# Fire Alarm Calculations

If you are preparing to take the NICET exam for Fire Alarm Systems, there are numerous fire alarm calculations you must understand in order to properly design a code compliant system.  These calculations can break down exact requirements for sound pressure (dB) levels, voice intelligibility, voltage drop on a circuit, back up battery sizes, candela settings and dB line loss for speaker circuits.  There are additional calculations however these are some of the most common and important so this article will concentrate on the following:

#### How to find the correct Candela Strobe to cover a given space

This is a very important measurement as it allows us to properly calculate the necessary candela power needed for a given space.  If you do not have NFPA 72 2013 edition tables 18.5.5.4.1(a) and 18.5.4.4.1(b) handy or memorized, this formula will save the day!

Take the selected candela (ex. 75 cd) and divide it by 0.0375
75 cd / 0.0375 = 2000
Now take the square root of 2000 to get a spacing of = 44.72136 feet.

If you consult NFPA 72 2013 tables 18.5.5.4.1(a) it shows a spacing of 45 x 45 feet and table 18.5.5.4.1(b) shows a spacing of 44 x 44 feet.

#### Voltage Drop Calculation

Step #1:  Find the total current from all of your field notification appliances.  If you consult the appliance's specification sheet, you will find the current draw for each setting.  For example, you have four appliances on the temporal high setting and they each draw 50mA or (0.050A).  If you add all four appliances together (4 x 0.050) you have a total current draw of   0.2A

Step #2:  Determine the to and from distance of the notification appliance circuit (NAC).  For this example, we will saw the NAC is 450 feet.  We have to double this distance to account for both conductors.  450 feet x 2  = 900 feet.

Step #3:  Now that we know the distance, we need to know what type of conductor we are using for the circuit.  For this example we will use a #12 AWG solid coated copper conductor.  Once this is determined, we will need to consult the Conductor Properties table 8 in the National Electrical Code or NEC 2011 (click the link to view a copy of the table).  This table can also be found in chapter 9 on page 721.   On the table, located the section at the top under coated.  Now follow the line down under ohm/kFT (ohms per 1000 feet).  Keep scrolling down until you reach the 12 AWG with a quantity of 1 since it is solid.  If you line the left and top rows up, you will see a resistance of 2.01 ohms for 1000 feet of conductor.

Step #4:  Since we do not have a distance of 1000 feet for a out circuit, we will need to break down this resistance according to our actual distance of 900 feet.  To do this simply divide 900 feet by 1000 feet sown as 900/1000 = 0.9.  Now multiply your resistance per 1000 feet (2.01) by your distance breakdown of 0.9.  2.01 X 0.9 = 1.809 ohms per 900 feet.

Step #5:  To determine the voltage at the end of the notification appliance circuit we need to use Ohm's Law.  Since we know know the total amps (0.2A) and the total resistance (1.809) we can now find the voltage.  I X R = E or Amps x Resistance = Voltage.  0.2 x 1.809 = 0.3618 volts.

Step #6:  To find the voltage drop subtract your answer found in step #5 (0.3618) from the starting voltage of 24 volts.  24 - 0.3618 = 23.6382 volts.

Step #7:  Sometimes you may be asked to know the voltage drop percentage.  To find this, take the voltage drop (0.3618 volts) divided by 24 volts and multiply it by 100.  This is shown as (0.3618/24) x 100 = 1.5075%

See more examples of voltage drop for NACs here

### Calculating Resistors in Series

If you come across multiple resistors in series with each other, simply add the resistor values. Resistors in Series
Example:
R1 = 3.3k
R2 = 4.7k
R3 = 10k
Total Resistance = 18k

### Calculating Resistors in Parallel

1/Rt = 1/R1 + 1/R2 + 1/R3

R1 = 200
R2 = 400
R3 = 800

1/Rt = 1/200 + 1/400 + 1/800

If there is a common denominator for the bottom numbers use it by multiplying up both the top and bottom numbers in the fraction.

Example: the common denominator is 800.

Resistor R1 has a resistance of 200.  200 goes into 800 4 times.  Therefore R1 = 4/800
Resistor R2 has a resistance of 400.  400 goes into 800 2 times.  Therefore R2 = 2/800
Resistor R2 has a resistance of 800.  800 goes into 800 1 times.  Therefore R3 = 1/800

Now add the top numbers together (4 + 2 + 1 = 7) and place it on top of 800 like this 7/800.  Now take the reciprocal to make the fraction reverse to 800/7.  Divide 800 by 7 to get your answer of  = 114.286k.

#### Battery Calculations

Take the total standby current and multiply by 24 (hours for standby)
Take the total alarm current and multiply by (.083 for 5 minutes or .249 for 15 minutes of alarm)
Add the total of (standby current x 24) to (alarm current x .083 or .249)
Multiply the total of above by a safety factor of 1.2.  This gives you a 20% spare buffer.
Round up to required battery amp hour size.

#### dB Loss and Gain

Every time you double the distance from the audible appliance, you loose 6 dB.

Example:  If you have a speaker with 75dB at 10 feet, you will have 69dB at 20 feet and 63dB at 40 feet and so on at 80 feet, 160 feet......  Please note, these are not multiples of 10 feet!!!  These are broken down by doubling the distance from the last measurement.
Correct: 10 feet - 20 feet - 40 feet - 80 feet - 160 feet
Incorrect:  10 feet - 20 feet - 30 feet - 40 feet - 50 feet - 60 feet

If you double the power output of the appliance, you gain 3dB.

Example:  If you have a speaker tapped at a 1/4 watt with 75dB and you double the wattage to 1/2 watt, you will then have 78dB.

#### dB Line Loss Calculation

TWR = Total Wire Resistance
TWR = Ohms/Foot X (Distance X 2)

12 AWG Ohm/FT is .00193
14 AWG Ohm/FT is .00307
16 AWG Ohm/FT is .00489
18 AWG Ohm/FT is .00777

TLR = (Voltage X Voltage) / Power
20 X Log (1- (TWR / TWR + TLR))

You cannot go over -1.5 dB