Lambertian Point Illuminance Calculator
Estimate horizontal-plane illuminance from a forward hemispherical cosine-power source with total lumens and half-intensity angle.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Normalize a cosine-power intensity distribution over the forward hemisphere and apply incidence cosine plus inverse-square spreading.
m=−ln2/ln(cos half-angle); I0=(m+1)Φ/(2π); E=I0 cos^(m+1)θ/distance²
Worked example
A Lambertian m=1 source with 1000 lm at 2 m height gives on-axis illuminance 1000/(4π)≈79.5774715 lux. At 1 m offset it gives about 50.9295818 lux.
Assumptions and input details
Ideal point source aimed normal to the plane, no luminaire photometric file, reflection, obstructions or maintenance factor. Half-intensity angle is one polar half-angle, not a full beam width. No real lighting design or minimum-illumination certification.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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