Compute trial probabilities until first success, cumulative likelihood P(X ≤ k), and expected trials 1/p.

Synthesize and decompose periodic square, sawtooth, and triangle waves into Fourier harmonics. Computes a_n, b_n coefficients, Gibbs phenomenon, and power spectrum.

Perform two-sample F-tests for equality of variances, calculate F-ratio (s1²/s2²), degrees of freedom, and exact p-values.

Compute right-tail ANOVA p-values, critical F-cutoffs, and variance ratio significance tests.

Calculate Exponential Moving Averages (EMA), smoothing factor alpha, SMA comparisons, and time-series forecast errors (MAE, MSE, MAPE) for financial and metric data.

Solve exponential equations a·b^(cx+d) = k using natural logarithms, change of base, and doubling/half-life analysis.

Calculate continuous waiting time PDF, cumulative failure CDF, survival reliability R(x), and MTTF.

Compute expected value E(X), variance Var(X), standard deviation, and evaluate investment or gaming risk-reward payoffs.

Solve linear equations (ax+b=c), systems of equations, and quadratic equations (ax²+bx+c=0) with step-by-step mathematical working online free.

Calculate Euclidean, Manhattan, and Chebyshev distances between two points in 2D or 3D coordinate space with steps.