Free Tools
Interactive tools to help you learn and practice. All free, all in your browser.
Enter any expression and watch it solve step by step following PEMDAS. Each operation is color-coded so you see exactly what happens and why.
See long division worked out step by step with the traditional layout, divide-multiply-subtract-bring-down explanations, and remainder or decimal results.
Type a decimal, fraction, or percent and the other two update instantly. Pie chart, 100-grid, and number line show the same value three ways.
Build visual factor trees, find prime factorizations, and compute GCF and LCM with a Venn diagram of shared prime factors.
Four modes for every percent problem: find the part, the percent, the whole, or percent change. 100-grid and bar model visuals with step-by-step math.
See expanded multiplication, area and volume models, powers tables, and rules for zero and negative exponents. Visual models for squares and cubes.
Add, subtract, multiply, or divide fractions with fraction bar models, area models, and step-by-step solutions. Supports mixed numbers.
Add or subtract integers on a visual number line. Arrow shows direction and distance, with step-by-step explanations for negative number operations.
Solve one-step and two-step equations visually with an SVG balance scale. See step-by-step operations applied to both sides.
Explore ratios with tape diagrams, equivalent ratio tables, unit rates, and cross-multiplication proportion solving.
See any number broken into place values with base-10 blocks, expanded form, and word form. Supports decimals.
Solve ax² + bx + c = 0 with an interactive graph. See roots, vertex, discriminant, and step-by-step solutions.
Solve systems of linear equations with step-by-step Gaussian elimination, interactive matrix visualization, and exact fraction arithmetic.
Explore the unit circle interactively. Drag a point to see trig values, exact forms, and geometric meanings for any angle.
Compute factorials, permutations, combinations, and multinomial coefficients with step-by-step breakdowns and an interactive Pascal's Triangle.
Compute determinants, inverses, row reduction, multiplication, and more with step-by-step solutions.
Solve any triangle with step-by-step Law of Sines and Law of Cosines solutions.
Factor polynomials up to degree 4 and find roots with step-by-step solutions.
Graph and solve linear and quadratic inequalities with number line shading, 2D region visualization, and interval notation.
Add, subtract, scale, dot product, and cross product of 2D vectors with SVG coordinate plane, tip-to-tail and parallelogram methods.
See how a 2x2 matrix transforms a unit square. Visualize rotation, scaling, shearing, and reflection with determinant and eigenvalues.
Evaluate logs in any base, solve log equations, use change-of-base formula, and see the graph with its exponential inverse. Log properties panel included.
Add, subtract, multiply, divide complex numbers with an Argand diagram. See polar form, modulus, argument, and step-by-step math.
Calculate P(A or B), P(A and B), P(not A), and conditional P(A|B) with a Venn diagram and step-by-step formulas.
Solve 2x2 through 5x5 systems with Gaussian elimination. Step-by-step row operations, augmented matrix display, determinant, and solution classification.
Find eigenvalues and eigenvectors of 2×2 and 3×3 matrices. Shows characteristic polynomial, real and complex eigenvalues, normalized eigenvectors, diagonalization matrices P and D, and an interactive eigenvector direction plot.
Visualize span, linear independence, basis, and dimension in ℝ². Input up to 4 vectors, see their span shaded on an interactive graph, check independence, find a basis, and compute Gram-Schmidt orthogonalization.
Factor any number into primes with a branching factor tree and step-by-step division. Animate the Sieve of Eratosthenes up to 500, watching multiples get crossed out by color as primes emerge.
Compute a mod n, modular addition, multiplication, and fast exponentiation. Find modular inverses with the extended Euclidean algorithm, solve systems via the Chinese Remainder Theorem, and visualize clock arithmetic on an interactive number circle.
Build and analyze graphs with draggable SVG nodes. Run BFS and DFS traversals, find shortest paths with Dijkstra's algorithm, compute minimum spanning trees with Prim's algorithm, and detect Eulerian circuits and paths.
Enter elements for 2 or 3 sets and see results highlighted on interactive Venn diagrams. Explore union, intersection, complement, difference, symmetric difference, power set, and Cartesian product with cardinality stats.
Enter a dataset to see mean, median, and mode on an interactive number line with a balance-point fulcrum, box plot, and step-by-step calculations.
Compute mean, median, mode, standard deviation, and more. Visualize data with interactive box plots and histograms.
Find the best-fit line for paired data. See slope, intercept, correlation, R-squared, scatter plot, and residual analysis.
Explore normal, binomial, Poisson, and uniform distributions. Visualize PDF/CDF plots, compute probabilities with draggable bounds, and find inverse values.
Run z-tests, t-tests, two-sample t-tests, and chi-square goodness-of-fit tests. See test statistics, p-values, critical values, and step-by-step breakdowns.
Calculate confidence intervals for means (z and t) and proportions. See margin of error, critical values, number line visualization, and sample size calculations.
Interactive bell curve with shaded probability regions. Convert between raw scores and Z-scores with numerical integration.
Compute posterior probability with an SVG tree diagram, contingency table, and natural frequency display. Step-by-step Bayes formula.
One-way ANOVA for comparing 2-6 group means. F-statistic, p-value, effect size, summary table, and side-by-side box plots.
Test independence with contingency tables up to 4x4. Chi-square statistic, p-value, Cramer's V, and grouped bar chart.
Draw repeated samples from non-normal populations and watch the sampling distribution become normal. Side-by-side histograms.
Fit linear, quadratic, cubic, exponential, logarithmic, and power models to data. Compare R-squared, residuals, and predict new values with scatter plots.
Calculate area and perimeter of rectangles, triangles, parallelograms, trapezoids, and circles with SVG visuals and step-by-step formulas.
Visualize complementary, supplementary, vertical angles, and parallel lines with transversals. Color-coded equal angle pairs.
Explore 15 classical geometry constructions step by step. Watch animations, drag points, and try constructions yourself.
Explore circles, ellipses, parabolas, and hyperbolas with interactive graphs, equations, foci, and tangent lines.
Calculate surface area and volume for 12 three-dimensional shapes with interactive SVG 3D diagrams, step-by-step KaTeX formulas, and real-world presets.
Five modes for distance and midpoint, slope and line equations, parallel and perpendicular lines, circle equations, and triangle properties. Interactive JSXGraph plot with special points.
Visualize translations, rotations, reflections, dilations, and compositions on a coordinate plane. See original and transformed shapes side by side with JSXGraph.
Solve for any missing side with step-by-step math, see the visual proof with colored squares on each side, generate Pythagorean triples, and extend to 3D distance.
Explore six circle theorems with interactive JSXGraph diagrams. Inscribed angles, tangent-radius, arc length, sector area, chord properties, secant-tangent, and cyclic quadrilaterals.
Calculate and visualize properties of regular polygons from 3 to 20 sides. SVG diagram with interior angles, diagonals, area, perimeter, apothem, and circumradius.
Plot functions, explore properties, and see step-by-step derivative analysis with interactive graphing.
Plot f(x), f'(x), and F(x) together. Drag a point to see the tangent line slope and accumulated area with step-by-step differentiation.
Explore arithmetic and geometric sequences with terms, partial sums, and convergence analysis.
Graph roses, cardioids, Lissajous curves, cycloids, and more with animated tracing and area/arc length computation.
Approximate definite integrals with left, right, midpoint, and trapezoidal methods. Slider for number of rectangles shows convergence.
Compute left-hand, right-hand, and two-sided limits numerically. SVG graph, approach table, and discontinuity classification.
Solve separable, first-order linear, and second-order constant coefficient ODEs. Slope fields, solution curves, characteristic equation analysis, and step-by-step math.
Calculate trajectory, range, max height, and time of flight for projectile motion. Visualize the parabolic path with an interactive time slider and velocity vectors.
Calculate voltage, current, resistance, and power with Ohm's law. Build series and parallel resistor networks with step-by-step equivalent resistance.
Visualize image formation with interactive ray diagrams for lenses and mirrors.
Solve constant-acceleration problems with step-by-step solutions and motion graphs.
Visualize transverse waves, superposition, interference, and standing waves.
Visualize two-source interference patterns, thin-film colors, and beats with animated canvas and path-difference analysis.
Explore Newton's second law with interactive free-body diagrams on surfaces, inclines, and more.
Simulate elastic, inelastic, and partially inelastic 1D collisions with energy analysis.
Visualize refraction, total internal reflection, and critical angles with an interactive ray diagram.
Track kinetic, potential, and spring energy as an object moves along ramps, roller coasters, and spring systems.
Animate mass-spring and pendulum systems with damping modes, displacement graphs, and phase portraits.
Calculate gravitational force, field strength, orbital velocity, and escape velocity with an SVG force diagram and step-by-step math.
Solve Q=mcΔT for any variable or find the equilibrium temperature when mixing two substances. Step-by-step thermal energy math.
Visualize exponential decay with an SVG curve and atom grid. Compute remaining quantity, decay constant, and activity for common isotopes.
Compute Lorentz factor, time dilation, and length contraction at relativistic speeds. Includes twin paradox scenario and γ vs v/c curve.
Calculate perceived frequency shift with SVG wavefront visualization. Handles approaching and receding sources with Mach number detection.
Place positive and negative charges on a canvas. See electric field arrows, field lines, and potential color maps update in real time.
Calculate force on a current-carrying wire or moving charge in a magnetic field. SVG diagram with right-hand rule visualization.
Shine light on metals and observe electron emission. Adjust frequency and intensity to discover Einstein's photoelectric equation.
Calculate torque, moment of inertia for common shapes, angular acceleration, and rotational kinetic energy with an SVG force diagram.
Four-mode rotational mechanics tool covering moment of inertia (10 shapes), angular momentum and dynamics, rolling without slipping on inclines, and rotational equilibrium with SVG visualizations.
Apply Bernoulli's equation and the continuity equation to solve for pressure, velocity, or height at two points in a fluid flow with pipe visualization.
Calculate electrostatic force with Coulomb's law, parallel plate capacitance, and series/parallel capacitor combinations with SVG diagrams and step-by-step math.
Convert between frequency, wavelength, and energy. Interactive EM spectrum bar from radio to gamma rays with Wien's displacement law for blackbody radiation.
Calculate mechanical advantage, effort force, and efficiency for fixed, movable, compound, and multiple pulley systems. SVG diagrams show rope paths and force arrows.
Configure upper and lower pulley blocks with 1-4 sheaves, toggle rope anchor, and see how compound friction affects a real block and tackle. Dynamic SVG rope threading diagram.
Calculate speed ratios, torque, belt tension, belt length, and power for belt-driven systems. Animated SVG shows two pulleys connected by a belt rotating at correct relative speeds.
Calculate gear ratios, output speed, and torque for simple gear pairs, compound gear trains (up to 4 pairs), and planetary epicyclic systems. Animated SVG shows meshing gear teeth rotating at correct relative speeds.
Visualize a particle's wave function tunneling through a potential barrier. Adjust energy, barrier height, and width to see transmission and reflection coefficients with exact formulas and animated waves.
Visualize hydrogen electron orbitals with a 2D probability density heatmap. Select quantum numbers (n, l, m) to see orbital shapes, radial probability plots, energy levels, and node structure.
Calculate orbital parameters with Kepler's laws, escape velocities for any solar system body, and Hohmann transfer orbits. SVG orbit diagrams, step-by-step formulas, and planetary data.
Analyze transient and AC steady-state behavior of RC, RL, and RLC circuits. Visualize voltage and current vs time, impedance resonance curves, damping classification, and step-by-step formulas.
Compare ideal (no drag) vs real (with drag) projectile trajectories side by side. RK4 numerical integration computes the drag trajectory. Calculates terminal velocity, range reduction, and time of flight difference for presets including baseball, golf ball, cannonball, tennis ball, feather, and skydiver.
Analyze forced oscillations with viscous damping. Plot the resonance curve (amplitude vs driving frequency), time-domain transient response, and steady-state amplitude. Adjust mass, stiffness, damping, force amplitude, and driving frequency. Classifies underdamped, critically damped, and overdamped regimes. Presets for car suspension, earthquake damper, and high-Q resonance.
Four modes: pressure basics (P = F/A) with unit conversions, hydrostatic pressure at depth (P = P₀ + ρgh), Pascal's law hydraulics with mechanical advantage, and atmospheric pressure vs altitude. SVG hydraulic press diagram, depth gradient, and altitude bar. Presets for deep ocean, hydraulic car lift, blood pressure, tire pressure, and scuba diving.
Explore Gauss's Law with five charge distributions: point charge, infinite line, infinite plane, uniformly charged sphere, and uniformly charged cylinder. SVG cross-section visualization, E(r) graph, step-by-step KaTeX derivation, and presets for inside/outside Gaussian surfaces.
Visualize magnetic fields from straight wires, current loops, solenoids, and parallel wires. Calculate B-field magnitude at a probe point, see 2D field line patterns, right-hand rule reminders, and step-by-step Biot-Savart and Ampere's Law derivations.
Interactive periodic table with all 118 elements. Search by name or symbol, compare elements side-by-side, and view by category, electronegativity, phase, or orbital block.
Enter any chemical formula to compute molar mass, element breakdown with mass percentages, and step-by-step calculations. Supports parenthesized groups.
Solve PV=nRT for any variable with unit support for pressure, volume, and temperature. Gas particle visualization and step-by-step math.
Enter pH, pOH, [H+], or [OH-] to compute all four. Color-coded pH scale bar, acid/base classification, and step-by-step KaTeX.
Three modes: compute molarity from mass, dilution M1V1=M2V2, and solution preparation. Beaker visualization and step-by-step math.
Enter an unbalanced chemical equation and get integer coefficients, color-coded atom counts, and step-by-step verification that every element balances.
Look up any of the 118 elements to see full electron configuration, noble gas shorthand, orbital box diagram, valence electrons, and oxidation states.
Enter a substance and quantity in grams, moles, molecules, or liters at STP to convert between all units with a mole map and dimensional analysis.
Enter a molecular formula to generate its Lewis structure with bonds, lone pairs, VSEPR geometry, and bond angles. Step-by-step valence electron counting.
Enter a chemical reaction to assign oxidation numbers, identify what is oxidized and reduced, and find oxidizing and reducing agents with electron transfer count.
Trace the complete radioactive decay series for U-238, U-235, and Th-232. See each isotope step with decay mode, half-life, and energy on a cascade diagram or N-Z nuclide chart.
Calculate boiling point elevation, freezing point depression, osmotic pressure, and vapor pressure lowering for any solution. Supports water, benzene, camphor, and more solvents with preset solutions like NaCl, antifreeze, and IV saline.
Select two elements to see electronegativity difference, bond type (nonpolar covalent, polar covalent, or ionic), dipole moment in Debye, percent ionic character, and partial charges. Interactive SVG shows electron density cloud shifted toward the more electronegative atom.
Select a VSEPR molecular geometry to see a 3D perspective SVG rendering with bond angles, lone pairs, and atom labels. Drag to rotate. Covers all 10 geometries: linear, bent, trigonal planar, tetrahedral, octahedral, and more. Includes preset molecules (H2O, NH3, CH4, SF6, PCl5).
Four equilibrium chemistry modes: build ICE tables and solve for equilibrium concentrations, compare reaction quotient Q to K and predict shift direction, calculate molar solubility from Ksp with optional common ion effect, and solve weak acid/base Ka or Kb for pH and percent ionization. Step-by-step solutions with KaTeX.
Interactive titration curve tool for strong acid-strong base, weak acid-strong base, weak base-strong acid, and diprotic acid titrations. See real-time pH curve, buffer regions, Henderson-Hasselbalch equation, equivalence points, buffer capacity, and indicator color overlays.
Interactive P-T phase diagram for water, CO₂, ethanol, and nitrogen. Click to identify phases, view heating curves at any pressure, explore triple and critical points, apply Clausius-Clapeyron to shift boiling points, and see colligative effects of dissolved solutes on phase boundaries.
Convert between binary, decimal, hexadecimal, and octal. Bit-level visualization, ASCII lookup, and step-by-step conversion methods.
Enter Boolean expressions with AND, OR, NOT, XOR, and IMPLIES to generate complete truth tables. Detects tautologies and contradictions.
Watch bubble, selection, insertion, merge, and quick sort in action with color-coded bars for comparisons, swaps, and sorted elements.
Compare O(1), O(log n), O(n), O(n log n), O(n^2), O(n^3), and O(2^n) on an interactive graph. See operation counts at any input size.
Select predefined circuits with AND, OR, NOT, XOR, NAND, NOR gates. Toggle inputs and see outputs update in real time with auto-generated truth tables.
Enter a regex pattern and test string to see highlighted matches, capture groups, match count, and a plain-English pattern explanation in real time.
Visualize BFS, DFS, Dijkstra, and A* on an interactive grid. Draw walls, set weighted cells, generate mazes, and watch each algorithm explore step by step.
Visualize stacks, queues, linked lists, binary search trees, and min heaps with animated operations. Push, pop, insert, delete, and traverse step by step.
Build and test finite state machines (DFA/NFA). Create states, define transitions, and test input strings with step-by-step animation showing the machine processing each symbol.
Build a binary search tree and watch inorder, preorder, postorder, and level-order traversals step by step with animated SVG node highlighting and numbered visit badges.
Compute A = P(1+r/n)^(nt) with various compounding frequencies, monthly contributions, growth chart, year-by-year table, and Rule of 72.
Convert across 10 categories: length, mass, volume, temperature, speed, area, energy, pressure, time, and data. See all conversions at once.
Calculate monthly payments, total interest, and generate a full amortization schedule. See the impact of extra payments with principal vs interest charts.
Enter experimental data (x, y pairs) or paste CSV, perform linear regression with R-squared, standard errors, and residual analysis. Propagate uncertainties through addition, multiplication, division, and power operations. Calculate percent error with significant figures. SVG scatter plot with best-fit line and error bars.
Generate Punnett squares for monohybrid, dihybrid, incomplete dominance, and sex-linked crosses. Color-coded SVG grid with genotype and phenotype ratios and step-by-step analysis.
Simulate exponential, logistic, and Lotka-Volterra predator-prey population models. Interactive JSXGraph plots with carrying capacity, inflection points, phase portraits, and ecological presets.
Transcribe DNA to mRNA and translate codons into amino acid chains. Beautiful sequence diagram with color-coded nucleotides, codon brackets, amino acid pills, full 64-codon table, and reverse translation.
Calculate allele and genotype frequencies, test populations for HW equilibrium with chi-square, and simulate evolutionary forces like selection, drift, mutation, and migration over generations.
Four modes: magnitude scales (Richter Mₗ, moment magnitude M𝑤, energy), energy comparison (each step = 31.6× more energy, logarithmic bar chart), Modified Mercalli Intensity I-XII with descriptions, and Richter magnitude from seismograph amplitude. Presets include Minor M3 through Great M8, 1906 San Francisco M7.9, and 2011 Japan M9.1.
Estimate annual CO₂ emissions from transportation (car miles, fuel type, flights), home energy (electricity, heating, AC), diet (meat consumption, food waste), and lifestyle (shopping, recycling). Pie chart breakdown, country comparison bar chart, trees-to-offset and equivalent-driving metrics. Five presets: Average American, Eco-Conscious, Heavy Commuter, Frequent Flyer, Work from Home.
Three modes: interactive HR diagram with 23 real stars (click to see properties), stellar evolution pathway from nebula to end state (white dwarf, neutron star, or black hole based on initial mass), and star properties calculator (luminosity L∝M^3.5, radius, lifetime t∝M^-2.5, apparent magnitude). Six presets: Sun, Red Dwarf (0.3 M☉), Sirius A (2 M☉), Blue Giant (20 M☉), Betelgeuse (15 M☉), Supergiant (50 M☉). Includes spectral class colour strip and SVG star visualization.