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Math Tools
256 tools in this collection. Choose a task below or search the complete FeuTex toolkit.
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2D Mahalanobis Distance
Measure a point displacement while accounting for correlated variable scales.
Open tool →Math2D Polar Rotation from a Matrix
Extract the closest proper rotation from an orientation-preserving 2×2 transform.
Open tool →Math2×2 Cholesky Factorization
Factor a symmetric positive-definite matrix into a lower triangular matrix and its transpose.
Open tool →Statistics2×2 Independence Statistic
Calculate Pearson’s independence statistic and signed association for a two-by-two count table.
Open tool →Math2×2 Matrix Inverse
Invert a nonsingular two-by-two matrix and inspect its determinant.
Open tool →Math2×2 Singular Values and Conditioning
Find both singular values and the spectral condition number of a nonsingular two-by-two matrix.
Open tool →StatisticsAdjusted R-Squared and Residual Scale
Adjust regression R-squared for predictor count and calculate residual scale and degrees of freedom.
Open tool →GeometryAffine Point Transformation
Apply a two-dimensional affine map and inspect its area scale and orientation.
Open tool →MathAitken Sequence Acceleration
Accelerate a linearly convergent sequence from three successive iterates.
Open tool →GeometryAnnulus Area Calculator
Calculate annulus area with labeled inputs, explicit units and the formula A = π(R² − r²).
Open tool →StatisticsAR(1) Conditional Forecast
Project a stationary autoregressive series and its innovation variance over a horizon.
Open tool →StatisticsAR(1) Effective Sample Size
Approximate the information loss in a mean estimate from positive first-order serial correlation.
Open tool →GeometryArc Length Calculator
Calculate arc length with labeled inputs, explicit units and the formula s = πrθ / 180.
Open tool →ProbabilityArcsine Bounded Interval Probability
Calculate probability between two points under the U-shaped arcsine distribution.
Open tool →MathArithmetic Sequence Sum Calculator
Calculate arithmetic sequence sum with labeled inputs, explicit units and the formula Sₙ = n[2a₁+(n−1)d]/2.
Open tool →MathArithmetic Sequence Term Calculator
Calculate arithmetic sequence term with labeled inputs, explicit units and the formula aₙ = a₁+(n−1)d.
Open tool →MathBalanced Parenthesis Structure Count
Count valid balanced-parenthesis sequences and equivalent ordered binary tree shapes.
Open tool →GeometryBarycentric Point Location
Express a point as three triangle weights to inspect its location relative to the triangle.
Open tool →MathBayes Probability Calculator
Calculate bayes probability with labeled inputs, explicit units and the formula P(A|B)=P(B|A)P(A)/[P(B|A)P(A)+P(B|¬A)(1−P(A))].
Open tool →StatisticsBernoulli KL Divergence
Measure the information penalty of using one binary event probability in place of another.
Open tool →ProbabilityBeta Distribution Moments
Inspect a beta distribution’s mean, variance and skewness on the unit interval.
Open tool →MathBilinear Grid Cell Interpolation
Interpolate a rectangular data cell from four corner values.
Open tool →StatisticsBinary Classification Scorecard
Evaluate precision, recall, specificity, F1 and Matthews correlation from a binary confusion matrix.
Open tool →ProbabilityBinary Entropy Profile
Calculate uncertainty, perplexity and success information for a Bernoulli probability.
Open tool →StatisticsBinary Mutual Information from Counts
Measure dependence between two binary variables using a positive 2×2 count table.
Open tool →StatisticsBinary Rater Agreement
Compare observed agreement with chance agreement and calculate Cohen’s kappa for two binary raters.
Open tool →MathBinomial Exact Probability Calculator
Calculate binomial exact probability with labeled inputs, explicit units and the formula P(X=k)=C(n,k)pᵏ(1−p)ⁿ⁻ᵏ.
Open tool →ProbabilityBirthday Collision Estimate
Estimate collision probability and expected matching pairs for independent draws from equal-probability categories.
Open tool →MathBisection Iteration Budget
Find iterations needed to reduce a root bracket below a target width.
Open tool →StatisticsBland–Altman Agreement Limits
Calculate mean bias and normal-theory limits of agreement from paired-difference summaries.
Open tool →MathBoole Five-Point Integration
Integrate a smooth function using five equally spaced samples and Boole weights.
Open tool →StatisticsBowley Quartile Skewness
Assess robust asymmetry using the lower quartile, median, and upper quartile.
Open tool →ProbabilityBurr XII Tail Distribution
Explore two-shape tail probabilities for positive continuous data.
Open tool →ProbabilityCantelli One-Sided Tail Bound
Bound a one-sided deviation from the mean using variance alone.
Open tool →GeometryCatenary Sag and Arc Length
Estimate the sag, total arc length and end slope of a symmetric mathematical catenary.
Open tool →ProbabilityCauchy Distribution Profile
Evaluate Cauchy cumulative probability, density and interquartile range without undefined moments.
Open tool →MathCentered Derivative Stencil
Estimate first and second derivatives from three equally spaced function measurements.
Open tool →ProbabilityChebyshev Coverage Guarantee
Bound the fraction outside a selected distance from the mean using only finite variance.
Open tool →GeometryCircle Area Calculator
Calculate circle area with labeled inputs, explicit units and the formula A = πr².
Open tool →GeometryCircle Chord Length Calculator
Calculate circle chord length with labeled inputs, explicit units and the formula c = 2r sin(θ/2).
Open tool →GeometryCircle Circumference Calculator
Calculate circle circumference with labeled inputs, explicit units and the formula C = 2πr.
Open tool →GeometryCircle Overlap Lens
Calculate the shared lens area and common chord where two circles partially overlap.
Open tool →GeometryCircle Sector Area Calculator
Calculate circle sector area with labeled inputs, explicit units and the formula A = πr²θ / 360.
Open tool →GeometryCircle through Three Points
Locate the center and radius of the unique circle passing through three noncollinear points.
Open tool →GeometryCircular Segment Profile
Find a circular segment’s area, chord width and central angle from its radius and height.
Open tool →GeometryClosed Cone Surface Area Calculator
Calculate closed cone surface area with labeled inputs, explicit units and the formula A = πr[r + √(r²+h²)].
Open tool →GeometryClosed Cylinder Surface Area Calculator
Calculate closed cylinder surface area with labeled inputs, explicit units and the formula A = 2πr(r+h).
Open tool →StatisticsCluster Sampling Design Effect
Estimate sample inflation from average cluster size and within-cluster correlation.
Open tool →StatisticsCochran Q from Study Summaries
Calculate meta-analysis heterogeneity metrics from Q, study count, and inverse-variance weight sums.
Open tool →MathCoefficient of Variation Calculator
Calculate coefficient of variation with labeled inputs, explicit units and the formula CV = 100σ/μ.
Open tool →GeometryCommon External Tangent of Two Circles
Find the straight external tangent length between circles for a geometric construction.
Open tool →MathComplex Exponential Evaluation
Evaluate exp(a+bi) as Cartesian real and imaginary parts.
Open tool →MathComplex Magnitude, Phase and Principal Root
Find magnitude, phase and the principal square root of a complex number.
Open tool →MathComplex Product and Quotient
Multiply and divide two complex numbers while keeping real and imaginary components separate.
Open tool →MathComposite Simpson Panel Budget
Estimate an even panel count sufficient for a supplied fourth-derivative bound.
Open tool →MathComposite Trapezoidal Error Bound
Bound integration error using a second-derivative bound and panel count.
Open tool →GeometryCone Frustum Flat Pattern
Calculate the annular-sector radii and sweep for unrolling a cone frustum.
Open tool →GeometryCone Frustum Volume Calculator
Calculate cone frustum volume with labeled inputs, explicit units and the formula V = πh(R²+Rr+r²)/3.
Open tool →GeometryCone Solid Angle and Sphere Fraction
Calculate a cone aperture’s solid angle and the fraction of a sphere it covers.
Open tool →GeometryCone Volume Calculator
Calculate cone volume with labeled inputs, explicit units and the formula V = πr²h/3.
Open tool →StatisticsCook Distance for One Observation
Estimate regression influence from residual, leverage, parameter count, and residual mean square.
Open tool →StatisticsCorrelated Measurement Uncertainty
Propagate correlated standard uncertainties through a sum, difference and product.
Open tool →StatisticsCorrelation Correction for Attenuation
Estimate a latent correlation under classical independent measurement-error assumptions.
Open tool →StatisticsCorrelation Fisher Interval
Construct an approximate Fisher-transformed confidence interval for a Pearson correlation.
Open tool →ProbabilityCoupon Collection Expectation
Calculate the expected draw count and variance needed to collect every uniformly distributed coupon type.
Open tool →StatisticsCronbach Alpha from Variance Summaries
Estimate internal consistency from item count, summed item variances, and total-score variance.
Open tool →MathCubic Hermite Endpoint Interpolation
Interpolate between endpoint values while preserving specified endpoint slopes.
Open tool →MathCubic Polynomial Evaluation
Evaluate a cubic polynomial, its first two derivatives and its signed integral from zero.
Open tool →GeometryCuboid Space Diagonal Calculator
Calculate cuboid space diagonal with labeled inputs, explicit units and the formula d = √(l²+w²+h²).
Open tool →GeometryCuboid Surface Area Calculator
Calculate cuboid surface area with labeled inputs, explicit units and the formula A = 2(lw + wh + lh).
Open tool →GeometryCuboid Volume Calculator
Calculate cuboid volume with labeled inputs, explicit units and the formula V = length × width × height.
Open tool →GeometryCyclic Quadrilateral from Four Sides
Calculate area and diagonal lengths of a convex cyclic quadrilateral.
Open tool →GeometryCycloid Point and Tangent
Locate a point on a rolling-circle cycloid and evaluate its parametric tangent.
Open tool →GeometryCylinder Volume Calculator
Calculate cylinder volume with labeled inputs, explicit units and the formula V = πr²h.
Open tool →StatisticsDescriptive Statistics
Summarize a numeric sample with count, mean, median, sample standard deviation and range.
Open tool →MathDistance Between Two Points Calculator
Calculate distance between two points with labeled inputs, explicit units and the formula d = √[(x₂−x₁)²+(y₂−y₁)²].
Open tool →GeometryEllipse Area Calculator
Calculate ellipse area with labeled inputs, explicit units and the formula A = πab.
Open tool →GeometryEllipse Foci and Eccentricity
Find an ellipse’s focal offset, eccentricity and latus rectum from its major and minor semi-axes.
Open tool →GeometryEllipse Local Radius of Curvature
Measure curvature and osculating radius at a location on an elliptical curve.
Open tool →GeometryEllipse Sector Area by Parameter
Measure an ellipse sector swept between two parametric angles.
Open tool →GeometryEllipse Tangent at Parametric Angle
Locate an ellipse point and its tangent line without a vertical-slope singularity.
Open tool →StatisticsEmpirical CDF Uniform Error Band
Calculate the Dvoretzky–Kiefer–Wolfowitz simultaneous CDF error bound.
Open tool →StatisticsExpected Binary Brier Score
Measure expected squared-probability error from a true binary event rate and a constant forecast.
Open tool →ProbabilityExponential Lifetime Profile
Calculate survival probability, cumulative probability and typical waiting times under constant hazard.
Open tool →MathExponential Relaxation Rate from Two Observations
Infer a first-order relaxation constant from a starting offset and a later offset from equilibrium.
Open tool →StatisticsExponential Smoothing Forecast Update
Update a simple level forecast from one new observation and a smoothing weight.
Open tool →MathExponential Trend Doubling or Halving Time
Translate a continuous fitted log-growth coefficient into a multiplicative trend timescale.
Open tool →MathFibonacci Index Values
Calculate Fibonacci and Lucas numbers at a bounded nonnegative integer index.
Open tool →MathFinite Arithmetic–Geometric Sum
Sum a sequence whose terms combine an arithmetic factor with a geometric weight.
Open tool →StatisticsFinite Population Sample Adjustment
Adjust an infinite-population sample-size requirement for sampling without replacement.
Open tool →MathFive-Point First Derivative
Estimate a first derivative with a fourth-order centered stencil.
Open tool →MathFixed-Point Contraction Error Bound
Bound remaining iteration error from a contraction factor and successive iterate difference.
Open tool →MathFour-Sample Fourier Transform
Transform four equally spaced real samples into their discrete Fourier frequency components.
Open tool →MathFraction Arithmetic
Add, subtract, multiply or divide two rational fractions and reduce the result exactly.
Open tool →ProbabilityFrechet Maximum Tail Model
Evaluate heavy-tailed maxima using a Frechet shape and scale.
Open tool →StatisticsFreedman–Diaconis Histogram Width
Plan histogram bin width and count from sample size, range, and interquartile range.
Open tool →StatisticsFrequency Table Builder
Count exact categorical values and show their percentage share.
Open tool →ProbabilityGambler Ruin Hitting Probability
Find the probability that a bounded random walk reaches its upper boundary before zero.
Open tool →ProbabilityGamma Distribution Moments
Inspect a gamma distribution’s mean, variance, skewness and excess kurtosis using shape and scale.
Open tool →StatisticsGaussian Bhattacharyya Overlap
Calculate a normal-model overlap coefficient based on means and variances.
Open tool →StatisticsGaussian KL Divergence
Quantify directed divergence between two univariate normal distributions.
Open tool →StatisticsGaussian Wasserstein Distance
Measure the transport distance between two one-dimensional Gaussian models.
Open tool →ProbabilityGeneralized Pareto Threshold Exceedance
Estimate excess-tail probability and a return-level quantile above a selected threshold.
Open tool →MathGeometric Sequence Sum Calculator
Calculate geometric sequence sum with labeled inputs, explicit units and the formula Sₙ = a₁(1−rⁿ)/(1−r), or na₁ when r=1.
Open tool →MathGeometric Sequence Term Calculator
Calculate geometric sequence term with labeled inputs, explicit units and the formula aₙ = a₁rⁿ⁻¹.
Open tool →ProbabilityGeometric Waiting-Time Probability
Calculate exact and cumulative waiting probabilities before the first successful trial.
Open tool →MathGompertz Growth Trajectory
Evaluate a Gompertz growth curve, its instantaneous growth and its inflection time.
Open tool →GeometryGreat-Circle Distance
Measure the shortest spherical surface route and straight chord between two latitude-longitude positions.
Open tool →ProbabilityGumbel Maximum Distribution
Evaluate a Gumbel maximum distribution’s cumulative probability, median and variance.
Open tool →MathHalley Root-Finding Step
Calculate a cubic-convergence root update using a function and its first two derivatives.
Open tool →GeometryHelix Path Profile
Measure a circular helix’s length, rise, curvature and torsion from radius, pitch and turns.
Open tool →StatisticsHistogram Bin Counter
Count values into equal-width bins and export the bin boundaries and frequencies.
Open tool →ProbabilityHoeffding Mean Deviation Bound
Bound sample-mean deviations for independent observations with known finite limits.
Open tool →StatisticsHolt Linear Trend Forecast Step
Update a level and trend then project a selected number of steps forward.
Open tool →GeometryHyperbola Foci and Asymptotes
Find focal distance, eccentricity and asymptote slope for a horizontal hyperbola.
Open tool →MathImplicit Curve Local Geometry
Compute slope and curvature of F(x,y)=0 from first and second partial derivatives.
Open tool →MathIndependent Event Union Probability Calculator
Calculate independent event union probability with labeled inputs, explicit units and the formula P(A or B) = a+b−ab.
Open tool →GeometryInternal Angle Bisector Length
Find the internal angle bisector and how it divides the opposite side.
Open tool →StatisticsInverse-Variance Two-Study Pooling
Combine two independent effect estimates using inverse-variance weighting.
Open tool →StatisticsJarque–Bera Normality Statistic
Calculate an asymptotic normality statistic from sample size, skewness, and raw kurtosis.
Open tool →ProbabilityKumaraswamy Bounded Probability
Evaluate a flexible continuous probability model for a quantity bounded between zero and one.
Open tool →ProbabilityLaplace Distribution Profile
Evaluate Laplace cumulative probability, density and variance from location and scale.
Open tool →GeometryLattice Polygon Area from Point Counts
Find the area of a simple lattice polygon from its interior and boundary lattice points.
Open tool →StatisticsLikelihood Information Criteria
Calculate AIC, small-sample AICc and BIC from a fitted model’s likelihood and parameter count.
Open tool →StatisticsLin Concordance Correlation
Measure agreement of two continuous measurements using means, spreads, and Pearson correlation.
Open tool →GeometryLine and Plane Intersection
Find the parameter and coordinates where a 3D parametric line crosses a plane.
Open tool →MathLine Slope Calculator
Calculate line slope with labeled inputs, explicit units and the formula m = (y₂−y₁)/(x₂−x₁).
Open tool →MathLinear Interpolation Calculator
Calculate linear interpolation with labeled inputs, explicit units and the formula y = y₁ + (x−x₁)(y₂−y₁)/(x₂−x₁).
Open tool →StatisticsLinear Regression
Fit y = intercept + slope × x to paired observations and report R².
Open tool →MathLinear System Solver
Solve a square system of linear equations with partial-pivot Gaussian elimination.
Open tool →ProbabilityLog-Logistic Lifetime Model
Calculate a log-logistic survival curve and instantaneous hazard at a chosen age.
Open tool →MathLogarithm in Any Base Calculator
Calculate logarithm in any base with labeled inputs, explicit units and the formula logᵦ(x) = ln(x)/ln(b).
Open tool →ProbabilityLogistic Distribution Profile
Evaluate logistic cumulative probability, density and variance from location and scale.
Open tool →MathLogistic Growth Trajectory
Evaluate a logistic growth model at a chosen time with an explicit carrying capacity.
Open tool →MathLogistic Map Dynamics
Inspect the next state, local derivative and nonzero fixed point of the logistic map.
Open tool →ProbabilityLognormal Moment Profile
Find a lognormal model’s median, mean, variance and mode from natural-log parameters.
Open tool →ProbabilityMarkov Nonnegative Tail Bound
Bound exceedance probability for a nonnegative random quantity from its expected value.
Open tool →StatisticsMcNemar Paired Discordance
Inspect corrected and uncorrected McNemar statistics from paired discordant outcomes.
Open tool →StatisticsMean Confidence Interval from Summary
Construct a mean confidence interval from summary statistics and a supplied t critical value.
Open tool →StatisticsMean Precision Sample Size
Estimate the sample count needed for a target mean-estimation precision with known variability.
Open tool →StatisticsMerge Two Sample Summaries
Combine two disjoint sample summaries into one count, mean and sample variance.
Open tool →StatisticsMoving Average Series
Smooth a numeric time series using a trailing simple moving average of your chosen window.
Open tool →StatisticsMultiple-Testing Error Budget
Allocate a family-wise error budget and adjust one p-value using Bonferroni’s method.
Open tool →GeometryNearest Point on a Line Segment
Find the nearest point on a finite line segment, including endpoint cases.
Open tool →StatisticsNested Regression F Comparison
Compare reduced and full least-squares models using residual sums of squares.
Open tool →MathNewton Root-Finding Step
Perform one Newton root-finding iteration using a supplied function value and derivative.
Open tool →ProbabilityNo-Fixed-Point Assignment Count
Count assignments with no item in its original position and calculate their random-permutation probability.
Open tool →GeometryOblique Cylinder Geometry
Compute perpendicular height and volume from an oblique cylinder axis.
Open tool →MathObserved Iterative Convergence Order
Estimate convergence order from three successive positive errors against a known solution.
Open tool →StatisticsOne-Way ANOVA Summary
Build one-way ANOVA statistics and effect size from between-group and within-group sums of squares.
Open tool →StatisticsOne-Way Intraclass Correlation
Estimate single-measure intraclass correlation from balanced one-way ANOVA mean squares.
Open tool →MathOrdered and Unordered Selections
Count selections without replacement with and without regard to ordering.
Open tool →StatisticsPaired Difference Test Statistic
Calculate a paired-sample test statistic from the mean and standard deviation of paired differences.
Open tool →GeometryPappus Solid of Revolution
Compute swept volume and surface using a region area, curve length, and centroid distances.
Open tool →GeometryParabola Focus and Directrix
Locate the focus and directrix of a vertical parabola and calculate its focal chord width.
Open tool →GeometryParallelogram Area Calculator
Calculate parallelogram area with labeled inputs, explicit units and the formula A = bh.
Open tool →ProbabilityPareto Tail Profile
Calculate Pareto exceedance probability and finite moments for a heavy-tailed model.
Open tool →StatisticsPartial Correlation Controlling One Variable
Remove one control variable from the relationship between two measured variables.
Open tool →GeometryPlane Angle and Intersection Direction
Find the acute angle between planes and a direction vector for their intersection line.
Open tool →GeometryPlatonic Solid Comparison
Compare the volumes of four regular Platonic solids sharing one edge length.
Open tool →GeometryPoint Inversion in a Circle
Map a planar point through a geometric inversion circle while preserving its radial direction.
Open tool →GeometryPoint Projection onto a Line
Find the perpendicular distance and closest point from a coordinate to an infinite line.
Open tool →GeometryPoint Projection onto a Plane
Project a three-dimensional point onto a plane and measure its perpendicular distance.
Open tool →GeometryPoint Rotation about a Center
Rotate a planar point counterclockwise around a chosen center.
Open tool →ProbabilityPoisson Event Window
Estimate the probabilities of no events, one event or multiple events in a constant-rate window.
Open tool →MathPolar Curve Curvature from Derivatives
Calculate local curvature of a polar curve from radius and angular derivatives.
Open tool →StatisticsPooled Standardized Mean Difference
Compare group means in pooled-standard-deviation units using two independent sample summaries.
Open tool →MathPower-Law Interpolation
Interpolate positive measurements along a straight line on log-log axes.
Open tool →MathPrime Factorization
Find the prime factors of an integer and show exponent notation.
Open tool →StatisticsProcess Capability Indices
Compare a stable process with specification limits using Cp, Cpk and one-sided capability indices.
Open tool →GeometryPyramid Volume Calculator
Calculate pyramid volume with labeled inputs, explicit units and the formula V = base area × height / 3.
Open tool →GeometryQuadratic Bézier Point and Tangent
Evaluate a point and tangent on a quadratic Bézier curve from three control points.
Open tool →MathQuadratic Discriminant Calculator
Calculate quadratic discriminant with labeled inputs, explicit units and the formula D = b²−4ac.
Open tool →MathQuadratic Real Root Solver
Find both real roots and the vertex of a quadratic polynomial from its coefficients.
Open tool →MathQuadratic Vertex and Axis
Find the turning point and completed-square constant of a quadratic.
Open tool →GeometryQuadrilateral Coordinate Survey
Calculate signed area and perimeter from four consecutive boundary coordinates.
Open tool →ProbabilityRandom Bin Occupancy
Estimate occupied, empty and singleton bins after independent uniform assignments.
Open tool →MathRank-One Determinant Update
Update a known matrix determinant from the scalar rank-one correction vᵀA⁻¹u.
Open tool →ProbabilityRayleigh Distribution Profile
Evaluate Rayleigh density, cumulative probability, mean and variance for a nonnegative magnitude.
Open tool →GeometryRectangle Area Calculator
Calculate rectangle area with labeled inputs, explicit units and the formula A = width × height.
Open tool →GeometryRectangle Diagonal Calculator
Calculate rectangle diagonal with labeled inputs, explicit units and the formula d = √(width² + height²).
Open tool →GeometryRectangle Perimeter Calculator
Calculate rectangle perimeter with labeled inputs, explicit units and the formula P = 2(width + height).
Open tool →GeometryReflect a Point across a Plane
Mirror a three-dimensional point across a plane given by its coefficients.
Open tool →GeometryRegular Polygon Area Calculator
Calculate regular polygon area with labeled inputs, explicit units and the formula A = ns² / [4 tan(π/n)].
Open tool →GeometryRegular Polygon Interior Angle Calculator
Calculate regular polygon interior angle with labeled inputs, explicit units and the formula θ = 180(n−2)/n.
Open tool →GeometryRegular Star Polygon Path Length
Measure edge length and total traversal length for a regular star polygon step.
Open tool →MathReverse Percentage Calculator
Calculate reverse percentage with labeled inputs, explicit units and the formula original = final / (1 + change/100).
Open tool →GeometryRhombus Area from Diagonals Calculator
Calculate rhombus area from diagonals with labeled inputs, explicit units and the formula A = d₁d₂/2.
Open tool →MathRichardson Extrapolation
Extrapolate two numerical estimates to zero step size using a known leading error order.
Open tool →GeometryRight Triangle Missing Leg Calculator
Calculate right triangle missing leg with labeled inputs, explicit units and the formula b = √(c² − a²).
Open tool →GeometryRounded Rectangle Outline and Area
Calculate area and perimeter for a rectangle with four equal circular corner fillets.
Open tool →MathRunge–Kutta Four-Stage Step
Combine four correctly evaluated Runge–Kutta stage slopes into one fourth-order solution step.
Open tool →ProbabilitySampling Without Replacement
Estimate the mean, variance and feasible success range when sampling without replacement.
Open tool →MathScientific Expression Calculator
Evaluate arithmetic, powers, roots, logarithms and trigonometry with explicit degree or radian mode.
Open tool →MathSecant Root-Finding Step
Calculate the next secant-method root estimate using two positions and function values.
Open tool →StatisticsSet Overlap from Cardinalities
Compare two finite sets using their sizes and shared-element count.
Open tool →GeometryShortest Distance Between Skew Lines
Find separation between two nonparallel 3D lines using their origins and direction vectors.
Open tool →StatisticsSimple Regression Prediction Interval
Calculate a prediction interval for one new response using regression summary quantities.
Open tool →MathSimpson Integration Panel
Integrate three equally spaced measurements using Simpson’s rule and compare a trapezoid estimate.
Open tool →MathSimpson Three-Eighths Panel
Integrate one cubic interpolating panel from four equally spaced function samples.
Open tool →StatisticsSpearman–Brown Test Length Projection
Project reliability after changing the length of a parallel-item test.
Open tool →GeometrySphere Cut by a Plane
Find a circular section area and radius for a plane at a given offset from a sphere center.
Open tool →GeometrySphere Intersection Volume
Measure the shared volume and intersection-circle radius of two partially overlapping spheres.
Open tool →GeometrySphere Surface Area Calculator
Calculate sphere surface area with labeled inputs, explicit units and the formula A = 4πr².
Open tool →GeometrySphere Volume Calculator
Calculate sphere volume with labeled inputs, explicit units and the formula V = 4πr³/3.
Open tool →GeometrySpherical Cap Profile
Measure a sphere cap’s volume, curved surface and base radius from cap height.
Open tool →GeometrySpherical Coordinate Position
Convert a spherical position to Cartesian coordinates with explicit polar-angle conventions.
Open tool →GeometrySpherical Triangle Excess and Area
Calculate spherical excess and surface area from three angles on a chosen sphere.
Open tool →GeometrySpherical Zone Surface and Volume
Find the sphere surface band and solid volume between two parallel cut planes.
Open tool →GeometryStadium Shape Area and Boundary
Calculate a capsule-shaped outline formed by a rectangle and two semicircular ends.
Open tool →MathStandard Error of the Mean Calculator
Calculate standard error of the mean with labeled inputs, explicit units and the formula SE = s/√n.
Open tool →StatisticsStandardized Regression Coefficient
Convert a fitted unstandardized slope and its error to standardized units.
Open tool →GeometrySuperellipse Boundary Point
Locate a point on a rounded rectangle or diamond-like superellipse using its exponent.
Open tool →MathSymmetric 2×2 Matrix Spectrum
Calculate the two real eigenvalues and principal-axis angle of a symmetric two-by-two matrix.
Open tool →GeometryTetrahedron Volume from Edge Vectors
Compute the volume and orientation of a tetrahedron from its three shared-origin edge vectors.
Open tool →StatisticsThree-Class Split Impurity
Evaluate Gini impurity and entropy of a node containing three class counts.
Open tool →MathThree-Level Continued Fraction
Evaluate a short continued fraction and its exact numerator-denominator recurrence.
Open tool →MathThree-Node Polynomial Interpolation
Interpolate a quadratic through three data points and evaluate its value and derivative.
Open tool →GeometryTorus Volume Calculator
Calculate torus volume with labeled inputs, explicit units and the formula V = 2π²Rr².
Open tool →GeometryTrapezoid Area Calculator
Calculate trapezoid area with labeled inputs, explicit units and the formula A = (a+b)h/2.
Open tool →ProbabilityTrials until Multiple Successes
Estimate trial count and variability required to reach multiple independent successes.
Open tool →GeometryTriangle Area Calculator
Calculate triangle area with labeled inputs, explicit units and the formula A = base × perpendicular height / 2.
Open tool →GeometryTriangle Area from Three Sides Calculator
Calculate triangle area from three sides with labeled inputs, explicit units and the formula A = √[s(s−a)(s−b)(s−c)], s = (a+b+c)/2.
Open tool →GeometryTriangle Centroid Coordinates
Locate a triangle’s centroid and measure its first median from three vertex coordinates.
Open tool →GeometryTriangle from Two Sides and Included Angle
Solve a triangle’s remaining side, angles and area from two sides and their included angle.
Open tool →GeometryTriangle Incircle and Circumcircle
Find the inscribed and circumscribed circle radii of a triangle from its three side lengths.
Open tool →GeometryTriangle Median Lengths
Find all three medians to plan centroid bracing or check a triangle construction.
Open tool →GeometryTriangle Orthocenter from Coordinates
Locate the intersection of triangle altitudes from three measured vertices.
Open tool →ProbabilityTriangular Distribution Profile
Evaluate cumulative probability and moments for a minimum-mode-maximum triangular distribution.
Open tool →GeometryTriaxial Ellipsoid Profile
Calculate the volume and three central cross-sections of an ellipsoid with unequal semi-axes.
Open tool →StatisticsTukey Inner and Outer Fences
Calculate boxplot screening fences from quartiles without deleting observations.
Open tool →StatisticsTwo-Bin Population Stability Index
Compare the share of observations in two fixed bins between reference and current populations.
Open tool →StatisticsTwo-Group Event Association
Compare two groups using risk ratio, risk difference, odds ratio and log-odds uncertainty.
Open tool →ProbabilityTwo-Group Exponential Survival
Model survival when a population contains two latent groups with different constant rates.
Open tool →MathTwo-Group Weighted Mean Calculator
Calculate two-group weighted mean with labeled inputs, explicit units and the formula mean = (a×w₁+b×w₂)/(w₁+w₂).
Open tool →GeometryTwo-Line Intersection
Find the unique intersection of two planar lines expressed in coefficient form.
Open tool →MathTwo-Node Gauss Integration Panel
Combine function values at the two mapped Gauss–Legendre nodes of an interval.
Open tool →StatisticsTwo-Proportion Z Statistic
Calculate the pooled large-sample z statistic comparing two independent event proportions.
Open tool →StatisticsTwo-Sample Variance Ratio
Compute an F variance-ratio statistic and degrees of freedom from two samples.
Open tool →ProbabilityTwo-State Markov Equilibrium
Calculate long-run state proportions and persistence for a two-state transition process.
Open tool →MathTwo-Value RMS Calculator
Calculate two-value rms with labeled inputs, explicit units and the formula RMS = √[(a²+b²)/2].
Open tool →MathTwo-Variable Quadratic Stationary Point
Find the stationary point and minimum value of a positive-definite quadratic form.
Open tool →MathTwo-Vector Gram–Schmidt in 2D
Create an orthonormal 2D basis from two independent input vectors.
Open tool →MathUneven Three-Point Derivative
Estimate the derivative at a center sample when left and right spacing differ.
Open tool →ProbabilityUniform Distribution Interval
Find interval probability, mean and variance for a bounded uniform distribution.
Open tool →StatisticsVariance Inflation and Tolerance
Measure coefficient variance inflation from the auxiliary regression R-squared.
Open tool →GeometryVector Angle and Projection
Measure the angle between two planar vectors and project the first onto the second.
Open tool →GeometryVector Cross Product
Calculate a three-dimensional cross product and the parallelogram area spanned by two vectors.
Open tool →ProbabilityWeibull Lifetime Profile
Evaluate Weibull survival, failure probability, instantaneous hazard and median lifetime.
Open tool →StatisticsWeight Effective Sample Size
Estimate weight-based effective sample size and efficiency from sums of weights and squared weights.
Open tool →StatisticsWelch Two-Sample Test Statistic
Calculate Welch’s two-sample statistic and approximate degrees of freedom from group summaries.
Open tool →StatisticsWelch–Satterthwaite Combined Degrees of Freedom
Calculate effective degrees of freedom for a sum of independent estimated variance components.
Open tool →StatisticsWilson Proportion Interval
Calculate a Wilson score confidence interval for a proportion from successes and trials.
Open tool →MathZ Score Calculator
Calculate z score with labeled inputs, explicit units and the formula z = (x−μ)/σ.
Open tool →StatisticsZero-Event Upper Risk Bound
Estimate a one-sided event-probability upper bound after observing no events.
Open tool →ProbabilityZero-Inflated Poisson Count Model
Estimate zero frequency and overdispersion when a count process has structural zeros.
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