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NEC Calculation Formulas
Terms in this set (29)
Calculating Voltage Drop
1.) EVD = I x R
2.) Refer to Chapter 9, Table 9 for the alternating current resistance and reactance for 600 volt cables. This table provides the ohms to neutral per 1000 feet for various size conductors.
3.) Divide the ohms given by 1000, then multiply that answer by the length of the cable (multiply that by the number of conductors) which gives you the total ohms.
4.) Then multiply the total ohms by the load amperage which will give you the voltage drop. *See page 90 in Mike Holt's work book
Continuous load calculations
Continuous load (3 or more hours) calculations is 125% of the determined load.
Example: 44 amps x 1.25 = 55 amps. This formula is also used when there is a combination of continuous and noncontinuous load.
Also note that when determining the maximum continuous load permitted on a predetermined OCPD, you can multiply the size of the OCPD by 0.80. Example: 20 amps x 0.80 = 16 amps
How to calculate percentages using a calculator
Using a calculator:
1.) Enter the number that you are trying to get a percentage of.
2.) Press the X's (multiplication) button then the percent number you want to calculate.
3.) Finally, press the % button without pressing the = button and the answer will appear.
Ex. To find out what what is 3% of 240 volts: 240x3% will give you an answer of 7.2
*Another way to calculate the answer is: 240 x 0.03 = 7.2
If the percentage number is 2 digit number like 15, then eliminate the zero after the decimal: Ex. 240 x 0.15 = 36
Calculating general lighting and general-use receptacle load. *Typically "Per 220.12(J)" for one-family, two-family, multi-family dwelling units and in guest rooms or guest suites of hotels and motels.
The general lighting load (Volt-Amps or VA) specified must be calculated in Table 220.12 must be calculated from the outside dimensions of the building or area involved. Example: A homes outside dimensions (excluding garage, car ports, and open porches) measuring 50' x 40' gives you a total square footage of 2000 square feet. The table states that the VA for a dwelling unit is 3 VA per square foot. Thus 2000 x 3 = 6000 VA.
220.14(I) Calculating Commercial General-Purpose Receptacle Load.
You must factor 180 VA per mounting strap for each 15 amp or 20 amp, 125 volt general-use receptacle outlet. *The mounting strap of the box or device ring determines the number of devices that can be installed. It doesn't matter if the device has one receptacle or three receptacles, it still counts as 180 VA. However, if there is a single device with four or more receptacles that can be mounted to one mounting strap then each receptacle will count as 90 VA.
*Example: To determine the maximum number of general purpose receptacles for a commercial occupancy on a 15 or 20 amp 125 volt circuit. Find the VA by multiplying the Volts x's Amps which is 120 (nominal voltage) x 20 = 2400 VA. Then divide 2400 x 180 which is 13.
Calculating the maximum number of lights with a predetermined amperage on a predetermined circuit breaker or OCPD.
Example: What is the maximum number of 1.34 amp fluorescent luminaires permitted on a 20 amp circuit if the luminaires operate for more than 3 hours?
Maximum load Permitted = 20 amps x 0.80
Maximum load Permitted = 16 amps
Luminaires on circuit = 16 amps / 1.34 amps
Maximum number of luminaires = 11.94 or 11
Calculating Commercial General-Use Receptacle Load
To calculate the receptacle load for an 18,000 square foot bank with 160, 15 amp, 125 volt receptacles goes as follows: Multiply 160 x 180 VA to get a total of 28,000 VA. *Refer to table 220.44 to make the appropriate adjustments for Demand Factor.
Commercial Show Window and Track lighting loads
1.) Show Windows - The feeder/service VA load must not be less than 200 VA per linear foot.
2,) Track lighting - The feeder/service VA load must not be less than 150 VA for every 2 feet of track lighting or fraction of that length.
Calculating a Fixed Multioutlet Assembly
Fixed multioutlet assemblies used in other than dwelling units or guest rooms or guest suites of hotels or motels shall be calculated in accordance with (H)(1) or (H)(2) of 220.14:
(1) Where appliances are unlikely to be used simultaneously, each 5 foot or fraction thereof of each separate and continuous length shall be considered as one outlet of not less than 180 volt-amperes.
(2) Where appliances are likely to be used simultaneously, each 1 foot or fraction thereof shall be considered as an outlet of not less than 180 volt-amperes.
Motor Load - 220.50
The feeder/service load for motors must be sized no less than 125 percent of the largest motor load, plus the sum of the other motor loads.
Fixed Electric Space Heating Load - 220.51
The feeder/service load for fixed electric space-heating equipment must be calculated at 100 percent of the total connected load.
Calculating Appliance Loads
220.51 through 220.56 - These sections provide demand factor rules, predetermined appliance (heaters, dryers, ranges, etc.) VA loads, grouping rules, etc.
Dwelling Unit-Appliance Load - 220.53
A demand factor of 75 percent can be applied to the total connected load of four or more appliances on the same feeder/service. This demand factor does not apply to electric space-heating equipment, (220.51), electric clothes dryers (220.54), electric ranges (220.55), electric air-conditioning equipment (Article 440, Part IV), or motors (220.50).
5000 Watts = 5000 VA
Kilovolt- Amperes (kVA) = Kilowatts (kW)
Change a fraction to a decimal or whole number
Divide the numerator (top number) by the denominator (the bottom number). Example: To change the fraction 1/6, divided 1 by 6 which is 0.166
Converting Percentages to Decimals
When changing a percent value to a decimal or whole number, drop the percentage symbol and move the decimal two paces to the left. Example: 32.5% = 0.325
When a number needs to be changed by multiplying it by a percentage, the percentage is called a multiplier. The first step is to convert the percentage to a decimal, then multiply the original number by the decimal value. Example: An overcurrent device (circuit breaker or fuse) must be sized no less than 125% of the continuous load. If the load is 80 amps, the overcurrent device will have to be sized no smaller than: Answer - 100 amps
Step-1: Convert 125% to a decimal: 1.25
Step-2: Multiply the value of the 80 amp load by 1.25 = 100 amps
Use the following steps to increase a number by a specific percentage:
Step-1: Convert the percent to a decimal value.
Step-2: Add one to the decimal value to create the multiplier.
Step-3: Multiply the original number by the multiplier found in Step 2.
Example: To increase the whole number 45 by 35%
Step-1: Convert 35% to decimal form: 0.35
Step-2: Add one to the decimal value: 1 + 0.35 = 1.35
Step-3: Multiply 45 by the multiplier 1.35: 45 x 1.35 = 60.75
To Obtain a Reciprocal of a Number
To obtain the reciprocal of a number, convert the number into a fraction with the number one as the numerator (the top number). It's also possible to to calculate the reciprocal of a percentage. Determine the reciprocal of a percentage number by the following steps:
Step-1: Convert the number to a decimal value.
Step-2: Divide the value into the number one.
Example: What's the reciprocal of 80 percent?
Step-1: Convert 80% into a decimal (move the decimal two places to the left). 80% = 0.80
Step-2: Divide 0.80 into the number one. 1 divided by 0.80 = 1.25 or 125%
Squaring a Number
Squaring a number means multiplying the number by itself.
Example: 10² = 10 x 10 = 100 or 23² = 23 x 23 = 529
Computing the "Area" of something
To compute the area of a space, raceway, pizza or anything, use the following formula: Area = π x r² (Pie 3.14 x half of the Radius) Squared. Example: To find the area in square inches of a trade size raceway with an inside diameter of 1.049 inches.
π = 3.14 x (0.50 x 1.049)²
r = radius (equal to 0.50 of the diameter)
Area = 3.14 x (0.50 x 1.049)²
Area = 3.14 x 0.5245²
Area = 3.14 x (0.5245 x 0.5245)
Area = 3.14 x 0.2751
Area = 0.86 Square Inches
Whenever numbers are in parentheses, complete the mathematical function within the parentheses before proceeding with the rest of the problem.
Using the Formula Wheel for 3-phase circuits
Get the square root of 3 (representing 3-phase) which is 1.732 and multiply it by the voltage. Afterwards, use the formula wheel as you normally would.
Example: The current of a 36,000 watt, 208 volt, three phase load is:
1.) Perform the operation inside the parentheses first...determine the product of: 208 volts x 1.732 = 360 volts
2.) Divide 36,000 watt by 360 volts = 100 amps
Volume (cubic inches)
The volume of an enclosure is expressed in cubic inches (cu in.). It's determined by multiplying the length, by the width, by the depth of the enclosure. Example: To determine the volume of a box that has dimensions of 4 x 4 x 1.5 inches.
Answer: 4 x 4 x 1.5 = 24 cubic inches
Memorizing the Formula Wheel
Top = E - P - P - E²
Bottom Left = I - I - I² - P
Bottom Right = R - E - R - R
When setting up the Formula Wheel, remember if you are finding the squared number, you must get the square root of the two given numbers. There are two square root numbers in the wheel, one for finding the voltage and the other for finding the amperage.
Determining Power Losses of Conductors
What's the conductor power loss in watts for a 10 AWG conductor that has a voltage drop of 3 percent in a 240 volt circuit, and carries a current flow of 24 amps?
Step-1: What is the problem asking you to find? What's the wasted "P" (Power)?
Step-2: What do you know about the conductors?
I = 24 amps
E = 240 volts x 3%
E = 240 volts x .03
E = 7.2 volts
Step-3: The formula is P = I x E
Step-4: Calculate the answer: P = 24 amps x 7.2 volts = 172.80 watts. The answer is 172.80 watts
Determining the Cost of Power
What does it cost per year (at 8.60 cents per kWh) for the power loss of two 10 AWG circuit conductors that have a resistance of 0.30 ohms with a current flow of 24 amps?
Step-1: Determine the amount of power consumed:
P = I² x R
P = 24A² x 0.30 ohms
P = 172.80 Watts
Step-2: Convert the answer in Step-1 to kW:
P = 172.80 Watts divided by 1000 Watts
P = 0.1728 kW
Step-3: Divide the cost of 8.60 by 100 (the number of pennies in a dollar) = 0.086
Step-4: Determine the cost per hour:
(0.086 dollars per kWh) x 0.17280 kW = 0.01486 dollars per hour.
Step-5: Determine the dollars per day:
0.01486 dollars per hour x (24 hours per day) = 0.3567 per day.
Step-6: Determine the dollars per year:
0.3567 dollars per day x (365 days per year) = $130.20 per year.
Determining Power Consumed
What is the power consumed by a 9.60 kW heat strip rated 230 volts connected to a 208 volt circuit?
Step-1: What is the problem asking you to find?
The power consumed by the resistance. *First find the resistance using the rated voltage then use resistance determined to calculated the Power.
Step-2: What do you know about the heat strip?
E = 208 connected volts, and R = E² divided by P
R = 230 rated volts squared (per formula) divided by 9,600 watts or 230²/9600
Step-3: P = E²/R
Step-4: The answer is:
P = 208V²/5.51 ohms
P = 7,851 Watts or 7.85 kW
Calculating the Total Resistance in a Parallel Circuit
1.) When all the resistors of a parallel circuit have the same resistance, the total circuit resistance is found by dividing the resistance of one resistive element by the total number of resistors in parallel.
Example: The total resistance of three 10 ohm resistors in parallel is 3.33. because 10 divided by 3 is 3.33
2.) When all the resistors don't have the same resistance, the total resistance can be found using the Reciprocal Method:
RT = 1/[(1/R1) + (1/R2) + (1/R3)....]
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