How To Calculate A Fourier Series
Learn how to calculate a Fourier series with this simple step-by-step math guide. We cover how to find the period, check the parts, and run the basic math.
Read the GuideMath Calculators
Solve everyday number problems with a growing set of math calculators, from percentages and fractions to averages and beyond. Every tool shows its formula, a worked example, and the rounding used, so you can check the result by hand and trust the answer.
All Math Calculators
Grading Bell Curve Calculator
Rescale any raw exam score to a target mean using the linear z-score bell curve method, built for teachers and students.
Open the CalculatorProjectile Motion Calculator
Find projectile range, max height, and flight time from launch velocity and angle. All three outputs shown with working. Assumes ground-level launch, no drag.
Open the CalculatorSimpson's Rule Calculator
Estimate a definite integral using Simpson's 1/3 rule over 4 subintervals. You enter 5 function values at equally spaced points; this calculator does the rest.
Open the CalculatorTrapezoidal Approximation Calculator
Estimate a definite integral using the trapezoidal rule with 4 subintervals. You supply 5 function values at equally spaced points; the formula does the rest.
Open the CalculatorPolynomial Multiplication Calculator
Multiply two linear binomials (a₁x + a₀) and (b₁x + b₀) using the FOIL method. Enter four coefficients and read the quadratic result term by term.
Open the CalculatorBoolean Expression Calculator
Evaluate AND, OR, NOT, XOR, NAND, and NOR expressions on boolean inputs A and B. Select the operator, enter true or false, and read the result instantly.
Open the CalculatorRadical Equation Calculator
Solve √(ax + b) = c for x by squaring both sides. The calculator shows each step and checks whether the solution is valid or extraneous.
Open the CalculatorGauss-Jordan Calculator
Solve a 2×2 linear system using Gauss-Jordan elimination. Enter the coefficients of both equations and read the solution for x and y with steps shown.
Open the CalculatorFisher's Exact Test Calculator
Compute the exact probability of a 2×2 contingency table using Fisher's exact test. Enter counts a, b, c, d and get the hypergeometric p-value with steps.
Open the CalculatorGeometric Distribution Calculator
Find P(X=k), P(X≤k), and the expected value for a geometric distribution. Enter the probability of success p and the trial number k to get all three results.
Open the CalculatorCircumcenter Calculator
Find the circumcenter of a triangle from its three vertex coordinates. Enter the six coordinate values and read the circumcenter x and y with full working shown.
Open the CalculatorInverse Functions Calculator
Find the inverse of a linear function f(x) = mx + b. Enter slope m and y-intercept b to get the inverse function f⁻¹(x) with the swap-and-solve method shown.
Open the CalculatorFourier Series Calculator
Compute the Fourier series of a square wave: amplitude A, odd harmonics n = 1, 3, 5, .... Enter amplitude and harmonic count to get each bₙ coefficient listed.
Open the CalculatorGrams to Troy Ounces Calculator
Convert between grams and troy ounces in either direction using the exact factor 1 troy oz = 31.1034768 g. Used for gold, silver, platinum, and other precious metals.
Open the CalculatorArchitectural Scale Calculator
Convert a scaled drawing measurement to its actual real-world size. Enter the drawing length and your scale ratio to find the true dimension in seconds.
Open the CalculatorVector Dot Product Calculator
Find the dot product of two three-dimensional vectors and the angle between them, with a step-by-step worked example showing every multiplication and sum.
Open the CalculatorInverse Normal CDF Calculator
Find the value at any given percentile of a normal distribution by entering the probability, mean, and standard deviation. Powered by the Acklam rational approximation.
Open the CalculatorSourdough Hydration Calculator
Find your sourdough dough's true total hydration percentage by entering the recipe flour, water, starter weight, and starter hydration, with the starter's own flour and water counted in full.
Open the CalculatorSourdough Starter Calculator
Find the exact gram weights of starter, flour, and water for any feeding ratio and target total weight, whether you use a 1:1:1, 1:2:2, or any other parts-based feed.
Open the CalculatorNormal CDF Calculator
Find the chance below, above, or between values on a normal curve from its mean, spread, and one or two cutoffs for each result.
Open the CalculatorExponential Growth Calculator
Find how a quantity grows or shrinks with a discrete or continuous rate, using a start value, rate, and number of time periods.
Open the CalculatorTwo's Complement Calculator
Turn a signed whole number into two's complement binary, or read a fixed-width binary pattern as decimal, at 4, 8, 16, or 32 bits.
Open the CalculatorPolynomial Long Division Calculator
Divide a polynomial from two coefficient lists, then see the quotient, remainder, and a direct check that recovers the dividend.
Open the CalculatorPartial Fraction Decomposition Calculator
Split a proper rational function with distinct linear factors into simpler fractions, with coefficients found from the factor roots.
Open the CalculatorRational Expressions Calculator
Simplify a factored rational expression, cancel shared roots, and keep all values blocked by the first denominator for algebra work.
Open the CalculatorSimplest Radical Form Calculator
Simplify square, cube, or fourth roots by pulling perfect powers from the radicand and showing each factor step for homework checks.
Open the CalculatorInterval Notation Calculator
Turn one-sided or two-sided rules for x into interval notation with the right square mark, round mark, and infinity sign.
Open the CalculatorVertex Form Calculator
Convert a quadratic from standard form to vertex form, see each completing-the-square step, and read the vertex for graphing.
Open the CalculatorBinomial Expansion Calculator
Expand (a + b)^n with the binomial theorem, list each coefficient and power, and compare the result with Pascal's triangle.
Open the CalculatorNull Space Calculator
Find all vectors that a 2 by 2 matrix sends to zero, then see the row steps and the basis for the null space during introductory verification.
Open the CalculatorDilation Calculator
Scale a point from the origin or from a custom center, then see the new x and y values for any scale factor in geometry work.
Open the CalculatorPoisson Distribution Calculator
Find the chance of an exact, at-most, or at-least event count from a mean rate and a whole-number target in statistics problems.
Open the CalculatorCandle Wax Calculator
Estimate wax and scent oil weights for a round candle jar, with user-set values for wax type and scent load for hobby or small-batch work.
Open the CalculatorCircle Skirt Calculator
Find the waist radius, hem radius, and least fabric width for a full circle skirt from waist, ease, and skirt length at home.
Open the CalculatorCross Stitch Calculator
Find the stitched design size and total fabric cut from the chart count, fabric count, and the margin added on every side.
Open the CalculatorSourdough Calculator
Find the water, starter, salt, and total dough weights for a sourdough batch from flour weight and baker's percentages for home baking.
Open the CalculatorRunning Record Calculator
Calculate running record accuracy and self-correction ratio from words, errors, and corrections, without assigning a reading level.
Open the CalculatorGoogle Review Calculator
Estimate how many top-score reviews may raise a current score to a goal on Google or any fixed score scale, using clear best-case terms.
Open the CalculatorProductivity Calculator
Calculate output per hour for a process, machine, or team, with a clear unit, time base, and neutral use of each result.
Open the CalculatorPercentage of Goal Calculator
Find the percent of a goal reached so far by entering a current value and a target value in the same unit.
Open the CalculatorAttendance Percentage Calculator
Find attendance rate from sessions attended and total sessions, for class records, work shifts, meetings, or training logs.
Open the CalculatorVote Percentage Calculator
Find the vote share for one option from votes received and total valid votes, for polls, contests, clubs, or surveys.
Open the CalculatorFraction Calculator
Add, subtract, multiply, or divide two fractions and see the reduced answer, decimal form, and working steps.
Open the CalculatorAverage Calculator
Find mean, median, and range from a list of numbers so students, teachers, and data readers can check center, middle, and spread.
Open the CalculatorPercentage Calculator
Find a percent of a number, compare part to whole, or measure percent change with the formula, steps, and a worked example shown.
Open the CalculatorWhat You Can Work Out With These Math Calculators
Math calculators turn a written problem into a checked answer in seconds. Most everyday arithmetic comes down to a handful of core ideas: percentages that compare one number with another on a scale of 100, fractions that split a whole into parts, and simple statistics such as an average that describe a set of numbers at a glance. These come up constantly, in discounts and tips, in test scores and grades, in recipes and measurements, and in any moment where you need to read one figure against another and trust the result.
Every tool in this section is built the same way: it states its formula in plain words, walks through a worked example with the rounding it used, and shows each step, so you can follow the maths or redo it by hand. That makes them useful for homework you actually want to understand, for a quick check at work, and for double-checking a figure before you rely on it. For the formulas on their own, see the formula reference.
Related Resources
- Guides & Blogs . Guides and blog posts on how to use our calculators and understand the concepts behind them.
- Formulas . The exact formulas behind each calculator, with the notation and reasoning explained.
- Glossary . Short definitions of the terms you will meet across our calculators, including BMI, BMR, amortization, and more.
- Methodology . How we choose formulas, test calculations, round results, select sources, and review our tools.
Recent Guides
View All →How To Calculate An Inverse Function
Learn how to calculate the inverse of a function in mathematics. This step-by-step procedure shows you exactly how to swap variables and solve the equation.
Read the GuideHow To Do Gauss Jordan Elimination
Learn how to do Gauss Jordan elimination with this simple step-by-step math guide. We cover how to build a matrix, use row operations, and solve the system.
Read the GuideFrequently asked questions
What can I work out with these math calculators?
You can work out percentages, simplify fractions, and find averages in seconds. Each tool shows the formula and a worked example. That makes the result easy to trust and easy to check.
Do these math tools show the formula and steps?
Yes, every math tool shows the formula in plain words and a full worked example. You see each step and the rounding used, so you can follow the math or redo it by hand.
Are the math calculators free to use?
Yes, every math tool on Calcumatix is free, with no sign-up and no limit. You can run as many calculations as you need. Nothing is held back behind a paid tier.