# Mathematical Formulas for Lighting

Discussion in 'Collaborative Articles' started by derekleffew, May 5, 2008.

1. ### derekleffewResident CurmudgeonSenior TeamPremium Member

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Link to various NEC calculators and Look-Up Tables: http://www.electrician2.com/calculators/elcal.html .
From Mike Wood, of Mike Wood Consulting:

See OSRAM SYLVANIA:Sylvania Automotive Lighting Catalog:

Link to an Excel workbook containing most of the above formulae.

Copied from this post by [user]ship[/user].

## LIGHT OUTPUT CALCULATIONS

A dinner candle provides about 12 lumens. A 60-watt Soft White incandescent lamp provides 840 lumens.
• [noparse]Foot-candles = candela / distance in feet * distance in feet[/noparse]
• [noparse]Foot-candles = Lux / 10.764 = lumens/sq. meter[/noparse]
• [noparse]1 fc=1/10.764 lux[/noparse]
• [noparse]Foot-candles * 10.764 = lumens/sq. meter = lux [/noparse]
• [noparse]Lumens/sq. ft. * 1 = foot-candles; (1fc=1 lumen/ft²)[/noparse]
• [noparse]Lumens/sq. ft. * 10.764 = lumens/sq. meter[/noparse]
• [noparse]Lumens * 0.07958 = spherical candle power[/noparse]
• [noparse]Lumens = Mean Spherical Candlepower x 12.57[/noparse]
• [noparse]Lux * 0.0929 = foot-candles[/noparse]
• [noparse]Lux = candela / (distance in meters * distance in meters)[/noparse]
• [noparse]Lambert * 0.3183 = candela/sq. cm (candela per sq. cm), Lambert * (1/pi) = candles/sq. cm[/noparse]
• [noparse]Lambert * 295.720 = candela/ sq. ft. (candela per sq. ft.)[/noparse]
• [noparse]Lambert * 1 = lumens/sq. cm[/noparse]
• [noparse]Illuminance (lx) = E = Luminous flux falling on area (lm) ÷ Illuminated area (m²)[/noparse]
• [noparse]Illuminance (lx) = E = Luminous intensity (cd) ÷ (distance in meters (m))²[/noparse]
• [noparse]Luminance (cd/m²) = L = Luminous intensidy (cd) ÷ viewed luminous area (M²)[/noparse]
• [noparse]Luminous efficacy (lm/w) = h = Generated luminous flux (lm) ÷ Electrical power consumed (w)[/noparse]
• [noparse]Efficacy=F(lu)/P(w)[/noparse]
• [noparse]F=Luminous Flux[/noparse]
• [noparse]P=Electrical Power (wattage), in watts[/noparse]

## LIGHT BEAM CALCULATIONS:

See Conventional Photometrics_v7.zip for a down-loadable MS Excel workbook containing most popular fixtures.
• [noparse]Beam diameter = distance * (2 * tan (beam angle in degrees / 2))[/noparse]
• [noparse]Throw distance = Square root ( (horizontal dist. * horizontal dist.) + (vertical dist. * vertical dist.) )[/noparse]
• [noparse]Inverse Square Law: E(fc)=I(cd)/D(ft)². E(fc)=F(lm)/A(ft)²[/noparse]
• [noparse]A=Area in square feet[/noparse]
• [noparse]D=Distance in feet[/noparse]
• [noparse]E=Illumination in footcandles[/noparse]
• [noparse]F=Luminous Flux in Lumens[/noparse]
• [noparse]I=Luminous intensity (Candlepower) in footcandles[/noparse]

[noparse]Mired Shift Value = (1,000,000/d) - (1,000,000/a); d=Desired Color Temperature (no units), a=Actual Color Temperature (no units)[/noparse]

## Fixture Lens Conversion Guide:

For a two-lens system: EFL= (f1*f2)/(f1+f2-d), where EFL=Effective Focal Length, f1=Focal Length of Lens1, f2=Focal Length of Lens2, d=Distance between Lenses.

• [*][noparse]50° - 3.5Q5 / 360Q-4.5x6.5 (45°)[/noparse]
[*][noparse]40° - 3.5Q6 / 360Q-6x9 (37°)[/noparse]
[*][noparse]30° - 3.5Q8 / 360Q-6x12 (27°)[/noparse]
[*][noparse]20° - 3.5Q10 / 360Q-6x16 (17°)[/noparse]
[*][noparse]10° / 12° - 3.5Q12 / 360Q-6x22 [single lens] (9.5°)[/noparse]
[*][noparse]5° - None[/noparse]
[*][noparse]8x8 (20°)[/noparse]
[*][noparse]8x10 (16°)[/noparse]
[*][noparse]8x16 (6°)[/noparse]
[*][noparse]1Kw PAR64:[/noparse]
[*][noparse]ACL (GE 4552-28V, 250W)- Beam: 7°x8°[/noparse]
[*][noparse]ACL (GE 4559-28V, 600W)- Beam: 11°x12°[/noparse]
[*][noparse]VNSP (FFN), CP60 - Beam: 6° x 12° Field: 10° x 24°[/noparse]
[*][noparse]NSP (FFP), CP61 - Beam: 7° x 14° Field: 14° x 26°[/noparse]
[*][noparse]MFL (FFR), CP62 - Beam: 12° x 24° Field: 21° x 44°[/noparse]
[*][noparse]WFL (FFS), CP95 - Beam: 24° x 48° Field: 45° x 71° [/noparse]

## POWER CALCULATIONS

• [noparse]Power = Voltage * Current (Watts = Volts * Amps)[/noparse]
• [noparse]P(w)=V(v)xI(a)[/noparse]
• [noparse]P=Electrical Power (Wattage) in watts[/noparse]
• [noparse]V=Voltage (EMF), in volts[/noparse]
• [noparse]I=Electrical Current(Amperage), in amps[/noparse]
• [noparse]Current = Power / Voltage (Amps = Watts / Volts)[/noparse]
• [noparse]RMS Volts = 0.707 * Peak Volts RMS Volts = 1.11 * Average Volts[/noparse]
• [noparse]Ohm’s Law: V(v)=I(a) * R([/noparse]Ω[noparse])[/noparse]
• [noparse]V=Voltage (EMF), in volts[/noparse]
• [noparse]I=Electrical Current (Amperage), in amps[/noparse]
• [noparse]R=Resistance, in ohms[/noparse]
• [noparse]Impedance: Z([/noparse]Ω[noparse])=[/noparse]√[noparse][R²([/noparse]Ω[noparse])²=X²([/noparse]Ω[noparse]²][/noparse]
• [noparse]Z=Impedance, in ohms[/noparse]
• [noparse]R=Resistance, in ohms[/noparse]
• [noparse]X=Reactance, in ohms[/noparse]
• [noparse]Power Factor: R([/noparse]Ω[noparse])/Z([/noparse]Ω[noparse])[/noparse]
• [noparse]pf=Power Factor[/noparse]
• [noparse]R=Resistance, in ohms[/noparse]
• [noparse]Z=Reactance, in ohms[/noparse]
• [noparse]DC VOLTAGE DROP OF CONDUCTOR (cable) OF L LENGTH[/noparse]
• [noparse]V = voltage drop, I = current[/noparse]
• [noparse]R = resistance of conductor per 1000 feet[/noparse]
• [noparse]L = length of conductor in feet[/noparse]
• [noparse]R for 18awg = 6.51, 16awg = 4.09, 14awg = 2.58[/noparse]
• [noparse]12awg = 1.62, 10awg = 1.02, 8awg = 0.64[/noparse]
• [noparse]V = I * L * (R / 1000) * 1.004[/noparse]

Lamp sizing:
Stage/Studio lamps are often expressed as a number representing the diameter of the lamp in 1/8s of one inch. A PAR64 Lamp has a diameter of 8". A T6 lamp is 3/4". The most common size of fluorescent tube is T8, or 1". The predecessor of the BTN fresnel lamp was the T20, 2.5". A G40 lamp is 5" at its widest diameter, and so on. The most common household lamp is the A19, 2 3/8" diameter.

Last edited: Jun 27, 2010