Lognormal Moment Profile
Find a lognormal model’s median, mean, variance and mode from natural-log parameters.
ProbabilityOpen tool ↗THE FEUTEX TOOLKIT
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Correlated Measurement Uncertainty
Propagate correlated standard uncertainties through a sum, difference and product.
StatisticsOpen tool ↗No-Fixed-Point Assignment Count
Count assignments with no item in its original position and calculate their random-permutation probability.
ProbabilityOpen tool ↗Balanced Parenthesis Structure Count
Count valid balanced-parenthesis sequences and equivalent ordered binary tree shapes.
MathOpen tool ↗Ordered and Unordered Selections
Count selections without replacement with and without regard to ordering.
MathOpen tool ↗Birthday Collision Estimate
Estimate collision probability and expected matching pairs for independent draws from equal-probability categories.
ProbabilityOpen tool ↗Coupon Collection Expectation
Calculate the expected draw count and variance needed to collect every uniformly distributed coupon type.
ProbabilityOpen tool ↗Random Bin Occupancy
Estimate occupied, empty and singleton bins after independent uniform assignments.
ProbabilityOpen tool ↗Sphere Intersection Volume
Measure the shared volume and intersection-circle radius of two partially overlapping spheres.
GeometryOpen tool ↗Cone Solid Angle and Sphere Fraction
Calculate a cone aperture’s solid angle and the fraction of a sphere it covers.
GeometryOpen tool ↗Helix Path Profile
Measure a circular helix’s length, rise, curvature and torsion from radius, pitch and turns.
GeometryOpen tool ↗Triangle from Two Sides and Included Angle
Solve a triangle’s remaining side, angles and area from two sides and their included angle.
GeometryOpen tool ↗Plane Angle and Intersection Direction
Find the acute angle between planes and a direction vector for their intersection line.
GeometryOpen tool ↗Quadrilateral Coordinate Survey
Calculate signed area and perimeter from four consecutive boundary coordinates.
GeometryOpen tool ↗Great-Circle Distance
Measure the shortest spherical surface route and straight chord between two latitude-longitude positions.
GeometryOpen tool ↗Reflect a Point across a Plane
Mirror a three-dimensional point across a plane given by its coefficients.
GeometryOpen tool ↗Nearest Point on a Line Segment
Find the nearest point on a finite line segment, including endpoint cases.
GeometryOpen tool ↗Circle through Three Points
Locate the center and radius of the unique circle passing through three noncollinear points.
GeometryOpen tool ↗Runge–Kutta Four-Stage Step
Combine four correctly evaluated Runge–Kutta stage slopes into one fourth-order solution step.
MathOpen tool ↗Cubic Polynomial Evaluation
Evaluate a cubic polynomial, its first two derivatives and its signed integral from zero.
MathOpen tool ↗Four-Sample Fourier Transform
Transform four equally spaced real samples into their discrete Fourier frequency components.
MathOpen tool ↗Point Inversion in a Circle
Map a planar point through a geometric inversion circle while preserving its radial direction.
GeometryOpen tool ↗Quadratic Real Root Solver
Find both real roots and the vertex of a quadratic polynomial from its coefficients.
MathOpen tool ↗Telescope Eyepiece Performance
Compare eyepiece magnification, exit pupil and approximate true field of view.
AstronomyOpen tool ↗Astrophotography Pixel Sampling
Compare angular pixel scale with seeing and estimate pixels across a target.
AstronomyOpen tool ↗Circular Orbit Profile
Calculate orbital velocity, period and specific energy around a specified body.
AstronomyOpen tool ↗Elliptic Orbit Apsides
Find eccentricity, semimajor axis and speed at the near and far points of an orbit.
AstronomyOpen tool ↗Hohmann Transfer Budget
Estimate two impulsive burns and coast time between coplanar circular orbits.
AstronomyOpen tool ↗Orbital Plane Change Burn
Estimate an ideal impulsive plane change at a selected orbital speed.
AstronomyOpen tool ↗Synodic Alignment Period
Estimate the time between repeated alignments of two bodies with constant orbital periods.
AstronomyOpen tool ↗Exoplanet Transit Depth
Estimate the fraction of stellar light blocked by a smaller opaque planet.
AstronomyOpen tool ↗Stellar Distance Modulus
Infer stellar distance from apparent and absolute magnitude with an extinction allowance.
AstronomyOpen tool ↗Combined Stellar Magnitude
Combine the apparent brightness of two unresolved stars.
AstronomyOpen tool ↗Blackbody Peak and Surface Flux
Estimate peak wavelength and emitted power per unit area for an ideal blackbody.
AstronomyOpen tool ↗Stellar Luminosity from Radius and Temperature
Estimate luminosity relative to the Sun under a spherical blackbody model.
AstronomyOpen tool ↗Spectral Line Redshift
Calculate redshift and radial velocity using both small-shift and relativistic formulas.
AstronomyOpen tool ↗Astrophotography Stack Signal-to-Noise
Estimate stacked signal-to-noise from source, background, dark current and read noise.
AstronomyOpen tool ↗Plane-Parallel Airmass Estimate
Estimate atmospheric path length relative to the zenith at moderate altitude.
AstronomyOpen tool ↗Apparent Angular Diameter
Calculate the angle subtended by a circular object of known diameter and distance.
AstronomyOpen tool ↗Telescope Obstruction and Light Collection
Estimate clear collecting area and the fractional loss from a central obstruction.
AstronomyOpen tool ↗Tidal Acceleration Difference
Estimate the leading-order radial tidal acceleration across a short object.
AstronomyOpen tool ↗Hyperfocal Focus Range
Calculate hyperfocal distance and the near sharp limit when focused at that distance.
PhotographyOpen tool ↗Thin Lens Image Position
Find image distance and signed magnification for a thin lens and real object.
PhotographyOpen tool ↗Macro Extension Exposure Compensation
Estimate magnification and exposure increase from lens extension beyond infinity focus.
PhotographyOpen tool ↗Diffraction Disk and Pixel Comparison
Compare Airy disk diameter with sensor pixel pitch.
PhotographyOpen tool ↗Manual Flash Working Distance
Estimate flash distance at an aperture, ISO and power fraction using a supplied guide number.
PhotographyOpen tool ↗ND Filter Long Exposure Planner
Calculate exposure duration after a neutral-density filter and display optical density.
PhotographyOpen tool ↗Panorama Coverage Planner
Plan image count and step angle for a chosen panorama width and overlap.
PhotographyOpen tool ↗No matching tools.