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.
Polynomial from roots calculator
Turn known roots into a polynomial in standard form: roots 1, 2 and 3 give (x − 1)(x − 2)(x − 3), which expands to x³ − 6x² + 11x − 6.
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Polynomial subtraction calculator
Subtract polynomials column by column: 4x^3 − 2x + 7 minus x^3 + 5x^2 − 3 gives 3x^3 − 5x^2 − 2x + 10, with every power lined up so you can check each step.
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FOIL method calculator
Multiply two binomials and see every FOIL product in order: (2x + 3)(4x − 5) gives 8x², −10x, 12x and −15, so the result is 8x² + 2x − 15.
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Inverse function calculator
Reverse a function and see each step: f(x)=2x+3 has the inverse f⁻¹(x)=0.5(x − 3), valid for all real numbers.
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Polynomial coefficients extractor
Paste a polynomial and get its coefficients in order, from the highest power down to the constant: 3x^2 + 2x − 5 gives 3, 2 and −5, and x^3 − 4x gives 1, 0, −4…
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Polynomial degree calculator
Read the degree of a polynomial straight off its coefficient list: 3, −2, 0 and 5 describe 3 − 2x + 5x³, a cubic of degree 3 whose leading coefficient is 5.
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Polynomial standard form calculator
Tidy a messy polynomial in one step: 3x^2 + 4x − 7 + 2x^3 − x^2 + 5 − 4x becomes 2x^3 + 2x^2 − 2, of degree 3. Fractions and decimals stay exact.
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Difference quotient calculator
Type the coefficients of a polynomial and see [f(x+h)−f(x)]/h already simplified: for f(x) = x² it becomes 2x + h, and letting h go to zero leaves the…
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Function evaluation calculator
Pick a function type, enter its coefficients and a value of x, and get f(x) at once: f(x)=2x+1 evaluated at 3 gives 7.
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Even or Odd Function Checker
Enter a polynomial and find out whether it is even, odd or neither: 3x⁴ − 2x² + 7 is even, because replacing x with −x leaves it unchanged.
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Function reflection calculator
Mirror a function across either axis and see the new rule with its points: across the y-axis, x² − 4x + 3 becomes (−x)² − 4(−x) + 3 and the point (2, −1) moves…
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Vertical asymptote calculator for rational functions
(x + 1)/(x^2 - x - 2) has a single vertical asymptote, at 2, because the factor for -1 cancels and leaves only a hole.
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Square root function domain calculator
√(x - 4) is defined only for x ≥ 4, so its domain is [4, ∞) and the graph starts at 4 on the x-axis.
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Common logarithm calculator
The common logarithm of 1000 is 3, because ten cubed is 1000: enter any positive number and get the power of ten behind it, negative for values between 0 and 1.
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Doubling Time Calculator
Enter a growth rate per period and see how long it takes to double: at 5% per period, growth compounded once per period doubles in 14.2066990829 periods, worked…
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Function iteration calculator
Feed a rule its own output step after step and see the whole orbit: x² − 1 starting at 1.5 reaches −0.68359375 after three steps and −0.532699584960938 after…
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Logarithm quotient rule calculator
Turn log(x/y) into log x − log y in one step, with the quotient rule spelled out. When the base and both values are numbers, the difference is also evaluated…
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Logarithmic to exponential form converter
Enter base 2, argument 8 and value 3 to see log₂(8) = 3 rewritten as 2³ = 8: the base stays the base, the value becomes the exponent and the argument becomes…
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One-to-one function checker
Find out whether a function has an inverse before you try to build one: f(x) = 2x − 1 passes the horizontal line test, because every output comes from exactly…
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Complex number addition calculator
(3 + 2i) + (1 − 4i) is 4 − 2i: enter the real and imaginary parts of two complex numbers and get their sum in standard form, with the rule shown next to the…
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Complex modulus calculator
The modulus of 3 + 4i is 5, its distance from the origin on the complex plane: enter the real and imaginary parts and get |z| and its square, never negative.
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Complex number power calculator
(1 + i)² is 2i: enter the real and imaginary parts and a whole exponent, and get the power in a + bi form with the modulus and angle behind it, no long…
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Complex Square Root Calculator
The square roots of 3 + 4i are 2 + i and −2 − i: enter the real and imaginary parts and get the principal root and its counterpart in rectangular form, ready to…
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Logarithmic inequality solver
Solve log₂(x − 1) > 3 and get x > 9, or (9, ∞): the tool checks that x − 1 stays positive, rewrites the inequality as x − 1 > 8 and flips the sign when the base…
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Simplify logarithmic expressions
Type log(100x²/y) + log(y) and get 2 + 2 log(x): the logs are split by the standard rules, the log of 100 becomes exactly 2, and the opposite log(y) terms…
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Number of terms in an arithmetic sequence
From 3 to 27 in steps of 4 there are 7 terms: enter the first term, the last term and the common difference, and get the count n with both ends included.
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Product of complex conjugates calculator
(3 + 4i) times its conjugate (3 − 4i) is 25: enter the real and imaginary parts and get a² + b², the squared modulus of the number, always real and never…
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Complex cube roots calculator
The three cube roots of 8 are 2, −1 + i√3 and −1 − i√3: enter any complex number and get all three roots, 120° apart, in polar and rectangular form, with angles…
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Imaginary part of a complex number calculator
The imaginary part of 7 − 4i is −4: enter a number as a + bi or by its size and angle, and get the signed coefficient of i, ready to compare, graph or reuse.
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Square of a Complex Number Calculator
(3 + 4i)² is −7 + 24i: enter the real and imaginary parts and get the square in a + bi form, with real part a² − b² and imaginary part 2ab.
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Common ratio calculator
Enter two consecutive terms and get the constant multiplier of the sequence: 6 followed by 18 gives a common ratio of 3, because 18 divided by 6 is 3.
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Nth roots of unity calculator
The fourth roots of unity are 1, i, -1 and -i, evenly spaced at 0°, 90°, 180° and 270° on the unit circle.
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Arithmetic sequence missing term calculator
In 4, 7, ?, 13, 16 every step is 3, so the missing third term is 10. Mark the gap with a question mark and get the missing value, its position, the step and the…
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Geometric sequence first term calculator
Work back to the start of a geometric sequence: if the fifth term is 162 and the ratio is 3, the first term is 2, because 162 divided by 81 is 2.
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Geometric mean of two numbers
Get the multiplicative middle of two positive numbers: the geometric mean of 4 and 9 is 6, the square root of their product 36.
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Sigma Notation Sum Calculator
The sum of k^2 + 2*k for k from 1 to 5 is 85, over 5 terms: enter the term, the index letter and both bounds, and every whole value in the range is added for…
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Sum of First n Natural Numbers Calculator
1 + 2 + … + 100 is 5,050: the formula n(n + 1)/2 gives the total of the first n natural numbers at once, without adding each one.
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Sum of first n odd numbers calculator
1 + 3 + 5 + 7 + 9 adds up to 25: the first n odd numbers always total exactly n squared. Enter n and get the sum along with the last odd number in the list…
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Binomial coefficient calculator
A committee of 3 chosen from 10 candidates can be formed in 120 ways: enter n and k and get the exact binomial coefficient, every digit correct and with no…
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Characteristic polynomial 2x2 calculator
For the matrix with rows 4, 1 and 2, 3, the trace is 7 and the determinant 10, so the characteristic polynomial is λ² − 7λ + 10, with coefficients 1, −7 and 10.
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2x2 determinant calculator
For rows 3, 8 and 4, 6, the diagonal products are 18 and 32, so the determinant is −14 and the matrix is invertible.
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Hadamard product calculator
Multiply matching cells of two equal-size matrices: entries 1, 2, 3, 4 times 5, 6, 7, 8 give a top row of 5 and 12.
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Matrix minor calculator
For the matrix with rows 1, 2, 3; 0, 4, 5; 1, 0, 6, crossing out row 1 and column 1 leaves rows 4, 5 and 0, 6, whose determinant 24 is the minor.
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Matrix of cofactors calculator
For rows 1, 2, 3; 0, 4, 5; 1, 0, 6, you get nine minors and nine cofactors: the minor at row 1, column 2 is −5, and after the alternating sign its cofactor is…
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Symmetric matrix checker
Find out at once whether a square matrix is symmetric: the 3×3 matrix with rows 1 2 3, 2 4 5 and 3 5 6 passes after 3 pairs are compared, and a failing one…
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Absolute Value Expression Evaluator at a Given Input
With x set to 4, |2*x − 5| + 3 gives 6, because the bars turn 3 into its distance from zero before adding 3.
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Multinomial Coefficient Expansion Calculator
Count how many ways distinct items can be shared among labeled groups: 8 people split into groups of 3, 3 and 2 give 560 arrangements, computed exactly and…
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Multiply rational expressions calculator
Multiply two polynomial fractions and get the reduced answer with its domain: (x + 1)/(x − 2) times (x − 2)/(x + 3) simplifies to (x + 1)/(x + 3), excluding the…
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Direct rule of three calculator
4 is to 10 as 7 is to 17.5: the direct rule of three scales the known value by the same factor, here 1.75, so both pairs keep the same ratio.
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Set-builder to interval notation converter
{ x | -1 < x ≤ 4 } becomes (-1, 4]: a parenthesis where the bound is left out, a square bracket where it is kept.
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Distributive property calculator
Expand one factor over a sum in parentheses and see each product separately: −2a(3a − 4b + 5) becomes −6a² + 8ab − 10a.
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Interval notation from inequality calculator
Write x < 4 as the interval (−∞, 4) without guessing which bracket goes where: an included limit gets a square bracket, an excluded one a parenthesis, and…
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What percent of calculator
Answer "what percent of the whole is this part?" in one step: 18 students out of 24 is 75%, and 30 against 24 is 125%.
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Midpoint of a segment calculator
Enter both end points and get the exact center of the segment: from (0, 0) to (4, 6) the midpoint is (2, 3).
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Solve for x in a ratio calculator
Solve the missing number in a proportion: 3/4 = 9/x gives 12 for x, and both cross-products equal 36, so you can see the answer holds.
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Slope from linear equation calculator
For 3x + 2y = 12 the slope is -1.5 and the y-intercept is 6: the calculator collects the terms from both sides and rewrites the line in slope-intercept form.
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Cross multiplication calculator
If 2/3 equals 4/d, then d is 6, because 2 × 6 and 3 × 4 both give 12: enter any three terms of a proportion and get the fourth, with the cross products and each…
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GCF of monomials calculator
Get the greatest common factor of algebraic terms, variables included: 12x²y, 18xy³ and 24x³y share 6xy.
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Cube surface area calculator
Enter the edge of a cube and get the area of all six faces: an edge of 2 cm gives 24 cm². The result stays in your unit, squared, which is what you need to…
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Cube volume, surface area and space diagonal from edge length
From one edge length, get the cube's volume, total surface area and space diagonal at once: an edge of 3 gives 27, 54 and 5.196152.
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