Spherical-Cap Surface Area from Radius and Cap Height Calculator
Compute the curved (spherical) surface area S_cap = 2·π·R·h of a spherical cap of height h cut from a sphere of radius R...
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 curved (spherical) surface area S_cap = 2·π·R·h of a spherical cap of height h cut from a sphere of radius R...
Compute the conditional probability P(A | B) from the joint probability P(A ∩ B) and the marginal P(B). Reports P(B | A)...
Approximate the definite integral ∫ from a to b of f(x) dx with Simpson's 1/3 rule on a single interval, using f(a), f(m...
Compute the midpoint of a line segment between two points in 2D (set z₁ = z₂ = 0) or 3D space — i.e. the component-wise...
Linearly interpolate (or extrapolate) the value of y at a target x given two known points (x₁, y₁) and (x₂, y₂).
Compute the angle between two 3D vectors using cos θ = (a·b) / (|a| · |b|), and report the angle in both degrees and rad...
Compute the great-circle distance between two latitude/longitude points on Earth using the Haversine formula (mean Earth...
Convert a polar coordinate (r, θ) into the Cartesian coordinate (x, y) = (r cos θ, r sin θ), with θ entered in degrees.
Convert a Cartesian coordinate (x, y) to polar (r, θ), with r = √(x² + y²) and θ = atan2(y, x).
Compute the factorial n! = 1 · 2 · 3 · ... · n for any non-negative integer up to 170 (the largest n that fits in a doub...
Compute the n-th Fibonacci number F(n), its neighbors F(n−1) and F(n+1), and the running sum of the first n terms.
Compute the geometric mean of a list of positive numbers — useful for averaging growth rates and ratios.
Compute the harmonic mean of a list of positive numbers — useful for averaging rates such as speeds or ratios.
Compute the midrange of a list of numbers — the simple average of the smallest and largest values.
Compute a weighted average from two equal-length lists of values and weights — useful for grades, weighted survey scores...
Compute the area of a parallelogram from a base and the perpendicular height to that base.
Compute the area of a rhombus from the lengths of its two diagonals.
Compute the area of a kite from the lengths of its two diagonals.
Add, subtract, multiply, or divide two complex numbers (a + bi) and (c + di), and see the result in both rectangular and...
Calculates the binomial coefficient C(n, r) — the number of ways to choose r items from n items without regard to order.
Computes an even perfect number using Euler's theorem: N = 2^(p−1) × M_p where M_p = 2^p − 1 is the Mersenne number. Kno...
Solves a system of two linear congruences using the Chinese Remainder Theorem. Requires the user to provide the modular...
Given a particular integer solution (x₀, y₀) and GCD d of a and b, computes the general solution: x = x₀ + (b/d)t, y = y...
Calculates closed-form sums of squares, cubes, and fourth powers from 1 to n. Also includes sum of first n integers. Ess...