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LIGHTING MATHEMATICS - COPYRIGHT LIGHTING & ELECTRONICS®
The following is a collection of math formulas that can prove useful to lighting designers and lighting installers when planning a stage lighting installation. You can also download simple spreadsheets that have several of these useful lighting formulas built into them. Click on one of the links below, choose "Save As" from your browser "File" menu and select the location to download Lighting Calculators in Microsoft Excel format.
EXCEL LIGHTING SPREADSHEET CALCULATORS:
• Lighting Calculator 1 for Excel '97 (26K)
• Lighting Calculator 3 for Excel 3.0 (30K)
POWER:
Watts = Volts * Amps
Amps = Watts / Volts
SINE WAVE (VAC):
RMS Volts = 0.707 x Peak Volts
RMS Volts = 1.11 x Average 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
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
UNIT CONVERSIONS:
inches = millimeters / 25.4
millimeters = inches * 25.4
feet = meters / 0.3048
meters = feet * 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
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
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.
A = B * (C/D)
P = D / B
DISTANCES, INTENSITIES, SPREADS, AND ANGLES:
 VIEW DRAWING
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 multiplying factor
Footcandles:
Footcandles = Candlepower / (D * D)
Candlepower:
Candlepower = Footcandles * (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 spread (oval width X if not straight on):
X = D * (2 * TAN(F / 2))
X = D * mf
Beam oval length (Y) (when beam hits surface at angle):
Y = V * ( TAN(K + F/2) - TAN(K - F/2) )
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)
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)
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 horizontal (C):
C = ATAN(V / H)
C = ASIN(V / D)
C = 90 - ASIN(H / D)
C = 90 - K
Focus angle off vertical (K):
K = ATAN(H / V)
K = ASIN(H / D)
K = 90 - ASIN(V / D)
K = 90 - C
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