# Mathematical Formulas for Lighting

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

lumens/LUMENS = (VOLTS/volts)^3.4

life/LIFE = (VOLTS/volts)^13 (I.e., reduce the volts to 90% and the life increases by 393%!)

EFFICIENCY/efficiency = (VOLTS/volts)^1.9

watts/WATTS = (volts/VOLTS)^1.6
(not 'squared' as you would get with a fixed resistance)

coltemp/COLTEMP = (volts/VOLTS)^0.42
See OSRAM SYLVANIA:Sylvania Automotive Lighting Catalog:

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

Copied from this post by ship.

## [hide][top]LIGHT OUTPUT CALCULATIONS

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

## [hide][top]LIGHT BEAM CALCULATIONS:

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

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

## [hide][top]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.

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

## [hide][top]POWER CALCULATIONS

• Power = Voltage * Current (Watts = Volts * Amps)
• P(w)=V(v)xI(a)
• P=Electrical Power (Wattage) in watts
• V=Voltage (EMF), in volts
• I=Electrical Current(Amperage), in amps

• Current = Power / Voltage (Amps = Watts / Volts)
• RMS Volts = 0.707 * Peak Volts RMS Volts = 1.11 * Average Volts
• Ohm’s Law: V(v)=I(a) * R(Ω)
• V=Voltage (EMF), in volts
• I=Electrical Current (Amperage), in amps
• R=Resistance, in ohms

• Impedance: Z(Ω)=√[R²(Ω)²=X²(Ω²]
• Z=Impedance, in ohms
• R=Resistance, in ohms
• X=Reactance, in ohms

• Power Factor: R(Ω)/Z(Ω)
• pf=Power Factor
• R=Resistance, in ohms
• Z=Reactance, in ohms

• DC VOLTAGE DROP OF CONDUCTOR (cable) OF L LENGTH
• V = voltage drop, I = current
• R = resistance of conductor per 1000 feet
• L = length of conductor in feet
• R for 18awg = 6.51, 16awg = 4.09, 14awg = 2.58
• 12awg = 1.62, 10awg = 1.02, 8awg = 0.64
• V = I * L * (R / 1000) * 1.004

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.

 Contributors: dvsDave , derekleffew Created by derekleffew , May 5th, 2008 at 02:18 AM Last edited by dvsDave , August 16th, 2011 at 04:02 PM 0 Comments, 9,210 Views