Lighting Point by Point Calculator

Point-by-point calculation abandons the averaging assumption of the lumen method and computes illuminance at one specific location from one specific luminaire. It rests on two physical laws acting together. The inverse-square law gives E equal to I divided by d squared, where I is luminous intensity in candela toward that point and d is the straight-line distance in meters, because a fixed solid angle of flux spreads over an area growing with the square of distance. The cosine law then corrects for the tilt of the receiving surface: flux striking a plane obliquely spreads across a larger footprint, reducing illuminance by the cosine of the incidence angle. Substituting d equal to h divided by cos theta into the inverse-square expression collapses both effects into the working form E equals I times cos cubed theta divided by h squared, where h is mounting height and theta is the angle from nadir. Vertical illuminance on a plane facing the fixture substitutes sin theta times cos squared theta, which matters for facial recognition in security lighting and for CCTV performance. The intensity value I is not a single number for a real luminaire. It must be read from the photometric file for the exact angle involved, distributed as candela per 1,000 lamp lumens across vertical and horizontal angles. The largest practical caveat is the point-source assumption: the inverse-square law is accurate only when the distance to the point is at least five times the maximum luminous dimension of the fixture, so it misrepresents long linear or large-area sources at close range. The result is also direct illuminance only, excluding inter-reflected light, which is acceptable outdoors but understates indoor levels.

The inverse-square relationship for light was stated by Johannes Kepler in Ad Vitellionem Paralipomena in 1604, reasoning from the geometric spreading of rays rather than from measurement. The angular correction came from Johann Heinrich Lambert, whose Photometria of 1760 established both the cosine law of incidence and the cosine emission law for diffuse surfaces that still carries his name. Lambert built the mathematical apparatus of photometry before any instrument existed to verify it precisely; visual comparison photometers of the Bunsen grease-spot type in the nineteenth century, and later physical photometers, supplied the empirical foundation. Applying these laws routinely to design work required standardized fixture data, and that arrived with photometric testing laboratories and the goniophotometer, an instrument that rotates a luminaire through vertical and horizontal angles while measuring intensity in each direction. The Illuminating Engineering Society, founded in 1906, developed the reporting formats that made such data comparable between manufacturers, culminating in the IES standard file format for electronic photometric data introduced in the 1980s and revised as LM-63. Before computers, engineers performed point calculations by hand using isolux charts and utilization curves, which limited them to a handful of check points. IES recommended practice documents such as RP-8 for roadway lighting codified minimum and uniformity criteria that only point calculation can verify. Software including Lumen Micro, AGi32, and DIALux automated the arithmetic from the 1980s onward, evaluating grids of hundreds or thousands of points and rendering the isolux maps now expected in exterior lighting submittals.