One-Sample t-Test Calculator
Compute the t-statistic and degrees of freedom for a one-sample t-test from the sample mean, the population mean under H...
Everyday arithmetic, algebra, and geometry — worked out clearly.
Percentages, fractions, ratios, geometry, and the little calculations that come up all the time — with formulas you can reuse anywhere.
Compute the t-statistic and degrees of freedom for a one-sample t-test from the sample mean, the population mean under H...
Compute the product of two 2×2 matrices A · B element-by-element, returning the four entries of the result matrix.
Compute the exterior angle of a regular n-gon (sum is always 360°): each = 360 / n. Reports the corresponding interior a...
Compute f(x, y) inside a rectangle [x₁, x₂] × [y₁, y₂] from its four corner values f₁₁, f₂₁, f₁₂, f₂₂ using bilinear int...
Compute the mean, variance, mode (when k ≥ 1) and standard deviation of a Gamma(k, θ) distribution in the shape-scale pa...
Compute the 2×2 matrix product C = A · B from the eight scalar entries: c₁₁ = a₁₁·b₁₁ + a₁₂·b₂₁; c₁₂ = a₁₁·b₁₂ + a₁₂·b₂₂...
Compute the two eigenvalues of a real 2×2 matrix [[a,b],[c,d]] via the characteristic polynomial λ² − T·λ + D = 0, where...
Compute a z-based confidence interval for a population mean when the population standard deviation σ is known: CI = x̄ ±...
Compute the OLS intercept of a simple linear regression y = a + b·x once the slope b has been determined: a = (Σy − b·Σx...
Compute the lateral (curved) surface area, base area, and total surface area of a right circular cone given its base rad...
Compute the mean and variance of a Pareto(x_m, α) distribution. The mean is finite only for α > 1, the variance only for...
Compute the one-way ANOVA F statistic, between-group MSB, and within-group MSW for three independent samples directly fr...
Compute the equation of the plane passing through three 3-D points P, Q, R. The normal vector is the cross product (Q −...
Compute a course grade as a weighted average of up to four components (e.g. homework, quizzes, midterm, final), given ea...
Compute the greatest common divisor (GCD) and the least common multiple (LCM) of two positive integers using the Euclide...
Compute the multiset coefficient C(n + k − 1, k) — the number of ways to distribute k indistinguishable items into n dis...
Compute the closed-form sum of the first n positive squares: 1² + 2² + ⋯ + n² = n(n+1)(2n+1)/6. The classical Faulhaber...
Compute the standard error of a sample proportion from successes and trials: p̂ = x/n, SE = √(p̂(1−p̂)/n). Also reports...
Compute the sample covariance, population covariance, Pearson correlation r, and the slope of the regression line from t...
Compute the sum of an arithmetic series: S_n = n(a₁ + aₙ)/2, where a₁ is the first term, aₙ the last, and n the count of...
Compute Cohen's h, the standardised effect-size between two proportions. h = 2·arcsin(√p₁) − 2·arcsin(√p₂). Interpretati...
Convert a 3-D point from cylindrical coordinates (r, θ, z) to Cartesian (x, y, z): x = r·cos θ, y = r·sin θ, z = z. Usef...
Compute the φ (phi) coefficient — the Pearson correlation between two binary variables — from a 2 × 2 contingency table...
Compute the minimum sample size required to estimate a proportion within a target margin of error E at a chosen confiden...