**HP 42S/DM42/Free42: Room Cavity Ratio, Luminous Intensity and Illuminance**

**Room Cavity Ratio**

The room cavity ratio is used to assist in calculating lighting efficiency in determining where to place ceiling lights in an office room. The formula is:

RCR = INT( ( 5 * H * ( L + W ) ) / ( L * W ) )

where:

L = length of the room

H = height difference between floor cavity and ceiling cavity

W = width of the room

**HP 42S/DM42/Free42: Solver RCR**

LBL “RCR”

MVAR “H”

MVAR “L”

MVAR “W”

MVAR “RCR”

5

RCL * “H”

RCL “L”

RCL + “W”

*

RCL “L”

RCL * “W”

÷

IP

RCL – “RCR”

END

**Examples**

Example 1:

Input: H = 5.5, L = 16.8, W = 13.7. Result: RCR = 3

Example 2:

Input: H = 5.5, L = 16.8, RCR = 4. Result: H = 7.1650

Sources:

Dilouie, Craig. “Lighting Design: Example of Role Surfaces Play in Lighting Efficiency” LightNOW https://www.lightnowblog.com/2010/06/example-of-role-surfaces-play-in-lighting-efficiency/ June 16, 2010. Retrieved March 31, 2019

“Room Cavity Ratio, RCR” Illuminating Engineering Society. https://www.ies.org/definitions/room-cavity-ratio-rcr/ July 5, 2018. Retrieved April 28, 2019

**Luminous Intensity and Illuminance**

The follow equation relates the luminous intensity (measured in candelas, cd) and illuminance (measured in lux) of a light source. The equation assumes the light source radiates a spherical matter.

E = I / R^2

E = illuminance

I = luminous intensity

R = radius of the sphere’s light (meters)

**HP 42S/DM42/Free42: Solver ILSPH**

LBL “ILSPH”

MVAR “E”

MVAR “I”

MVAR “R”

RCL “E”

RCL “I”

RCL “R”

x ↑ 2

÷

–

END

**Examples**

Example 1:

Input: I = 10 cd, R = 2 m. Result: 2.5 lux

Example 2:

Input: R = 3.65 m, E = 30 lux. Result: I = 399.6750 cd

Sources:

Daryanani, Sital __Building Systems Design With Programmable Calculators__ Architectural Record Books. McGraw-Hill Book Company: New York. 1980. ISBN 0-07-015415-5

Zumtobel “The Lighting Handbook” Zumtobel Lighting GmbH. Dornbirn, Austria. 6th Edition: 2018 https://www.zumtobel.com/PDB/Ressource/teaser/en/Lichthandbuch.pdf

Eddie

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