QiLing Tools

📐Free Online Math Tools: Graphing Calculator, Equation Solver, Geometry & Probability

Over 30 free math tools in your browser: type a formula and graph it (functions, parametric and polar curves, data fitting, roots and extrema), plus a scientific calculator, equation solver, inequality solver, linear systems, regression, logarithms, conic sections, number theory, a Bézier curve editor, a LaTeX equation editor, confidence intervals and hypothesis tests, eigenvalues, Bayes’ theorem, Pascal’s triangle, derivatives and integrals, geometry and triangle solvers, trigonometry, statistics and probability distributions, combinations, matrices, sequences, fractions, percentages, ratios, complex numbers, unit conversion, interest, coordinate geometry, vectors, polynomials, set operations, truth tables, sudoku, GPA, significant figures, long division, arithmetic worksheets, mortgages, China income tax, 3D surface plots, Taylor series, a geometry sketchpad, a probability simulator, time calculator, discounts, step-by-step matrices, limits, function analysis, mental math practice, times tables, angle conversion, radicals, decimal ↔ fraction, big-number math, scale calculation, step-by-step derivatives, linear programming, graph algorithms, normal tables, box plots, a China salary calculator, step-by-step integrals, differential equations, Fourier series and FFT, sample size, IRR/NPV analysis, game theory, classical ciphers, fractals, Markov chains, the 24 game, an abacus, telling time, fraction visuals, polyhedra, linear transforms, domain coloring, CLT simulations, chi-square and ANOVA, FIRE planning and matrix decompositions. Everything runs locally.

📈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.