QiLing Tools📐Math Tools
Function graphing, calculators, equation solvers, calculus, matrices, geometry and number theory tools, ready to use.
109 tools tagged "Math"
📈Graphing CalculatorFree online function graphing calculator: type sin(x), x^2 or 1/x and see the curve at once, with several functions, parametric and polar curves, PNG export.🧮Scientific CalculatorFree online scientific calculator: type 2*(3+4)^2, sin(pi/6) or log(8,2) and see the answer as you type, with degrees or radians and a history list.🟰Equation SolverFree online equation solver: enter coefficients for linear, quadratic (with discriminant, vertex and complex roots) and cubic equations, plus 2×2 systems.½Fraction CalculatorFree online fraction calculator: add, subtract, multiply and divide fractions with automatic reduction, plus fraction ↔ decimal with repeating digits.％Percentage CalculatorFree online percentage calculator: X% of Y, X as a percent of Y, increase and decrease, a value after a percentage change and the original behind it.🔢Prime FactorizationFree online prime factorization: factor an integer with exponents, list every divisor and their sum, test primality with neighbouring primes, or list a range.🔗GCD and LCMFree online GCD and LCM calculator: works with two or more integers, says whether they are coprime, shows each prime factorization and every Euclidean step.📊Statistics CalculatorFree online statistics calculator: paste a data set for the mean, median, mode, range, quartiles, variance, standard deviation, standard error and outliers.🎯CombinationsFree online combination and permutation calculator: exact C(n,r), P(n,r) and n! with big integers, plus repetition variants and the total number of subsets.🔲Matrix CalculatorFree online matrix calculator: add, subtract and multiply matrices up to 8×8, transpose, and compute the determinant, inverse, matrix power and rank.📏Unit ConverterFree online unit converter: length, area, volume, weight, temperature, time, speed, data, pressure, energy and angle — one value converts every unit at once.🎲Random NumbersFree online random number generator: integers or decimals in any range, with no-repeats and sorting, list shuffling and dice, from a cryptographic source.🏛️Roman NumeralsFree online Roman numeral converter: a number to its Roman numeral or back, with validation of standard notation, a symbol-by-symbol breakdown and a table.🈶Number to WordsFree online number to words converter: English words, English currency amounts, Chinese numerals and the financial uppercase form used on invoices.📐Geometry CalculatorFree online geometry calculator: area and perimeter of circles, triangles, polygons and more, plus volume and surface area of solids, with the formulas shown.🔺Triangle SolverFree online triangle solver: SSS, SAS, ASA, AAS and SSA inputs give every side and angle plus the area, perimeter, heights, circumradius and inradius.🔗Sequence CalculatorFree online sequence calculator: nth term, sum of n terms, mean and infinite sum for arithmetic and geometric sequences, plus exact big-integer Fibonacci.⚖️Ratio CalculatorFree online ratio calculator: solve a:b = c:x, reduce decimal ratios to whole numbers, divide a total in a given ratio, and scale sizes by ratio.🌀Complex NumbersFree online complex number calculator: arithmetic on a+bi, powers and nth roots by De Moivre, with modulus, argument, conjugate and polar form for each result.🔬Scientific NotationFree online scientific notation converter: switch between plain numbers and a×10ⁿ, accept 3.5e6, and get engineering notation with SI prefixes and rounding.∫Derivative & IntegralFree online calculus calculator: first and second derivative at a point with the tangent line, or a definite integral by adaptive Simpson with an error bound.🎰Probability DistributionsFree online probability calculator: z-scores and cumulative normal probabilities, P(X=k) and P(X≤k) for binomial and Poisson, plus the mean and variance.📐TrigonometryFree online trigonometry calculator: sin, cos, tan, cot, sec and csc from degrees or radians, inverse functions, DMS conversion and a special-angle table.⚖️Average CalculatorFree online average calculator: arithmetic mean, median, mode, geometric and harmonic mean and RMS in one pass, plus weighted averages for grades and GPAs.💰Interest CalculatorFree online interest calculator: compound interest at any frequency with the effective annual rate, simple interest, monthly savings growth and loan payments.🧭Coordinate GeometryFree online coordinate geometry calculator: distance, midpoint, slope, line equations, point-to-line distance with the foot, triangle centres and polar form.➡️Vector CalculatorFree online vector calculator for 2D and 3D: addition, scalar multiples, dot and cross products, magnitude, angle, unit vector and projections, with checks.🧮Polynomial CalculatorFree online polynomial calculator: type x^3-2x^2-5x+6 for all real and complex roots, factoring, the derivative and antiderivative, plus long division.🔵Set OperationsFree online set calculator: union, intersection, differences and symmetric difference of two groups, with subset and disjoint checks and Jaccard similarity.≤Inequality SolverFree online inequality solver: linear, quadratic and absolute-value inequalities with the answer in set and interval notation, a number line and the reasoning.🧩System of EquationsFree online linear system calculator: fill in the augmented matrix for 2 to 6 unknowns and get the RREF, ranks and the unique, empty or general solution.📉Linear RegressionFree online linear regression and curve fitting: paste x and y columns for the least-squares line, r, R², residuals, predictions and quadratic or cubic fits.㏒Logarithm CalculatorFree online logarithm calculator: log_b(x) for any base with ln, lg and log₂ alongside and the change-of-base working, plus b^x and exponential equations.🎓GPA CalculatorFree online GPA calculator: enter credits and grades for a GPA on the 4.0 scale, US letters, WES bands or a 5-point scale, with a target GPA planner.🎯Significant Figures CalculatorFree online sig fig calculator: count significant figures digit by digit, round to N sig figs or decimals with six rounding modes, and compute by sig fig rules.🔢Sudoku SolverFree online sudoku solver and generator: solve any 9×9 grid in milliseconds, flag invalid or multi-solution puzzles, get single-based hints and candidates.🔣Truth Table GeneratorFree online truth table generator: enter a Boolean or propositional expression for the full table, tautology check, canonical DNF/CNF and Quine–McCluskey.🥚Conic SectionsFree online conic section calculator: from Ax²+Bxy+Cy²+Dx+Ey+F=0 identify the curve and get the standard form, centre, foci, eccentricity and asymptotes.🔐Number TheoryFree online number theory tools: modular exponentiation, modular inverses and Bézout coefficients, the Chinese remainder theorem and Euler's totient φ(n).🧾China Income Tax Calculator (IIT)Free China individual income tax calculator: monthly gross to take-home with social insurance, 2023 deductions, cumulative withholding and annual bonus options.➗Long Division CalculatorFree long division calculator that shows the work: the bracket layout with every divide–multiply–subtract step, remainders, decimals and repeating bars.🏠Mortgage CalculatorFree mortgage calculator: monthly payment, fixed-payment vs equal-principal, total interest, taxes and insurance, extra payments and a yearly schedule as CSV.📝Math Worksheet GeneratorFree printable math worksheet generator for kids: addition and subtraction within 10 to 1000, times tables, division and mixed operations, with an answer key.🏔️3D Surface PlotterFree online 3D surface plotter: type z = f(x, y) and drag to rotate a height-coloured surface — solid, wireframe or contour, several at once, with PNG export.🎲Probability SimulatorFree online probability simulator: coin flips, d4-d20 dice, weighted spinners and urn draws over a million trials, with live histograms and a chi-square test.📏Geometry SketchpadFree online geometry sketchpad: construct points, lines, circles and polygons, drag a free point and watch dependents update, with automatic measurements.∑Taylor SeriesFree online Taylor series calculator: exact coefficients for f(x) at centre a up to order 20, as fractions, with truncation error and a plot against f.🔬Confidence Intervals & TestsFree online statistical inference: confidence intervals for means and proportions, one- and two-sample tests with the statistic, df, p-value and decision.λEigenvaluesFree online eigenvalue calculator: 2×2 and 3×3 matrices — characteristic polynomial, eigenvalues (complex too), eigenvectors, trace and diagonalizability.🎲Bayes’ TheoremFree online Bayes calculator: enter a prior and likelihood (or prevalence, sensitivity, specificity) for the posterior, PPV, NPV and a natural frequency table.🔺Pascal’s TriangleFree online Pascal's triangle tool: generate any number of rows, highlight one for the full (a+b)ⁿ expansion and row sum, and look up any C(n, k) exactly.🛍️Discount CalculatorFree discount calculator: sale price after % off and stacked discounts, spend-and-save deals, deal and unit price comparison, margin, markup, sales tax, tips.→Limit CalculatorFree limit calculator: lim x→a and x→±∞, left- and right-hand limits, 0/0, ∞/∞ and 1^∞ forms by series expansion; spots limits that do not exist.🪜Matrix Step-by-StepStep-by-step matrix calculator: Gauss-Jordan elimination to RREF showing every row operation, plus determinant, inverse, rank and Ax = b in exact fractions.⏲️Time CalculatorFree time calculator: add or subtract hours, minutes and seconds, time between two clock times (even overnight), timesheet totals and decimal hours.∠Angle Converter & Unit CircleConvert degrees ↔ radians (exact, as π/6 or 3π/4) ↔ DMS ↔ gradians ↔ turns, find coterminal and reference angles, and drag an interactive unit circle.🔭Function AnalyzerAnalyze f(x): domain, range, even/odd, period, zeros, monotonic intervals, extrema, concavity, inflection points and asymptotes, with a sign chart and graph.⚡Mental Math PracticeTimed math facts drills for kids: +, −, × and ÷ in 60-second sprint, 20-question or endless mode, with instant feedback, mistake review and personal bests.✖️Multiplication TableInteractive multiplication chart up to 12×12 or 20×20 with row and column highlighting, hide-the-answers practice, a times tables quiz, printing and PNG export.💯Big Number CalculatorArbitrary-precision calculator: exact + − × ÷, 2^1000, 1000!, n choose k, Fibonacci, modular power, GCD/LCM, integer roots, primality and base conversion.⅓Decimal to Fraction ConverterConvert terminating and repeating decimals (0.1(6), 0.[142857], 0.1666…) to fractions with steps, and fractions or percents to decimals with the repetend shown.√Radical Simplifier & CalculatorSimplify square, cube and nth roots (√72 = 6√2, ∛54 = 3∛2) with steps, rationalize denominators, add and multiply radicals, and get roots to 1000 digits.🗾Scale CalculatorMap distance ↔ real distance for any scale, find the scale from two lengths, 1:24, 1:64 and HO 1:87 model sizes, drawing scales, print DPI and area scale.✒️Bézier Curve EditorFree online Bézier curve tool: pen out anchors and handles to join degree 3, 4 or 5 segments into any shape, morph between shapes, export SVG or PNG.∑LaTeX Equation EditorFree online LaTeX equation editor with live preview, a symbol palette and common formulas. Export transparent PNG or SVG, or copy MathML to paste into Word.∂Derivative CalculatorSymbolic derivative calculator with steps: product, quotient, chain and power rules, log differentiation, higher-order and partial derivatives, point values.🗳️Box Plot MakerBox and whisker plots from pasted columns: Tukey, TI-84, Excel INC/EXC or Minitab quartiles, 1.5×IQR and 3×IQR outliers, mean, notches, PNG/SVG export.🪢Graph Theory Algorithm VisualizerDraw a graph, step through BFS, DFS, Dijkstra, Bellman-Ford, Floyd–Warshall, Prim, Kruskal, topological sort, SCCs, bipartite check, Euler paths and max flow.🏭Linear Programming SolverSolve linear programs typed naturally: every simplex tableau with the pivot (two-phase or Big M), graphical method, integer programs and shadow prices.⛰️Standard Normal Table (Z Table)Interactive z table with left, right, mean-to-z and central areas, shaded charts and inverse lookup, plus t, chi-square and F critical value tables.💵China Salary Calculator (Take-Home Pay)China take-home pay calculator: editable city social insurance and housing fund rates, special deductions, monthly IIT, bonus tax, employer cost, net-to-gross.∿Fourier Series & FFT VisualizerFourier series coefficients and animated partial sums for square, sawtooth, triangle or any function (Gibbs), draw-your-own epicycles and FFT spectra.∮Integral Calculator (Step by Step)Step-by-step integral calculator: substitution, by parts, partial fractions, trig powers, completing the square. Every answer is checked by differentiation.💹IRR & NPV CalculatorInvestment calculator: NPV, IRR (detects multiple IRRs), MIRR, XNPV/XIRR on real dates, payback, discounted payback and PI. Matches Excel.🌪️Differential Equation SolverODE tool: slope fields with click-to-trace solutions (RK4/RK45), Euler vs RK4 errors, phase portraits with equilibrium types, and 2nd-order linear ODEs.👥Sample Size & Power CalculatorSample size and power: survey proportions and means, two proportions, two-sample and paired t-tests (matches G*Power), A/B test size and duration.🔑Classical Cipher LabEncode and decode Caesar/ROT13, Vigenère (with Kasiski auto-crack), Playfair, rail fence, affine, Bacon and substitution ciphers, plus an Enigma I simulator.🐚Fractal ExplorerZoom into the Mandelbrot set, Julia sets, Burning Ship, Tricorn and Newton fractals with multithreaded rendering, plus L-systems and the Barnsley fern.♟️Game Theory CalculatorEnter a two-player payoff matrix to find pure and mixed Nash equilibria with exact fractions, eliminate dominated strategies and solve zero-sum games.🐸Markov Chain CalculatorEnter a transition matrix with exact fractions to get the state diagram, n-step matrix Pⁿ, stationary distribution, classification and absorbing-chain results.♠️24 GamePlay the 24 game online with timer, hints and scoring, or solve any 3–6 numbers for 24 (or any target) and see every distinct solution with duplicates removed.📿Online AbacusFree online abacus: soroban (1/4) or suanpan (2/5). Move beads, set any number, watch step-by-step addition and subtraction, and practise flash anzan.🕒Learn to Tell TimeInteractive teaching clock: drag linked hands, see the time in words (quarter past three), work out elapsed time, take quizzes and print clock worksheets.🍕Fraction VisualizerSee fractions as pies, bars and number lines: equivalent fractions, comparing, adding unlike fractions, mixed numbers, simplifying and printable worksheets.🥛Ksp CalculatorFree solubility product calculator with 80 Ksp values at 25 °C: Ksp to molar solubility, the common-ion effect, Q vs Ksp precipitation and hydroxide pH.🧊Colligative Properties CalculatorFree colligative properties calculator: freezing point depression, boiling point elevation, osmotic pressure and Raoult's law, with Kf/Kb and molar mass.⏳Chemical Kinetics CalculatorFree chemical kinetics calculator: reaction orders and k with units by initial rates, zero, first and second-order rate laws, and Ea from the Arrhenius plot.🌡️Calorimetry & Specific Heat CalculatorFree calorimetry calculator: solve q = mcΔT with a specific heat table, find the final temperature of mixtures, get ΔH from coffee-cup and bomb calorimetry.🕸️SMILES Molecule ViewerFree online SMILES viewer: draw a 2D skeletal structure and get the formula, molar and exact mass, unsaturation, rings, H-bond counts and a Lipinski check.📶Isotope Pattern CalculatorFree isotope pattern calculator: enter a formula, pick M, [M+H]+, [M+Na]+ or [M−H]− and get monoisotopic m/z, average mass and the isotope distribution.💎Unit Cells & Crystal StructuresInteractive 3D unit cells (SC, BCC, FCC, HCP, NaCl, CsCl, ZnS, diamond, perovskite) with atoms per cell, coordination number, packing efficiency and density.🌠Light Energy & Atomic SpectraConvert wavelength, frequency and photon energy (eV, J, kJ/mol), compute hydrogen spectral lines, photoelectric stopping potential and de Broglie wavelength.🔬Beer–Lambert & Calibration CurveFree Beer-Lambert calculator: solve A = εbc for any variable, convert absorbance and %T, and fit a calibration curve with R², unknowns, 95% CI and LOD/LOQ.🧩Ionic Compound Formula & NamingWrite ionic formulas from cation and anion by criss-cross, name compounds from formulas and find formulas from names, with acids, hydrates and a quiz.📛IUPAC Name GeneratorName organic compounds from SMILES: IUPAC 2013 and traditional names, highlighted parent chain and step-by-step reasoning. Also name-to-structure and a quiz.🪞Isomer GeneratorList every structural isomer of a formula like C5H12, C4H10O or C3H6Cl2, with drawings, IUPAC names, SMILES, class counts and stereoisomer totals.🔀Molecular Orbital DiagramMO diagrams for H₂–Ne₂, O₂²⁻, N₂⁺, CO, NO, CN⁻ and HF with Hund’s-rule filling: MO configuration, bond order, unpaired electrons, magnetism and HOMO/LUMO.♻️Born–Haber Cycle CalculatorBorn–Haber cycle for NaCl, MgO, CaF₂, Al₂O₃ and more: built-in data, lattice energy or any unknown via Hess’s law, a scaled diagram and Kapustinskii comparison.🫧Net Ionic Equation CalculatorFree net ionic equation calculator: it balances the equation, splits strong electrolytes by solubility rules, cancels spectator ions and checks the charge.〰️IR Spectroscopy TableFree interactive IR correlation table: 60+ functional group bands with range, intensity and shape on a 4000–400 cm⁻¹ chart; enter peaks to identify groups.🧲¹H NMR Spectrum SimulatorSimulate ¹H NMR spectra at 60–600 MHz from shifts, integrals and J values: splitting trees, multiplicity (t, q, dd, dt), journal peak lists and a shift table.🧫Peptide & Protein CalculatorPeptide calculator: formula, monoisotopic and average mass, pI with charge vs pH curve, extinction coefficient, GRAVY, ESI m/z and DNA-to-protein translation.🎳Central Limit Theorem SimulatorProbability simulations: an animated Galton board vs binomial and normal curves, the central limit theorem, law of large numbers and Monte Carlo π.🎇Complex Function Plotter (Domain Coloring)Plot complex functions f(z) by domain coloring: argument as hue, modulus contours, zeros, poles and singularities, with a Riemann sphere view and zoom.▱Linear Transformation VisualizerEnter a 2×2 or 3×3 matrix and watch the grid rotate, scale, shear, reflect or project, with basis vectors, determinant, eigenvectors, inverse and composition.🧊Polyhedra ViewerRotate the 5 Platonic and 13 Archimedean solids, prisms and pyramids in 3D: truncation, duals, Euler’s formula, area and volume, unfolding and printable nets.🥧Chi-Square & ANOVA CalculatorChi-square goodness of fit and independence (Yates, Fisher exact, Cramér’s V), one-way and two-way ANOVA, Tukey HSD, Kruskal–Wallis and Levene’s test.🔨Matrix Decomposition CalculatorStep-by-step LU with pivoting in exact fractions, Cholesky, QR (Gram–Schmidt or Householder) and SVD with rank, condition number and low-rank approximation.🏝️FIRE CalculatorFind your FIRE number and years to financial independence from income, spending and real returns, with Monte Carlo success rates, Coast FI and Barista FI.