep exactly three decimal places, with a leftover 5 pushing…
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SAS triangle solver
Sides of 3 and 4 that meet at 90° close a triangle with a third side of 5, an area of 6 and a perimeter of 12.
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Scatter plot calculator
For the points (1, 2), (2, 4), (3, 5), (4, 4) and (5, 5), the line of best fit has a slope of 0.6 and an intercept of 2.2, with a correlation of about 0.775.
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Scientific notation
1234.5 becomes 1.2345 × 10³: a coefficient of at least 1 and below 10, times a power of ten. Enter any finite number and get the coefficient, the exponent and a…
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Segment addition postulate calculator
If AB is 5 and BC is 8, the whole segment AC is 13, because the two parts of a segment add up to the whole.
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Segment area calculator
A circle of radius 10 cut by a chord at a 90° central angle leaves a segment of 28.539816339745 square units.
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