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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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…
A
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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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➗ MathFree
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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