Maths tools from arithmetic to advanced calculus

Explore exchange ratios between currencies, follow multiplication and reverse conversion, and optionally load a dated daily reference rate.

Partition three lists into seven disjoint membership regions with an SVG diagram, counts and a complete member table.

Find a percentage of an amount in one step.

Measure an increase or decrease from an original value.

Find what percentage one number is of another.

Recover the original value before a percentage increase or decrease.

Raise a number to a selected exponent.

Find the non-negative square root of a number.

Find the real cube root of a positive or negative number.

Find the exponent needed to reach a number from a base.

Multiply a whole number by all positive integers below it.

Find the largest positive integer that divides both numbers.

Find the smallest non-negative common multiple of two integers.

Find the nth term and sum of a sequence with a fixed difference.

Find the nth term and sum when each term multiplies by a fixed ratio.

Find a consecutive attended-class requirement and a current absence allowance from an entered threshold.

Solve the final-score requirement from a normalized current grade, final weight and target course percentage.

Simplify two to twenty nonnegative ratio terms and distribute a supplied quantity into exact proportional shares.

Plot unjoined Cartesian points, identify quadrants and axes, and calculate exact mean coordinates, reflections and bounding extents.

Compare left, right and midpoint rectangle sums with an exact polynomial integral and an SVG explanation.

Find exact prime powers, the count of positive divisors and their sum in one worked breakdown.

Compute a large exponent modulo a whole number using repeated squaring and inspect each selected power.

Solve a·x ≡ b modulo m, including cases with multiple residues or no solution.

Combine two congruences with coprime moduli into one exact residue class.

Count integers coprime to n from 1 through n using its distinct prime factors.

Find the first positive power of a that gives remainder one modulo m.

Expand a rational number into a finite simple continued fraction and inspect every convergent.

Turn a stated repeating decimal block into an exact reduced fraction, including a non-repeating prefix.

Convert a signed whole number between numeral bases 2 through 36 without floating-point rounding.

Find an exact indexed Fibonacci number, inspect early terms and sum through the selected index.

Calculate octal permission bits, symbolic display and a separate new-object umask example.

Calculate a credit-weighted GPA from your grade points, optional course bonuses and an explicit maximum point value.

Compare multipack offers on the same kilogram, litre or item basis, including the percentage saving relative to offer A.

Solve ax+b=cx+d with balancing steps, substitution checks and a graph of the two linear expressions.

Solve ax+b < cx+d or its inclusive and greater-than variants, with explicit boundary inclusion and sign reversal.

Roll one to one hundred virtual polyhedral dice with individual results, a total and a visual roll display.

Convert whole numbers from 1 to 3999 to Roman numerals and validate canonical Roman notation.

Reduce an integer numerator and denominator to lowest terms while preserving the value and explaining the decimal form.

Convert an exact integer fraction to a terminating decimal or an explicitly marked recurring expansion.

Turn a finite decimal string into a power-of-ten fraction and reduce it without floating-point guessing.

Combine whole units and a fractional remainder with an explicit sign for the entire value.

Extract perfect square or cube factors from an integer and compare the exact radical with its real decimal approximation.

Explore fair coin and six-sided die events or supply equally likely favorable and total outcome counts.

Solve one unknown position in a/b = c/d and distinguish unique solutions from invalid or undetermined cases.

Practice finding an entered tax percentage and adding it to a price with the arithmetic shown.

Divide a polynomial by x minus c using exact rational coefficients and inspect every multiply-add step.

Find union intersection directional differences symmetric difference subset relations and schematic Venn-region counts.

Create a browser-local SVG pie chart with labeled categories percentage and angle calculations a data table and downloadable vector output.

Calculate an IPv4 network block mask address range binary representation and explicit host interpretation from a CIDR prefix or dotted mask.

Play a local Sudoku puzzle with keyboard navigation, new unique boards, mistake checks, digit counts, reset and solution reveal.

Calculate a circle’s area, circumference, radius and diameter from either a radius or diameter.

Find area, perimeter and diagonal from two side lengths.

Find triangle area using a base and perpendicular height.

Solve a missing hypotenuse or either missing leg of a right triangle, with the squared relationship explained.

Find the volume and surface area of a sphere.

Calculate the volume and total surface area of a right circular cylinder.

Find the volume of a cone from its base radius and height.

Find the volume and surface area of a rectangular box.

Distinguish semiaxes from full axes and exact area from an explicitly approximate perimeter.

Use a side circumradius or apothem to derive a regular convex polygon’s dimensions and angles.

Separate perpendicular height slant length curved area and circular end closures.

Keep the parent sphere radius cap height and cut-disk radius distinct.

Validate a three-side triangular base before deriving prism volume lateral area and closed surface.

Count inner and outer arcs plus exposed radial cuts with a separate full-turn boundary rule.

Separate the straight cylindrical middle from the overall length of two hemispherical ends.

Keep the major centerline radius distinct from tube radius and outside radius.

Compare enclosed area and boundary length for a rectangle square circle or right triangle with a proportional SVG sketch.

Classify an angle from zero to a full turn and see its counterclockwise rays and arc.

Add the exterior face areas of a cube rectangular prism or closed cylinder and compare surface area with enclosed volume.

Solve planar triangle sides angles area perimeter and radii using four stated input configurations and an SVG sketch.

Summarize unweighted numbers with mean, median, tied modes, range, frequencies and sample or population variance.

Combine values that contribute different amounts to the overall average.

Express a value as a number of standard deviations from the mean.

Estimate the standard error of a sample mean.

Compare standard deviation with the magnitude of a mean.

Calculate known-SD z and sample-SD t mean intervals, plus Wilson or Wald proportion intervals, with standard errors and critical-value diagrams.

Estimate responses needed for a population proportion with a target margin.

Find the chance of an exact number of successes in repeated trials.

Count unordered selections without replacement.

Count ordered selections without replacement.

Find exact-count and cumulative probabilities for events in a fixed interval.

Calculate an exact success-count probability for sampling without replacement.

Find when the first success occurs in independent trials with a constant probability.

Find the normal area between two bounds and in the tails outside them.

Estimate the chance of a wait ending before a chosen time under a constant-rate model.

Update a prior probability using evidence likelihoods and inspect the expected groups.

Evaluate a known distribution’s MGF and inspect its logarithm, domain, mean and second moment.

Preserve repeated observations in an ordered plot with an explicit leaf unit and negative-value key.

Find a sample percentile, quartiles and IQR using an explicitly chosen convention.

Compare strict-below, at-or-below and midpoint-tie ranks for a value in a sample.

Group observations into equal-width bins with counts, relative frequencies and cumulative totals.

Fit a straight line to paired data and inspect correlation, residuals and a prediction.

Keep observations matched while summarizing individual changes and their spread.

Create rolling one-step forecasts without including the period being predicted.

Inspect prior-level forecasts and updated levels with a stated initialization and smoothing factor.

Evaluate aligned actual and predicted values with explicit bias and zero-denominator conventions.

Preserve pairing and use average tied ranks to describe monotonic association.

Compare three equal-weight averages of positive data and understand their different meanings.

Evaluate four fixed classification counts without hiding undefined metrics or changing the positive class.

Normalize category weights and compare uncertainty with an equal-category reference.

Build a finite probability distribution and inspect each outcome’s exact contribution to its expected value.

Find real or complex eigenvalues, P, D and P inverse, check reconstruction and visualize real eigendirections or complex eigenvalues.

Evaluate both orders of function composition, follow the inner and outer steps and compare the functions in an SVG graph.

Differentiate bounded expressions using product, quotient and chain rules, evaluate a slope and inspect the function, derivative and tangent.

Compute symbolic x, y and z partial derivatives, evaluate the gradient and explore a rotatable fixed-z surface slice.

Inspect two-sided straight and curved approaches to a two-input target, with a rotatable surface and honest finite-sample assessments.

Classify a general quadratic curve, inspect degeneracy and graph rotated conics using an adjustable implicit SVG contour.

Integrate polynomial vector fields around a rectangle or axis-aligned ellipse, with working.

Find slope, intercept and the line through two distinct points.

Solve ax² + bx + c = 0, including repeated and complex roots.

Find the smaller angle between ideal hour and minute hands.

Normalize a bearing and see its nearest 16-point compass direction.

Find Euclidean distance and midpoint between two points in two or three Cartesian dimensions.

Estimate a value between two reference points using a straight line.

Add, subtract, multiply or divide two fractions with exact integer arithmetic.

Add or subtract matching matrices, or multiply every entry of one matrix by an exact scalar.

Multiply compatible matrices with exact entries and a row-by-column worked example.

Find the exact determinant of a square matrix and follow the elimination steps.

Invert a square matrix using exact row operations, or see why no inverse exists.

Reduce a rectangular matrix exactly and identify its rank, nullity and pivot columns.

Solve small rational linear systems and distinguish unique, inconsistent and free-variable cases.

Calculate sums, dot and cross products, lengths, angles and projections in one place.

Find exact area, centroid, orientation and angle type from three planar vertices.

Find a 3D plane equation, a normal vector and its distance from the origin.

Find the exact center, squared radius and equation of a planar circumcircle.

Calculate a simple polygon’s exact area and centroid from its ordered vertices.

Add, subtract, multiply or divide rational complex numbers and inspect the result.

Generate modular or polygon-symmetry tables, or verify a complete custom group table.

Generate a subgroup from chosen elements and compare its left and right cosets.

Compose two permutations and find cycles, inverse, order and parity with each mapping shown.

Convert a vector between two ordered bases and inspect the exact transition matrix.

Select a basis from entered spanning vectors and check independence and ambient dimension.

Find an exact basis for the homogeneous solutions A x = 0 and verify rank plus nullity.

Express a standard-coordinate linear operator in a chosen ordered basis.

Compute exact positive, zero or negative powers of a small square matrix.

Build an exact orthogonal basis, identify dependent columns and separately display approximate unit-length vectors.

Find perpendicular and parallel lines through a point, plus its perpendicular foot and distance.

Invert affine, nondegenerate linear-fractional or restricted quadratic forms and evaluate an entered output.

Add, subtract or multiply coefficient-defined polynomials with exact rational coefficients.

Find quotient and remainder and inspect the exact dividend-divisor identity.

Find all rational zeros and multiplicities within a bounded integer-polynomial search.

Expand (ax+b)ⁿ with rational coefficients and inspect every resulting power.

Generate finite Taylor polynomials for entered expressions with symbolic derivative steps, or use the existing four-function modes with analytic remainder bounds.

Find a tangent and normal, inspect local curvature and compare a linear prediction with the actual polynomial.

Compare endpoints and approximate stationary candidates for a degree-six-or-lower polynomial on a closed interval.

Approximate one real polynomial root using a sign bracket or Newton updates, with residuals and honest stopping states.

Interpolate ordered data with natural endpoint conditions, inspect local cubic coefficients and evaluate slope and curvature.

Build the derivative matrix of a two-output polynomial map and compare a local linearization with its actual displacement.

Plot sampled two-dimensional field arrows and calculate local divergence and scalar curl from analytic partial derivatives.

Compare fixed-step Euler, Heun or classical RK4 with a half-step run for y′=P(x,y).

Decompose a real two-by-two matrix, inspect its singular values and check reconstruction error.

Calculate residues, powers and inverses in Fₚ[x]/(m), with a genuine irreducibility check.

Swap rows and columns of a bounded exact rational matrix and inspect the resulting dimensions.

Generate a principal ideal in Z/nZ, partition residues into cosets and inspect exact quotient addition and multiplication tables with an SVG diagram.

Check topology axioms on a finite point set, find failure witnesses and analyze connectedness, compactness and separation with an SVG membership diagram.

Find an exact row-space basis over a prime field, inspect modular row reduction and visualize every span point in two dimensions.

Approximate a signed definite integral with trapezoidal or Simpson quadrature, inspect node weights and compare resolutions with SVG panel outlines.

Calculate left, right and midpoint Riemann sums for an entered function, inspect every rectangle contribution and export the SVG graph.

Graph transformed sine and cosine waves with amplitude, period, phase and vertical shifts, quarter-cycle values and a downloadable SVG.

Find the vertex and symmetry axis of y=ax²+bx+c, inspect completed-square steps and symmetric values, and export the SVG parabola graph.

Plot multiple formula-and-condition pieces with included or excluded endpoints, inspect a query x and export an SVG without joining branch gaps.

Plot a slope field and forward/backward RK4 initial-value curves for an entered f(x,y), choose an initial point and export the SVG.

Plot bounded-expression vector fields in a plane or space, rotate the 3D SVG view, inspect component magnitudes and export the current view.

Differentiate a two-output map, inspect its signed local area factor and compare a finite square’s mapped boundary with the linearized image.

Find numerical stationary candidates for an entered function, inspect its symbolic derivative and nearby sign changes, and export the function graph.

Find a symbolic gradient, normalize a direction and calculate the directional slope with a rotatable surface section, tangent and SVG export.

Calculate planar work or circulation along an entered parametric curve, inspect symbolic velocity and Simpson samples, and export the field-and-path SVG.

Compute curl flux and boundary circulation independently for an entered graph surface, compare resolutions and rotate the surface, boundary and curl SVG.

Recognize limited elementary antiderivatives, plot a numerical base and constant-shifted family with a slope field, and export the SVG.

Check a function value, bounded continuity rules and shrinking one-sided samples, with explicit hole candidates and a function-behavior SVG.

Explore finite quotient limits with separate symbolic derivative steps, repeated 0/0 checks, one-sided probes and a quotient SVG.