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Lighting Point by Point Calculator

Free Lighting point point Calculator for electrical engineering projects. Enter dimensions to get material lists and cost estimates.

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Construction & Engineering

Lighting Point by Point Calculator

Calculate illuminance at any specific point using the inverse square law and cosine correction. Determine horizontal and vertical lux values from luminaire candela data, mounting height, and distance.

Last updated: December 2025

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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.

Last reviewed: December 2025

Worked Examples

Example 1: Parking Lot Light

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 Angle from nadir: atan(6/8) = 36.87 degrees cos(36.87) = 0.8 E_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

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 Angle: atan(4/12) = 18.43 degrees cos(18.43) = 0.9487 E_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
Expert Insights

Background & Theory

The Lighting Point by Point Calculator applies the following established principles and formulas. Structural and construction engineering is governed by fundamental load analysis, material science, and regulatory standards that ensure the safety and durability of built structures. The primary distinction in load analysis is between dead loads โ€” the permanent self-weight of structural elements, finishes, and fixed equipment โ€” and live loads, which represent variable occupancy, furniture, and environmental forces such as wind and snow. These are combined using factored load equations, such as the ASCE 7 formula U = 1.2D + 1.6L, where D is dead load and L is live load. Concrete mix design is governed by the water-cement (w/c) ratio, which is the primary determinant of compressive strength and durability. A w/c ratio of 0.40โ€“0.45 typically yields concrete with 28-day compressive strengths of 30โ€“40 MPa. Common mix ratios by weight for structural concrete are approximately 1 part cement : 1.5โ€“2 parts sand : 3 parts coarse aggregate. Structural steel is characterized by its yield strength (the stress at which permanent deformation begins, typically 250โ€“350 MPa for mild steel) and ultimate tensile strength (typically 400โ€“500 MPa). Mid-span deflection of a simply supported beam under a central point load is given by ฮด = FLยณ / (48EI), where F is force, L is span length, E is Young's modulus, and I is the second moment of area. Building insulation is rated by R-value, a measure of thermal resistance in units of mยฒยทK/W (SI) or ftยฒยทยฐFยทh/BTU (imperial). Higher R-values indicate greater resistance to heat flow. Foundation design depends on the allowable bearing capacity of the underlying soil, which ranges from approximately 75 kPa for soft clay to over 10,000 kPa for bedrock. Drainage gradients for surface water are typically specified as a minimum of 1โ€“2% slope away from building foundations to prevent hydrostatic pressure and water infiltration.

History

The history behind the Lighting Point by Point Calculator traces back through the following developments. The history of construction engineering spans thousands of years of accumulated empirical knowledge and, more recently, rigorous scientific analysis. The ancient Egyptians built the Great Pyramid of Giza around 2560 BCE using an estimated 2.3 million stone blocks, demonstrating sophisticated logistics, geometry, and workforce organization. Roman engineers advanced the field dramatically through the use of pozzolanic concrete โ€” a mixture of volcanic ash, lime, and seawater โ€” enabling the construction of the Pantheon dome (43.3 m diameter, completed around 125 CE) and a vast network of aqueducts and roads across the empire. Cast iron emerged as a structural material during the Industrial Revolution, first used prominently in the Iron Bridge at Coalbrookdale, England, completed in 1779. Wrought iron and later steel allowed far greater spans and heights. The Eiffel Tower, completed in 1889, demonstrated the structural possibilities of wrought iron at scale and influenced the development of steel-frame skyscraper construction in Chicago and New York. Reinforced concrete was systematically developed by Joseph Monier, a French gardener, who patented iron-reinforced concrete pots and panels in the 1860s, and later by engineers including Franรงois Hennebique who created the first comprehensive reinforced concrete framing system in the 1890s. The 1906 San Francisco earthquake caused widespread devastation and galvanized the engineering profession to develop seismic design provisions. Subsequent earthquakes โ€” including the 1971 San Fernando and 1994 Northridge events โ€” drove successive improvements in seismic codes, base isolation technology, and ductile detailing of reinforced concrete and steel frames. Building codes became increasingly standardized in the twentieth century, with the International Building Code (IBC) first published in 2000 providing a unified model code adopted across much of the United States. Building Information Modeling (BIM) emerged in the 2000s as a digital workflow integrating architectural, structural, and MEP design into a unified three-dimensional model, fundamentally changing coordination practices across the industry.

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Frequently Asked Questions

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.
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.
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.
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.
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
Educational Note: This calculator is provided for educational and informational purposes. Results are based on the formulas and inputs provided. Always verify important calculations independently. NovaCalculator processes calculator inputs client-side; optional analytics follow visitor consent settings. ยฉ 2024โ€“2026 NovaCalculator.

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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.

Why might my result differ from another tool or reference?

Differences typically arise from rounding conventions, the specific version of a formula (for example, simple vs compound interest), or unit inconsistencies between inputs. Check that both tools are using the same formula variant and the same units. The References section links to the authoritative source behind the formula used here.

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.

References

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