Lighting Point by Point Calculator
Free Lighting point point Calculator for electrical engineering projects. Enter dimensions to get material lists and cost estimates.
Formula
E_h = (I x cos^3 theta) / h^2
Horizontal illuminance at a point equals the luminous intensity (candela) in the direction of the point multiplied by the cube of the cosine of the angle from nadir, divided by the square of the mounting height. Vertical illuminance uses sin(theta) x cos^2(theta) instead. The angle theta is calculated from the mounting height and horizontal distance using arctangent.
Worked Examples
Example 1: Parking Lot Light
Problem: A luminaire with 8,000 cd peak intensity is mounted at 8 meters. Calculate horizontal illuminance at a point 6 meters away horizontally.
Solution: Distance to point: sqrt(8^2 + 6^2) = sqrt(100) = 10 m\nAngle from nadir: atan(6/8) = 36.87 degrees\ncos(36.87) = 0.8\nE_h = (8000 x 0.8^3) / 8^2 = (8000 x 0.512) / 64 = 64 lux
Result: Horizontal: 64 lux (5.94 fc) | Vertical: 48 lux | Angle: 36.9 deg
Example 2: Floodlight on Building
Problem: A floodlight with 25,000 cd is mounted 12 meters high. Calculate illuminance at a point 4 meters from directly below.
Solution: Distance: sqrt(144 + 16) = 12.65 m\nAngle: atan(4/12) = 18.43 degrees\ncos(18.43) = 0.9487\nE_h = (25000 x 0.9487^3) / 144 = (25000 x 0.854) / 144 = 148.3 lux
Result: Horizontal: 148.3 lux (13.78 fc) | Direct: 156.3 lux
Frequently Asked Questions
What is the point-by-point method in lighting design?
The point-by-point method calculates the illuminance at a specific point on a surface from one or more light sources using the inverse square law and cosine law. Unlike the lumen method which gives average illuminance, point-by-point calculations show the exact light level at any location. This method is essential for exterior lighting design, sports lighting, parking lots, roadway lighting, and any application where uniformity and minimum illuminance at specific points must be verified. Modern lighting software uses this method with hundreds of calculation points to create detailed illuminance maps.
What is the inverse square law in lighting?
The inverse square law states that illuminance decreases with the square of the distance from the light source. If you double the distance from a light source, the illuminance drops to one-quarter. Mathematically, E = I / d2, where E is illuminance in lux, I is luminous intensity in candela, and d is the distance in meters. This law applies to point sources and is the foundation of point-by-point calculations. In practice, most fixtures are not true point sources, so the law is most accurate when the distance from the fixture is at least five times the maximum fixture dimension.
How accurate are the results from Lighting Point by Point Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
What formula does Lighting Point by Point Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.