Ratio Simplifier
Reduce a ratio a:b to its lowest terms by dividing both terms by their greatest common divisor, and report the equivalen...
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.
Reduce a ratio a:b to its lowest terms by dividing both terms by their greatest common divisor, and report the equivalen...
Compute the area of a circular segment (the region between a chord and an arc) from the circle radius and the central an...
Compute a semester GPA as a credit-weighted average of up to four courses, given each course's grade-point value (4.0 sc...
Given a discrete random variable with three outcomes x₁, x₂, x₃ and corresponding probabilities p₁, p₂, p₃ (summing to 1...
Fit an ordinary least-squares regression line y = m·x + b directly from the standard running sums Σx, Σy, Σxy, Σx², and...
Find one real root of a depressed cubic t³ + p·t + q = 0 using Cardano's formula in the discriminant-positive case (Δ =...
Compute the n-th term of a harmonic progression — a sequence whose reciprocals form an arithmetic progression with first...
Compute the Shannon entropy H of a 3-outcome discrete distribution: H = −Σ pᵢ · log₂ pᵢ, in bits. Entropy is the average...
Compute the pooled (combined) sample standard deviation of two independent samples that are assumed to share a common po...
Convert a complex number from rectangular form a + b·i to polar form r∠θ, with r = √(a² + b²) and θ = atan2(b, a). Repor...
Compute the perpendicular distance from a 3-D point (x₀, y₀, z₀) to the plane a·x + b·y + c·z + d = 0, using d_pt = |a·x...
Compute the negative binomial PMF — the probability that the r-th success occurs on the k-th trial, given a per-trial su...
Compute Cohen's d effect size = (M₁ − M₂) / SD_pooled, with rule-of-thumb interpretation (0.2 small, 0.5 medium, 0.8 lar...
Compute the one-sample z-test statistic for a population mean when σ is known: z = (x̄ − μ₀) / (σ / √n). Compare to ±1.9...
Compute the excess kurtosis of a distribution from its centred fourth moment m₄ = E[(X − μ)⁴] and the variance σ²: exces...
Compute the perpendicular distance from a 2-D point (x₀, y₀) to the line a·x + b·y + c = 0, using d = |a·x₀ + b·y₀ + c|...
Compute the Pearson chi-square goodness-of-fit statistic from up to six (observed, expected) pairs: χ² = Σ (O − E)² / E....
Compute the volume of a frustum of a cone (a truncated right circular cone) from the two parallel-circle radii and the h...
Compute the mean of grouped data from up to six (midpoint, frequency) pairs: x̄ = Σ(fᵢ · xᵢ) / Σfᵢ.
Compute the (x, y) intersection of two lines a₁·x + b₁·y = c₁ and a₂·x + b₂·y = c₂ via the determinant. Returns the uniq...
Approximates the gamma function Γ(z) using Stirling's series for z > 0: Γ(z) ≈ √(2π/z) · (z/e)^z. For integer z, Γ(n) =...
Compute the n-th partial sum of the harmonic series Hₙ = Σₖ₌₁ⁿ 1/k. Also reports the Euler-Mascheroni approximation Hₙ ≈...
Compute Markov's inequality upper bound on the right-tail probability of a non-negative random variable X with mean μ: P...
Compute the attendance percentage from classes attended and total classes, plus the maximum number of additional absence...