# Learning & Teaching Tools

> Tools for students and teachers: step-by-step solvers, math drills, handwriting sheets, timetables, flashcards, certificates and visual demos.

- URL: https://qilingtools.com/en/tags/education
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

## Tools (105)

- [Graphing Calculator](https://qilingtools.com/en/math/graph): Free 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 Calculator](https://qilingtools.com/en/math/calculator): Free 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 Solver](https://qilingtools.com/en/math/equation): Free online equation solver: enter coefficients for linear, quadratic (with discriminant, vertex and complex roots) and cubic equations, plus 2×2 systems.
- [Fraction Calculator](https://qilingtools.com/en/math/fraction): Free online fraction calculator: add, subtract, multiply and divide fractions with automatic reduction, plus fraction ↔ decimal with repeating digits.
- [GCD and LCM](https://qilingtools.com/en/math/gcd-lcm): Free online GCD and LCM calculator: works with two or more integers, says whether they are coprime, shows each prime factorization and every Euclidean step.
- [Matrix Calculator](https://qilingtools.com/en/math/matrix): Free online matrix calculator: add, subtract and multiply matrices up to 8×8, transpose, and compute the determinant, inverse, matrix power and rank.
- [Geometry Calculator](https://qilingtools.com/en/math/geometry): Free online geometry calculator: area and perimeter of circles, triangles, polygons and more, plus volume and surface area of solids, with the formulas shown.
- [Triangle Solver](https://qilingtools.com/en/math/triangle): Free online triangle solver: SSS, SAS, ASA, AAS and SSA inputs give every side and angle plus the area, perimeter, heights, circumradius and inradius.
- [Sequence Calculator](https://qilingtools.com/en/math/sequence): Free online sequence calculator: nth term, sum of n terms, mean and infinite sum for arithmetic and geometric sequences, plus exact big-integer Fibonacci.
- [Ratio Calculator](https://qilingtools.com/en/math/ratio): Free 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 Numbers](https://qilingtools.com/en/math/complex): Free 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 Notation](https://qilingtools.com/en/math/scientific-notation): Free online scientific notation converter: switch between plain numbers and a×10ⁿ, accept 3.5e6, and get engineering notation with SI prefixes and rounding.
- [Derivative & Integral](https://qilingtools.com/en/math/calculus): Free 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.
- [Trigonometry](https://qilingtools.com/en/math/trigonometry): Free online trigonometry calculator: sin, cos, tan, cot, sec and csc from degrees or radians, inverse functions, DMS conversion and a special-angle table.
- [Coordinate Geometry](https://qilingtools.com/en/math/coordinate): Free online coordinate geometry calculator: distance, midpoint, slope, line equations, point-to-line distance with the foot, triangle centres and polar form.
- [Polynomial Calculator](https://qilingtools.com/en/math/polynomial): Free 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 Operations](https://qilingtools.com/en/math/set): Free online set calculator: union, intersection, differences and symmetric difference of two groups, with subset and disjoint checks and Jaccard similarity.
- [Inequality Solver](https://qilingtools.com/en/math/inequality): Free 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 Equations](https://qilingtools.com/en/math/linear-system): Free 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.
- [Logarithm Calculator](https://qilingtools.com/en/math/logarithm): Free 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 Calculator](https://qilingtools.com/en/math/gpa): Free 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 Calculator](https://qilingtools.com/en/math/significant-figures): Free 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.
- [Truth Table Generator](https://qilingtools.com/en/math/truth-table): Free online truth table generator: enter a Boolean or propositional expression for the full table, tautology check, canonical DNF/CNF and Quine–McCluskey.
- [Conic Sections](https://qilingtools.com/en/math/conic): Free 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.
- [Chinese to Pinyin](https://qilingtools.com/en/pinyin): Free online Chinese to pinyin converter: tone marks, numbers or none, initials only, context-aware polyphones, surname readings and ruby annotation.
- [Long Division Calculator](https://qilingtools.com/en/math/long-division): Free long division calculator that shows the work: the bracket layout with every divide–multiply–subtract step, remainders, decimals and repeating bars.
- [Math Worksheet Generator](https://qilingtools.com/en/math/worksheet): Free printable math worksheet generator for kids: addition and subtraction within 10 to 1000, times tables, division and mixed operations, with an answer key.
- [Typing Speed Test](https://qilingtools.com/en/typing-test): Free online typing test: WPM, CPM and accuracy over 30s, 60s, 120s or a full passage, with live error highlighting, a speed chart and personal bests.
- [3D Surface Plotter](https://qilingtools.com/en/math/3d-graph): Free 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.
- [Geometry Sketchpad](https://qilingtools.com/en/math/geometry-board): Free online geometry sketchpad: construct points, lines, circles and polygons, drag a free point and watch dependents update, with automatic measurements.
- [Taylor Series](https://qilingtools.com/en/math/taylor): Free 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.
- [Eigenvalues](https://qilingtools.com/en/math/eigenvalue): Free online eigenvalue calculator: 2×2 and 3×3 matrices — characteristic polynomial, eigenvalues (complex too), eigenvectors, trace and diagonalizability.
- [Pascal’s Triangle](https://qilingtools.com/en/math/pascal): Free 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.
- [Flashcards](https://qilingtools.com/en/flashcards): Free online flashcards with SM-2 spaced repetition: grade each card Again, Hard, Good or Easy; several decks, CSV and Anki import, saved in your browser.
- [Limit Calculator](https://qilingtools.com/en/math/limit): Free 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-Step](https://qilingtools.com/en/math/matrix-steps): Step-by-step matrix calculator: Gauss-Jordan elimination to RREF showing every row operation, plus determinant, inverse, rank and Ax = b in exact fractions.
- [Function Analyzer](https://qilingtools.com/en/math/function-analysis): Analyze f(x): domain, range, even/odd, period, zeros, monotonic intervals, extrema, concavity, inflection points and asymptotes, with a sign chart and graph.
- [Mental Math Practice](https://qilingtools.com/en/math/mental-math): Timed math facts drills for kids: +, −, × and ÷ in 60-second sprint, 20-question or endless mode, with instant feedback, mistake review and personal bests.
- [Multiplication Table](https://qilingtools.com/en/math/times-table): Interactive 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.
- [Online Whiteboard](https://qilingtools.com/en/whiteboard): Free online whiteboard: infinite canvas, pressure-aware pen, highlighter, eraser, shapes, arrows, text and sticky notes, undo/redo, pages and PNG/SVG export.
- [Big Number Calculator](https://qilingtools.com/en/math/big-number): Arbitrary-precision calculator: exact + − × ÷, 2^1000, 1000!, n choose k, Fibonacci, modular power, GCD/LCM, integer roots, primality and base conversion.
- [Decimal to Fraction Converter](https://qilingtools.com/en/math/decimal-fraction): Convert 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 & Calculator](https://qilingtools.com/en/math/radical): Simplify 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 Calculator](https://qilingtools.com/en/math/scale): Map 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.
- [LaTeX Equation Editor](https://qilingtools.com/en/math/latex): Free 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.
- [Regex Visualizer](https://qilingtools.com/en/regex-visualizer): Visualize JavaScript regexes as railroad diagrams with a plain-language breakdown of groups, quantifiers, classes and lookarounds. Export SVG or PNG.
- [Chemical Equation Balancer](https://qilingtools.com/en/math/chemical-equation): Balance chemical equations by the algebraic method: smallest whole-number coefficients, brackets, hydrates, ionic charges, electrons, atom and charge checks.
- [Derivative Calculator](https://qilingtools.com/en/math/derivative): Symbolic derivative calculator with steps: product, quotient, chain and power rules, log differentiation, higher-order and partial derivatives, point values.
- [Interactive Periodic Table](https://qilingtools.com/en/math/periodic-table): Interactive periodic table of all 118 elements: colour by category, block, electronegativity, atomic mass, phase or melting point; search and click for details.
- [Certificate Maker](https://qilingtools.com/en/certificate): Make award certificates in bulk: classic, gold, modern and simple templates, a pasted list of names, {name}/{award} placeholders, seal, PDF or PNG ZIP.
- [Class Timetable Maker](https://qilingtools.com/en/timetable): Make a class timetable online: Mon–Fri to Mon–Sun, periods with times, auto colors, quick fill, merged double periods, A4 landscape print, PNG, CSV and JSON.
- [Graph Theory Algorithm Visualizer](https://qilingtools.com/en/math/graph-theory): Draw a graph, step through BFS, DFS, Dijkstra, Bellman-Ford, Floyd–Warshall, Prim, Kruskal, topological sort, SCCs, bipartite check, Euler paths and max flow.
- [Flexbox & Grid Playground](https://qilingtools.com/en/flex-grid): Interactive Flexbox and CSS Grid playground: tweak container and item properties live, drag to name grid-template-areas, and copy CSS, HTML or Tailwind classes.
- [Handwriting Practice Sheet Maker](https://qilingtools.com/en/copybook): Make printable handwriting sheets: Chinese tian/mi grids, pinyin grids, manuscript paper, English four-line paper, tracing or model-and-trace, PDF or PNG.
- [Seating Chart Maker](https://qilingtools.com/en/seating-chart): Make classroom, U-shape, round-table or conference seating charts: seeded random, by height, boy–girl, keep-apart/together rules, locks, rotation, print.
- [Fourier Series & FFT Visualizer](https://qilingtools.com/en/math/fourier): Fourier 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)](https://qilingtools.com/en/math/integral): Step-by-step integral calculator: substitution, by parts, partial fractions, trig powers, completing the square. Every answer is checked by differentiation.
- [Graph Paper Generator](https://qilingtools.com/en/graph-paper): Make printable paper: square grid, dot, isometric, hex, polar, log, engineering, music staff, guitar tab, Cornell notes, lined and calligraphy as vector PDF.
- [Word Search & Crossword Maker](https://qilingtools.com/en/word-puzzle): Make printable word search and crossword puzzles from your words and clues: diagonal and backwards words, compact numbered crosswords, answer keys, seeds.
- [Sorting Algorithm Visualizer](https://qilingtools.com/en/sorting-visualizer): Watch 14 sorting algorithms animate: bubble, insertion, shell, merge, quick, heap, counting, radix, bucket and Timsort, with counters, step mode and races.
- [24 Game](https://qilingtools.com/en/math/24): Play 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 Abacus](https://qilingtools.com/en/math/abacus): Free 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 Time](https://qilingtools.com/en/math/clock): Interactive teaching clock: drag linked hands, see the time in words (quarter past three), work out elapsed time, take quizzes and print clock worksheets.
- [Fraction Visualizer](https://qilingtools.com/en/math/fraction-visual): See fractions as pies, bars and number lines: equivalent fractions, comparing, adding unlike fractions, mixed numbers, simplifying and printable worksheets.
- [Chord & Scale Finder](https://qilingtools.com/en/audio/chords): Free chord library: every chord type in all 12 keys with guitar and ukulele voicings, piano view, a chord finder for inversions, and scale charts.
- [Circle of Fifths](https://qilingtools.com/en/audio/circle-of-fifths): Interactive circle of fifths: key signatures, relative minors, diatonic chords with Roman numerals, playable progressions, transposer and capo tips.
- [Electron Configuration Calculator](https://qilingtools.com/en/math/electron-config): Free electron configuration calculator for any element or ion (Fe3+, O2-): full and noble-gas notation, an orbital diagram, unpaired electrons and shells.
- [VSEPR Molecular Geometry](https://qilingtools.com/en/math/vsepr): Free VSEPR calculator: enter SF4, NH4+ or SO4^2- for the steric number, lone pairs, AXE notation, electron and molecular geometry, angles and hybridization.
- [Ksp Calculator](https://qilingtools.com/en/math/ksp): Free 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.
- [Ionic Compound Formula & Naming](https://qilingtools.com/en/math/ionic-compound): Write 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 Generator](https://qilingtools.com/en/math/organic-name): Name 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 Generator](https://qilingtools.com/en/math/isomers): List every structural isomer of a formula like C5H12, C4H10O or C3H6Cl2, with drawings, IUPAC names, SMILES, class counts and stereoisomer totals.
- [Molecular Orbital Diagram](https://qilingtools.com/en/math/mo-diagram): MO 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.
- [Net Ionic Equation Calculator](https://qilingtools.com/en/math/net-ionic): Free net ionic equation calculator: it balances the equation, splits strong electrolytes by solubility rules, cancels spectator ions and checks the charge.
- [Projectile Motion Simulator (with Air Resistance)](https://qilingtools.com/en/math/projectile): Animated projectile simulator: set speed, angle, height and gravity (Earth, Moon, Mars, Jupiter), add air drag (RK4), compare paths and find the best angle.
- [Pendulum & Double Pendulum Simulator](https://qilingtools.com/en/math/pendulum): Simulate a nonlinear pendulum (RK4) beside its small-angle twin: exact period, damping, phase space and energy plots, plus a chaotic double pendulum.
- [Collision Simulator (Momentum & Energy)](https://qilingtools.com/en/math/collision): Simulate 1D cart collisions with any masses, velocities and restitution e, see momentum and KE before and after, plus 2D billiard collisions.
- [Orbit & Gravity Simulator](https://qilingtools.com/en/math/orbit): Drag a satellite's velocity to get circular, elliptic or hyperbolic orbits with live orbital elements, Kepler's equal areas, N-body demos and Δv tools.
- [Lens & Mirror Ray Diagram](https://qilingtools.com/en/math/optics): Interactive ray diagrams for converging and diverging lenses and concave and convex mirrors: drag the object to see image position, size and magnification.
- [Refraction & Total Internal Reflection Simulator](https://qilingtools.com/en/math/refraction): Drag a light ray through water, glass or diamond: refraction angle, Fresnel reflectance, critical angle, Brewster angle, prism dispersion and apparent depth.
- [Wave Superposition & Standing Waves](https://qilingtools.com/en/math/waves): Interactive wave simulator: superpose traveling waves, see standing waves on strings and pipes with nodes and harmonics, hear beats, and explore a ripple tank.
- [Doppler Effect Simulator](https://qilingtools.com/en/math/doppler): Doppler effect calculator with animation: moving source and observer, Mach cone and sonic boom, relativistic redshift, radar speed guns and pass-by audio.
- [Electric Field & Potential Simulator](https://qilingtools.com/en/math/electric-field): Drag point charges and watch electric field lines and equipotentials update live. Probe E and V anywhere, compute Coulomb forces and launch a test charge.
- [Spring Oscillator & Resonance](https://qilingtools.com/en/math/spring): Animated spring-mass-damper with driving force: live x(t), damping regime with ω₀, ζ and Q, resonance curves, and coupled normal modes with beats.
- [Central Limit Theorem Simulator](https://qilingtools.com/en/math/clt): Probability 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)](https://qilingtools.com/en/math/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 Visualizer](https://qilingtools.com/en/math/linear-transform): Enter 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 Viewer](https://qilingtools.com/en/math/polyhedra): Rotate the 5 Platonic and 13 Archimedean solids, prisms and pyramids in 3D: truncation, duals, Euler’s formula, area and volume, unfolding and printable nets.
- [Brain Tests](https://qilingtools.com/en/brain-tests): Free quick brain tests: reaction time, sequence, number, verbal and visual memory, aim trainer, chimp test, Stroop test and Schulte tables, with personal bests.
- [Reading Speed Test](https://qilingtools.com/en/reading-speed): Test your reading speed: original English and Chinese passages at three levels, a comprehension quiz, effective WPM vs. average, plus an RSVP speed reader.
- [Matrix Decomposition Calculator](https://qilingtools.com/en/math/decomposition): Step-by-step LU with pivoting in exact fractions, Cholesky, QR (Gram–Schmidt or Householder) and SVD with rank, condition number and low-rank approximation.
- [Magnetic Field Simulator](https://qilingtools.com/en/math/magnetic-field): Drag current-carrying wires and bar magnets to see field lines, compass needles and |B|. Exact loop and solenoid fields, on-axis B(z) and forces between wires.
- [Charged Particle in E & B Fields](https://qilingtools.com/en/math/charged-particle): Electrons, protons or alphas in any uniform E and B in 3D: gyroradius, period, pitch and E×B drift, plus a velocity selector, mass spectrometer and cyclotron.
- [Electromagnetic Induction & Generator](https://qilingtools.com/en/math/induction): Move a magnet through a coil and watch flux, EMF and the galvanometer obey Lenz's law, plus an AC generator, a rod on rails and a transformer.
- [DC Circuit Builder & Solver](https://qilingtools.com/en/math/dc-circuit): Build DC circuits on a grid with batteries, resistors, bulbs, switches and meters. Nodal analysis gives every voltage, current and power, plus KCL/KVL.
- [Diffraction, Interference & Polarization](https://qilingtools.com/en/math/diffraction): Free wave-optics simulator: slit and grating patterns in white light, Airy disks and the Rayleigh limit, thin-film colours, Newton's rings and Malus's law.
- [Heat Conduction Simulator](https://qilingtools.com/en/math/heat-conduction): Simulate heat conduction: animated 1D rod (Crank–Nicolson) with real materials, paintable 2D plate, composite wall U-value calculator and Newton cooling fit.
- [Fluid Mechanics Simulator (Bernoulli, Buoyancy, Pipe Flow)](https://qilingtools.com/en/math/fluid): Interactive fluid mechanics: drag a pipe to see Bernoulli at work, Venturi meter, Torricelli tank draining, buoyancy, Pascal press and Reynolds number.
- [Moment of Inertia & Rotational Dynamics](https://qilingtools.com/en/math/rotation): Moment of inertia for rods, disks, spheres, plates and composites with the parallel-axis theorem; rolling race, spinning skater, Atwood machine.
- [Circular Motion & Centripetal Force Simulator](https://qilingtools.com/en/math/circular-motion): Animated circular motion: velocity and centripetal vectors, cut the string, centrifugal force, banked curves, coaster loops, conical pendulum.
- [Quantum Mechanics Simulator (Schrödinger Equation)](https://qilingtools.com/en/math/quantum): Solve the 1D Schrödinger equation online: energy levels and wavefunctions for wells, oscillators or a drawn potential, plus tunneling wave packets and T(E).
- [Heat Engine Cycles & PV Diagrams](https://qilingtools.com/en/math/thermo-cycle): Interactive PV and TS diagrams for Carnot, Otto, Diesel, Brayton, Stirling and custom cycles. Drag states, see Q, W, ΔU, ΔS per step, efficiency and COP.
- [Kinetic Theory of Gases Simulator](https://qilingtools.com/en/math/gas-kinetics): Watch hundreds of colliding molecules: speed histogram vs Maxwell–Boltzmann, pressure from wall impacts, mean free path, piston heating, effusion and mixing.
- [Simple Machines Simulator (Levers, Pulleys, Gears)](https://qilingtools.com/en/math/simple-machines): Drag a lever’s fulcrum, lift loads with pulleys, mesh gear trains and bike gears, and compare inclines, screw jacks and wedges: force and efficiency.
- [ASCII Table](https://qilingtools.com/en/ascii-table): Free online ASCII table: codes 0-127 in decimal, hex, octal, binary and escape form, every control character explained, Latin-1 128-255 and a code point lookup.