Master foundational physics, finance, calculus, and engineering equations with live evaluators, derivations, and worked examples.
Generalizes the Pythagorean theorem to any oblique triangle by adding the −2ab cos(C) projection term.
States that the ratio of any side length of a triangle to the sine of its opposite interior angle is constant and equal to the circumcircle diameter 2R.
Computes the exact surface area, altitudes, inradius, and circumradius of any triangle directly from its three side lengths a, b, c without measuring angles.
Euclidean metric distance, segment midpoint, and gradient slope between two Cartesian points (x₁, y₁) and (x₂, y₂).
Analytic geometry equations for circles and ellipses including center (h, k), semi-major/minor axes (a, b), eccentricity e, focal points, area, and Ramanujan perimeter.
Fundamental orthogonal metric relating legs and hypotenuse in right triangles and rectangular 3D box diagonals.
Archimedes' solid geometry formulas comparing volumes and surface areas of spheres, right circular cylinders, and cones.
Relates circular radius r and central angle θ to arc length s, sector area, chord length, sagitta, and circular segment area.
Complete trigonometric reference for angle-sum, double-angle, half-angle, and power-reduction identities.
Computes the shortest great-circle surface distance between two latitude/longitude coordinates on a sphere of radius R (Earth mean R = 6,371 km).