The Following is a collection of math formulas that can prove useful to lighting designers and electricians.

#### POWER:

Watts = Volts * Amps

Amps = Watts / Volts

#### SINE WAVE (VAC):

RMS Volts = 0.707 x Peak Volts

RMS Volts = 1.11 x Peak Volts

Peak Volts = 1.57 x Average Volts

Peak Volts = 1.414 x RMS Volts

Average Volts = 0.637 x Peak Volts

Average Volts = 0.9 x RMS Volts

#### UNIT CONVERSIONS:

Inches = millimeters / 25.4

millimeters = inches * 25.4

feet = meters / 0.3048

footcandles = lux / 10.8

lux = footcandles * 10.8

Centigrade = 0.556 * (Fahrenheit - 32)

Fahrenheit = 1.8 * (Centigrade + 32)

pounds = kilograms * 2.205

kilograms = pounds * 0.454

degrees = 180 * radians / PI

radians = PI * degrees /180

#### 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

#### PATTERN PROJECTION MAGNIFICATION AND REQUIRED PATTERN SIZE:

A = new pattern size

B = old pattern size

C = new projection size

D = old projection size

P = projection magnification

A = B * (C / D) P = D / B

For standard AQ61 (or Altman 360Q) ellipsoidals, consider old pattern size to be 3" (size of gate), and old projection size to be the beam spread using the field angle information. Check diameter of gate (shutter plane opening) for other fixtures.

#### DISTANCES, INTENSITIES, SPREADS, AND ANGLES:

As seen in the drawing to the right:

D = throw distance

V= vertical height

H = horizontal distance

C = focus angle off horizontal

K = focus angle off vertical

F = beam or field angle of fixture

X = beam spread (beam oval width)

Y = beam oval length

mf=beam spread

#### FOOTCANDLES:

Footcandles = Candlepower / (D * D)#### THROW DISTANCE (D):

D = X / mf

D = SQUARE ROOT( (V * V) + (H * H)

D = H / COS( C )

D = V / SIN( C )

D = H / SIN(K)

D = V / COS(K)

D = SQUARE ROOT(Candlepower / Footcandles)

#### CANDLEPOWER:

Candlepower = Footcandle * (D * D)

#### BEAM ANGLE MULTIPLYING FACTOR (mf

mf = 2 * TAN (F / 2)

mf = X / D

#### BEAM ANGLE (F):

F = 2 * ATAN (MF / 2)

F = 2 * ATAN(X / (2 * D)

#### BEAM OVAL LENGTH (Y) (WHEN BEAM HITS SURFACE AT ANGLE):

Y = V * ( TAN(K + F/2) - TAN(K - F/2) )

#### HORIZONTAL DISTANCE (H):

H = SQUARE ROOT( (D * D) - (V * V) )

H = V / TAN( C )

H = D * COS( C )

H = D * SIN(K)

H = V * TAN(K)

#### BEAM SPREAD (OVAL WIDTH X IF NOT STRAIGHT ON):

X = D * (2 * TAN(F / 2))

X = D * mf

#### VERTICAL HEIGHT (V):

V = SQUARE ROOT( (D * D) - (H * H) )

V = H * TAN( C )

V = D * SIN( C )

V = D * COS(K)

V = H / TAN(K)

#### FOCUS ANGLE OFF VERTICAL (K):

K = ATAN(H / V)

K = ASIN(H / D)

K = 90 - ASIN(V / D)

K = 90 - C

#### FOCUS ANGLE OFF HORIZONTAL ( C ):

C = ATAN(V / H)

C = ASIN(V / D)

C = 90 - ASIN(H / D)

C = 90 - K

###### Dallas

101 Turtle Creek Blvd.

Dallas, TX 75207

###### Shreveport

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Shreveport, LA 71101

###### Lubbock

2028 82nd St, Unit 101

Lubbock, TX 79423