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.
Sig fig calculator
1234.567 rounded to 3 significant figures is 1230, written 1.23 × 10³ in scientific form. Enter a number and how many meaningful digits to keep, from 1 to 15…
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Similar right triangles
If side 3 of a right triangle with sides 3 and 4 becomes 6 on a similar copy, the 4 becomes 8: the scale factor is 2.
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Simplify radicals calculator
The square root of 72 simplifies to 6√2, because 72 is 6 squared times 2. Enter a positive whole number and get the exact form a√b, with every square factor…
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Sine calculator
sin(30°) is 0.5 and sin(90°) is 1: enter an angle in degrees or radians and get its sine, plus the radian measure actually used, so you can check the…
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Sin degrees calculator
The sine of 30 degrees is 0.5, but the sine of 30 radians is about −0.988: this calculator always converts your degrees first.
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Sine function calculator
Find y for the general sine y = a·sin(bx + c) at the x you choose: amplitude 2, frequency 1 and phase 0 give 0 at x zero.
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Sin triangle calculator
With a 30° angle and an opposite side of 5, the hypotenuse is 10, because sine is opposite over hypotenuse.
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Slant height calculator
Get a cone's slant height from its base radius and vertical height, so radius 3 and height 4 give exactly 5, the side length you cut for a funnel, a party hat…
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Solving by completing the square
Solve a quadratic the classroom way: x² − 6x + 5 = 0 becomes (x − 3)² = 4, giving the roots 1 and 5.
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Sphere equation
Write the equation of a sphere from its center and radius: center (1, 2, 3) and radius 5 give (x − 1)² + (y − 2)² + (z − 3)² = 25, plus the expanded general…
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Square feet of a rectangle
Multiply length by width in feet and get the square footage of a room, patio, slab or garden bed: 10 feet by 5 feet is 50 square feet.
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Triangle square feet calculator
Enter a triangle's base and perpendicular height in feet or inches and get the area in square feet: a 10-foot base with an 8-foot height gives 40 square feet.
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Standard form calculator
Rewrite any line as Ax + By = C in whole numbers and lowest terms: 0.5x + 1.5y equals 3 becomes x + 3y equals 6, with a non-negative x coefficient and a label…
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Square of a binomial
Expand the square of a binomial in one step: (2x + 3)² becomes 4x² + 12x + 9, giving you the leading, middle and constant coefficients a², 2ab and b².
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Star shape calculator
Get the area and perimeter of a regular pointed star from its number of tips and its two radii: five tips on radii 2 and 1 cover 5.877852522925 square units…
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Substitution method
Solve two linear equations by substitution, with the isolated variable shown: for 2x + y equals 5 and x − y equals 1, x comes from the first equation and the…
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Sum and difference identities
Expand the sine or cosine of a sum or difference of two angles in degrees: sin(30° + 45°) is worked out as sin 30 cos 45 plus cos 30 sin 45, giving…
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Sum of series calculator
Add the first n terms of an arithmetic or geometric series with one closed formula: 3 + 5 + 7 + 9 + 11 is 35, and 2 + 6 + 18 + 54 is 80.
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Surface area of a triangular prism
Add up all five faces of a triangular prism: a 3-4-5 triangle with height 4 on the side of 3, stretched to a length of 10, gives two ends of 6 each plus 120 of…
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Surface area calculator
Get the total surface area of a cube, sphere, cylinder or cone from its dimensions: a cube with a side of 2 covers 24 square units, six faces of 4 each.
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Surface area to volume ratio
Find how much outer surface sits on each unit of volume for a cube, sphere or cylinder: a cube with a side of 2 has 24 of area over 8 of volume, a ratio of 3…
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Systems of equations solver
Find the one point where two straight lines meet: the lines 2x + y equals 5 and x − y equals 1 cross at (2, 1), worked out with Cramer's rule from three…
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Tangent of an angle
The tangent of 45° is 1: enter an angle in degrees or radians and get its tangent, with the angle shown in both units.
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Tangent circle calculator
A circle of radius 3 seen from a point 5 away from its center has a tangent 4 long. Enter the radius and that distance and get the tangent segment, worked out…
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Tensor product calculator
Two 2×2 matrices give a 4×4 Kronecker product made of scaled copies of the second one. Enter both matrices as rows of numbers and get A⊗B with the size of each…
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Tan inverse calculator
Turn a tangent ratio back into its angle: the tan inverse of 1 is 45°, or 0.785398163397 radians, and you always get both units, inside the principal range…
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Trapezoid area
A trapezoid with parallel sides of 8 and 12 and a height of 5 has an area of 50. Enter both bases and the perpendicular height and get the area as the average…
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Trapezoid height calculator
A trapezoid with an area of 50 and bases of 8 and 12 is 5 high. Enter the area and both parallel sides and get the height, worked out as twice the area divided…
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30-60-90 triangle sides
In a 30-60-90 triangle with a short side of 5, the long side is 5√3 and the hypotenuse is 10. Enter one side, say whether it is the short leg, the long leg or…
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Triangle angle calculator
Two angles of 50° and 60° leave 70° for the third. Enter the two interior angles you know, in degrees, and get the missing one as 180° minus their sum.
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Triangle degree calculator
Angles of 60° and 40° leave 80° for the third corner. Type the two interior angles you measured, in degrees, and the third comes from subtracting both from…
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Triangle proportionality theorem
With AD of 4, DB of 6 and AE of 6, the missing piece EC is 9, because 4/6 equals 6/9. Enter any three of the four pieces cut by a line parallel to one side of a…
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Triangle ratio calculator
If two sides of a triangle are in the ratio 2:5 and the side matching the 2 measures 6, the other side is 15.
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Triangle side calculator
Legs of 3 and 4 give a hypotenuse of 5. Enter the two sides of a right triangle you already know, choose whether the missing one is the hypotenuse or a leg, and…
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Triangle side from two sides and included angle
Sides of 3 and 4 with a 90° angle between them leave a third side of 5. Enter two sides and the angle they enclose, in degrees, and get the opposite side from…
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Triangle sum theorem
Angles of 50°, 60° and 80° add up to 190°, which is 10° too many for a triangle. Enter three interior angles in degrees and the checker tells you whether they…
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Triangle vertices calculator
The points (0, 0), (3, 0) and (0, 4) form a triangle with sides of 3, 4 and 5, a perimeter of 12 and an area of 6.
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Trig functions
At 30°, the sine is 0.5, the cosine √3/2 and the tangent 1/√3. Enter a single angle in degrees or radians and get all three values side by side, with the angle…
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Trig identities calculator
At 30°, sin² + cos² comes out at exactly 1 and the double-angle formulas return the sine and cosine of 60°.
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Six trigonometric functions from radians
At π/6 the six values are sine 1/2, cosine √3/2, tangent 1/√3, cosecant 2, secant 2/√3 and cotangent √3.
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Truncated cone calculator
A truncated cone with radii of 3 and 5 and a height of 4 has a volume of (1/3)π × 4 × 49 and a total surface of 34π + 8π√20.
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Two's complement
In 8 bits, −5 becomes 11111011 and +5 becomes 00000101. Enter a signed whole number and a word width from 2 to 64 bits and get its exact two's complement…
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Unit rate calculator
Divide a total by a number of units and see how much belongs to one: 240 miles in 4 hours is 60 miles per hour.
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Vector calculator
Enter the two components of a flat vector and get its length, heading and unit vector: (3, 4) has a length of 5 and a unit vector of (0.6, 0.8).
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Vector addition calculator
Add two vectors by pairing their components: (3, 4) plus (1, -2) gives (4, 2), and (1, 2, 3) plus (4, 5, 6) gives (5, 7, 9).
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Volume calculator
Pick a cube, box, sphere, cylinder or cone, type its measurements and get the volume: a cube with a side of 2 holds 8 cubic units.
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Volume of a triangular prism
Find a triangular prism's volume from three measurements: a triangle with base 3 and height 4, stretched over a length of 10, gives a base area of 6 and a…
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Width of a rectangle calculator
Divide the area by the known length to get the width: a rectangle with an area of 40 and a length of 8 is 5 wide.
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Y-intercept calculator
Give a slope and a point, or two points, and get the spot where the line crosses the vertical axis: slope 2 through the point (3, 7) crosses at 1.
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A/B test calculator
Find out whether your variant really beat the control: 130 conversions from 1000 visitors against 100 from 1000 gives a z-score of 2.10274060562 and a two-sided…
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Ascending order
Sort numbers from smallest to largest: with 9, -2, 0, 1 and four and a half entered twice, you get -2 first and 9 last, with both copies of four and a half kept…
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Benford's law calculator
Under Benford's law about 30.103 percent of numbers start with 1, but only about 4.576 percent start with 9.
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Bonferroni correction calculator
A significance level of 0.05 spread over 10 comparisons gives a per-test cutoff of 0.005. Enter the original level and the number of planned tests, and judge…
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Mode calculator
In 1, 2, 2, 3 and 4 the mode is 2, which appears twice. Every value is counted, all values tied for the top count are returned, and a list where each number…
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Normal distribution calculator
On the standard normal curve the density at 0 is about 0.3989, the height of the bell's peak. Choose density or cumulative probability, enter the value, mean…
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Ordering numbers
Enter 3, 1/2, -2.5, 4 and 7/4 and get -2.5, 1/2, 7/4, 3, 4: each entry is turned into its real value, so fractions and decimals line up correctly, and your…
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Permutation without repetition
Choosing and ranking 3 of 5 items can be done in 60 different orders, the value of P(5,3). Enter how many distinct items you have and how many places to fill…
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Point estimate calculator
For the sample 12, 15, 18, 21 and 24, the point estimate of the population mean is 18. Paste your sample and choose the mean, a proportion, the variance or the…
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Three events probability calculator
For the classic set with P(A) of 0.5, P(B) of 0.4 and P(C) of 0.3, plus their overlaps, the chance that at least one occurs is 0.8.
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Range calculator
For the list 3, 7, 2, 9 and 5 the range is 7: the maximum 9 minus the minimum 2. Paste any numbers, negatives and decimals included, and get the count, the…
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