Mathematics
Algebra, geometry, trigonometry, sequences, combinatorics and inferential statistics.
Applied statistics
8 tools
- Binomial and Poisson distributionsP(X = k), P(X ≤ k) and P(X ≥ k) for the binomial and Poisson distributions, computed in log space, tails summed from the right side.
- Chi-square test calculator, goodness of fit and independenceχ² statistic, degrees of freedom, p-value and critical value, with cell-by-cell detail and Cochran’s rule checked.
- Confidence interval calculatorConfidence interval for a mean (Student’s t or normal) and for a proportion (Wilson, with Wald for comparison).
- Correlation and linear regression calculatorLeast-squares line, r and r², slope p-value, confidence and prediction intervals, residuals point by point.
- Descriptive statistics, mean, median, standard deviationMean, median, range, variance and standard deviation of a series of values, with the sample / population distinction.
- Normal distribution calculatorProbabilities, z-scores and critical values of the normal distribution (P(X ≤ x), P(a ≤ X ≤ b), quantiles) at machine precision, tails included.
- One-way ANOVA calculator, comparing multiple meansComparison of means across several groups with the complete ANOVA table: sums of squares, F, p-value and cautious conclusion.
- Student's t-test calculator, comparison of meansA mean against a reference value or two independent samples (Welch's t-test): t, degrees of freedom, p-value, confidence interval and conclusion.
Applied mathematics
18 tools
- Area and volume calculator for common shapesArea and perimeter of ten plane figures, volume and surface of eight solids, with the formula shown and whatever is not determined flagged.
- Arithmetic and geometric sequence calculatorGeneral term, sum of terms and infinite sum of an arithmetic or geometric sequence, with the starting index of the textbook (u₀ or u₁).
- Combinations and permutations calculator (nCr, nPr, n!)C(n, k), P(n, k) and n! as exact values, computed in integers, with the rule that separates combinations (order ignored) from permutations (order counted).
- Cross multiplication calculator (rule of three)The fourth proportional by cross multiplication, in direct or inverse proportionality, with the worked calculation.
- Doubling time and compound growthDoubling time of a growth (exact and rule of 70), rate from an observed doubling, or value after n periods.
- Equation of a line calculatory = mx + b from two points or a slope and a point: slope, y-intercept, root, vertical line included.
- GCD and LCMGCD and LCM of two or three integers, with the Euclidean algorithm unrolled line by line and the simplified fraction.
- Intercept theorem (Thales)Missing length of a Thales configuration, or the parallelism test by the converse, with the exact-ratio sketch.
- Linear interpolation calculatory from x or x from y between two points, with slope, y-intercept, line equation and extrapolation alert.
- Logarithms and exponentialslog_b(x) in any base, a power b^y, or a^x = c solved, with the logarithm rules and their conditions of existence.
- Map and plan scaleMap distance and real distance at a 1:n scale, or the scale of a document recovered from two measurements.
- Matrix calculator, 2×2 and 3×3: determinant, inverse, systemDeterminant, inverse, transpose, products AB and BA, and linear system solving, with singularity detected at a relative threshold.
- Percentage and percentage change calculatorPercentage of a value, ratio, increase or decrease, variation between two values, or the original value recovered.
- Pythagorean theoremHypotenuse or missing leg of a right triangle, or the right-angle test on three lengths (converse).
- Quadratic equation solver with stepsax² + bx + c = 0 with every step shown: discriminant, real or complex roots, vertex form, sum and product.
- Slope: percent, degrees, ratioA slope between percent, degrees and 1:n ratio, or from rise and distance, with the real road length.
- Triangle solver (law of sines and cosines)A triangle solved from SSS, SAS, ASA or SSA, with the ambiguous case handled: zero, one or two triangles, all displayed.
- Vector calculator, dot product, cross product and angleNorms, sum, dot product, cross product, angle, projection and a collinearity test, in the plane as in space.