ELECTRICAL UNIT CONVERSION
This site offers formulas for converting between electrical units. It is dedicated to sharing information, formulas and other documentation to aide in the conversion of given electrical, force or power values into other electrical, force or power values. The formulae below are commonly known and used universally. I use them here in examples to demonstrate the application of conversion formulae. I have done my best to be accurate but I cannot guarantee that all of the following information is correct or appropriate for your purposes.
I welcome any comments or corrections. Thanks to all who have notified me of inaccuracies. This type of participation makes this site more valuable. Please click here for a link to email your comment, correction, suggestion or question.
How to convert Watts to Amps
Basics
You cannot convert watts to amps, since watts are power (ultimately horsepower) and amps are current (or flow if you like) unless you have the added element of voltage to complete the equation. You must have at least least two of the following three: amps, volts and watts, to be able to calculate the missing one. Since watts are amps multiplied by volts, there is a clear relationship between them.
Choose Your Topic Below
Computing Watts
Computing Volt-AMPS
Computing Kilovolt-AMPS
Computing Kilowatts
Converting Between
KW and KVA
Computing kBTUs
Short and sweet formulae:
Go to the Shotgun
Section and browse or select:
Convert Watts to Volts
Convert Watts to AMPS
Convert AMPS to Watts
Convert Horsepower
to AMPS
Convert KVA to AMPS
Convert KW to AMPS
HOW TO FIND AMPS
HOW TO FIND WATTS
HOW TO FIND KILOWATTS
HOW TO FIND KILOVOLT-AMPS
HOW TO FIND HORSEPOWER
A tiny bit of Mechanical and Motors;
Energy Measurement with Joules and Dynes
Definitions of electrical and power terms from University of Wisconsin - Stevens Point web site
Introduction
You may need to convert voltage, amperage and electrical specifications from equipment into KW, KVA and BTU information that can be used to calculate overall power and HVAC requirements. The following section addresses the process of taking basic electrical values and converting them into other types of electrical values.
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The specification nameplates on most pieces of computer, radio or network equipment usually list required electrical power values. These values are usually expressed in volts, AMPS, kilovolt-AMPS (KVA), watts or some combination of all of the above.
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If you are an architect or engineer using equipment nameplate information to compute power and cooling requirements, you will find that the total power and cooling values will exceed the actual run requirements of the equipment. Reason: the nameplate value is designed to ensure that the equipment will start and run safely. Manufacturers build in a "safety factor" (sometimes called an "engineering cushion") when developing nameplate specifications. Some nameplates specify power requirements that are higher than the equipment will ever need. The most common engineering solution is to utilize only 80% of available capacity and therefore your computed results will overstate the power and cooling equipment requirement by a factor close to 20%.
Develop the power and cooling budget using the nameplate specifications inserted into the formulae below and use the resultant documentation as your baseline. Document everything. There will come a day when you will need every amp of power you projected. Power budgets are notoriously consumed in a much shorter time than predicted. Don't forget to add a "future factor" to your power and cooling budget. Power supplies double in power draw and produced heat every two to three years. If you don't include these factors in your budgets, you will consume a 10 year power and cooling budget in three years (this happened to me, I know this is true).
Three Phase Power
You will notice that all of the equations that refer to three phase power contain the value 1.73 in the formula somewhere. The value 1.73 is the square root of 3. Intuitively, you can see how this value is applied in the formulae. (3 phases therefore 1 phase = square root of 3)
Computing Watts When Volts and AMPS are Known
POWER (WATTS) = VOLTS x AMPS
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For example, a small computer has a nameplate that shows 2.5 amps. Given a normal 120 Volt, 60 Hz power source and the ampere reading from equipment, make the following calculation:
POWER (WATTS) = 2.5AMPS x 120VOLTS = 300 WATTS
Generally: P=IE
P= Power(WATTS) I = Current(AMPS) and E = Voltage(VOLTS).
So: I = P/E and E =
P/I therefore: 1 watt = 1 ampere x 1 volt
Click here to see my Ohm's Law Pie Chart for complete relationships between power, current and voltage.
Computing Volt-AMPS (VA)
Same as above. VOLT-AMPS (VA) = VOLTS x AMPS = 300 VA
Computing kilovolt-AMPS (KVA)
KVA stands for "Thousand Volt-Amps".
A 2-Pole Single Phase 208-240 power source requires 2 hot wires from 2 different circuits (referred to as poles) from a power distribution panel.
SINGLE PHASE
KILOVOLT-AMPS (KVA)
= VOLTS x AMPS / 1000
Using the previous example: 120
x 2.5 = 300 VA 300 VA
/ 1000 = .3 KVA
208-240 SINGLE-PHASE (2-POLE SINGLE-PHASE)
-
Example: An enterprise server with a 4.7 amp rating and requiring a 208-240 power source. Use 220 volts for our calculations.
KILOVOLT-AMPS
(KVA) = VOLTS x AMPS /1000
220 x 4.7 = 1034
1034 / 1000 = 1.034 KVA
THREE-PHASE
-
Example: A large disk storage system loaded with disks. The equipment documentation shows a requirement for a 50-amp 208-240 VAC power source. Do not calculate any value for the plug or receptacle. Use 220 volts for the calculation.
KILOVOLT-AMPS (KVA) = VOLTS
x AMPS x 1.73 / 1000
220 x 50 x 1.73 = 19,030
19,030 / 1000 = 19.030 KVA This
would be rounded to 19 KVA
Computing Kilowatts
-
Finding Kilowatts requires using a power factor in the computation. The power factor is a number that adjusts the power calculation to reflect the efficiency of the use of the electricity supplied to the system. This factor can vary widely (usually from 60% to 95%) and is never published on the equipment nameplate and is not often supplied with product information. For purposes of these calculations, we use a power factor of .85. This random number places a slight inaccuracy into the numbers. Its OK and it gets us very close for the work we need to do. Most UPS equipment will claim a power factor of 1.00. It is common for the power factor to be considered 1.0 for devices less than 3 years old.
SINGLE PHASE
- Example: We have a medium-sized Intel server that draws 6.0 amps and the power supply has a power factor of .85.
KILOWATT (KW)
= VOLTS x AMPS x POWER FACTOR / 1000
120 x 6.0 = 720 VA
720 VA x .85 = 612 612 / 1000
= .612 KW
208-240 SINGLE-PHASE (2-POLE SINGLE-PHASE)
-
Example: An enterprise server with a 4.7 amp rating and requiring a 208-240 power source. I'll use 220 volts and a power factor of .85 for our example calculations.
KILOWATT (KW)
= VOLTS x AMPS x POWER FACTOR x 2 / 1000
220 x 4.7 x 2 = 2068
2068 x .85 = 1757.8 1757.8
/ 1000 = 1.76 KW
THREE-PHASE
-
Example: A large storage system loaded with disks. The equipment documentation shows a requirement for a 50-amp 208 VAC Power source. Do not calculate any value for the plug or receptacle. Use 220 volts for the calculation.
KILOWATT (KW) =
VOLTS x AMPS x POWER FACTOR
x 1.73
1000
220 x 50 x .85 x 1.73 = 16,175.50 16,175.50/1000 = 16.175 KW
To Convert Between KW and KVA
-
The only difference between KW and KVA is the power factor. Once again, the power factor, unless ascertained from the manufacturer, is an approximation. For this example, we use a power factor of .85. The KVA value is always higher than the value for KW.
KW to KVA
KW / .85 = SAME VALUE EXPRESSED IN KVA
KVA TO KW
KVA x .85 = SAME VALUE EXPRESSED IN KW
Computing BTUs
-
Known Standard: 1 KW = 3413 BTUs (or 3.413 KBTUs)
-
If you divide the electrical nameplate BTU value by 3413 you may not get the published KW value. If the BTU information is provided by the manufacturer, use it, otherwise use the above formula.
Shotgun Section
Here are conversions, short and sweet:
-
To convert Watts to Volts when amps are known:
Voltage = Watts / AMPS
E = P / I
-
To convert Watts to AMPS when volts are known:
AMPS = Watts / Voltage
I = P / E
For 3 Phase power divide by 1.73 -
To convert AMPS to Watts when volts are known:
Watts = Voltage x Amps
P = E x I
For 3 Phase power multiply by 1.73
-
To convert Horsepower to AMPS:
HORSEPOWER= (E x I x EFF) / 746
EFFICIENCY= (746 x HP) / (V x A)
Multiply Horsepower by 746w (1 HP = 746 Watts)
Find Circuit Voltage and Phase
Example:
40 HP at 480 (3 Phase) 746 multiplied by 40 = 29,840
29,840 divided by 480 (3 Phase) = 62.2
62.2 divided by 1.73 = 35.95AMPS -
To convert KVA to AMPS:
Multiply KVA by 1000/voltage [ (KVA x 1000) / E ]
For 3 Phase power divide by 1.73 [ (KVA x 1000) / E x 1.73 ] -
To convert KW to AMPS:
Multiply KW by 1000/voltage and then by power factor [ (KW x 1000) / E x PF ]
for 3 Phase power divide by 1.73 [ ( KW x 1000) / E x PF x 1.73 ]
Basic Horsepower Calculations
Horsepower is work done per unit of time. One HP equals 33,000 ft-lb of work per minute. When work is done by a source of torque (T) to produce (M) rotations about an axis, the work done is:
radius x 2
x rpm x lb. or 2
TM
When rotation is at the rate N rpm, the HP delivered is:
HP = radius x
2
x rpm x lb. / 33,000 = TN / 5,250
For vertical or hoisting motion:
HP = W x S / 33,000 x E
Where:
W = total weight in lbs. to be raised by motor
S = hoisting speed in feet per minute
E = overall mechanical efficiency of hoist and gearing.
For purposes of estimating
E = .65 for eff. of hoist and "connected gear.
Energy measurement with Joules and Dynes
Energy is measured in joules (watt-seconds) or kilowatt-hours. A power level of one watt that continues for one second equals one joule. The integrated energy from a 100-watt light that runs for 60 seconds equals 6000 joules.
4.18 joules equal 1 calorie, which is enough energy to raise the temperature of one gram of water by one degree Celsius (or Centigrade).
When it comes to energy density (watts per liter or watts per kilogram) it is difficult to beat gasoline. A lead-acid battery is good for about 125 thousand joules per kilogram. Lithium batteries can provide as much as 1.5 million joules per kilogram. Gasoline tends to run about 45 million joules per kilogram.
Joules:
1 joule is exactly 107 ergs.
1 joule is approximately equal to:
- 6.2415 x 1018 eV (electron volts)
- 0.2390 cal (calorie) (small calories, lower case c)
- 2.3901 x 10−4 kilocalorie, Calories (food energy, upper case C)
- 9.4782 x 10−4 BTU (British thermal unit)
- 0.7376 ft-lb (foot-pound force)2.7778 x 10−7 kilowatt hour
- 2.7778 x 10−4 watt hour
Units defined in terms of the joule include:
- 1 thermo chemical calorie = 4.184 J
- 1 International Table calorie = 4.1868 J
- 1 watt hour = 3600 J
- 1 kilowatt hour = 3.6 x 106 J (or 3.6 MJ)
- 1 ton TNT = 4.184 GJ
Useful to remember:
- 1 joule = 1 Newton meter = 1 watt second
Dynes:
In physics, the dyne (symbol "dyn", from Greek δύναμις (dynamis) meaning power, force) is a unit of force specified in the centimeter-gram-second (CGS) system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 micronewtons. Equivalently, the dyne is defined as "the force required to accelerate a mass of one gram at a rate of one centimeter per second squared":
1 dyn = 1 g x cm/s2 = 10 - 5 kg x m/s2 = 10 µN
The dyne per centimeter is the unit usually associated with measuring surface tension. For example, the surface tension of distilled water is 72 dyn/cm at 25°C (77°F).
| newton (SI unit) |
dyne | kilogram-force, kilopond |
pound-force | poundal | |
|---|---|---|---|---|---|
| 1 N | = 1 kg x m/s2 | = 105 dyn | ≈ 0.10197 kp | ≈ 0.22481 lbf | ≈ 7.2330 pdl |
| 1 dyn | = 10-5 N | = 1 g x cm/s2 | ≈ 1.0197 x 10-6 kp | ≈ 2.2481 x 10-6 lbf | ≈ 7.2330 x 10-5 pdl |
| 1 kp | = 9.80665 N | = 980665 dyn | = gn x (1 kg) | ≈ 2.2046 lbf | ≈ 70.932 pdl |
| 1 lbf | ≈ 4.448222 N | ≈ 444822 dyn | ≈ 0.45359 kp | = gn x (1 lb) | ≈ 32.174 pdl |
| 1 pdl | ≈ 0.138255 N | ≈ 13825 dyn | ≈ 0.014098 kp | ≈ 0.031081 lbf | = 1 lb x ft/s2 |
| The value of gn as used in the official definition of the kilogram-force is used here for all gravitational units. | |||||
Mechanical
General Approximations - RULES OF THUMB
Use these in the field
for fast approximations:
At 3600 rpm, a motor develops a 1.5 lb-ft of torque per
HP at rated HP output
At 1800 rpm, a motor develops a 3 lb-ft of torque per HP
at rated HP output
At 1200 rpm, a motor develops a 4.5 lb-ft of torque per
HP at rated HP output
At 900 rpm, a motor develops a 6 lb-ft of torque per HP
at rated HP output
At 575 volts, a 3-phase motor draws 1 AMP per HP at rated
HP output
At 460 volts, a 3-phase motor draws 1.25 AMP per HP at rated
HP output
At 230 volts a 3-phase motor draws 2.5 AMP per HP at rated
HP output
At 230 volts, a single-phase motor draws 5 AMP per HP at
rated HP output
At 115 volts, a single-phase motor draws 10 AMP per HP at
rated HP output
Definitions:
These are from The University of Wisconsin - Stevens Point web site at http://www.uwsp.edu/cnr/wcee/keep/Mod1/Unitall/definitions.htm- Ampere - (abbrev. Amp; pl. AMPS [Amps]) A unit of electric current. One ampere of current is equal to one coulomb (6.25 x 1,018) of electrons passing a point in an electric circuit in one second. See Electric current.
- Battery - A device that converts chemical energy into electrical energy, producing an electric current when connected in a circuit.
- British thermal unit - (abbrev. Btu) 1. A unit of energy equal to 1,055 joules or 252 calories. 2. The amount of energy needed to raise the temperature of one pound of water one degree Fahrenheit. 3. The approximate amount of potential energy in one match tip.
- Calorie - (abbrev. cal; pl. calories; also small calorie) 1. A unit of energy content of food. One calorie equals 4.187 joules or 0.003969 Btu. 2. The amount of energy needed to raise the temperature of one gram of water one degree Celsius.
- CCF - One hundred cubic feet of water or natural gas. One CCF of natural gas is about equal to one therm.
- Conduction - 1. Heat transfer from particle to particle, occurring most effectively in solids. 2. Transfer of electrical energy through a material via the flow of charged particles, usually electrons.
- Electrical circuit - A closed, conducting path or route through which an electric current travels.
- Electrical (electromagnetic) energy - Kinetic and potential energy associated with electric charges (e.g., electrons) and their movement. See Electrical potential energy.
- Electrical potential energy - Energy stored by separating positive and negative electrical charges against electrical forces. A charged battery has electrical potential energy. See Electrical (Electromagnetic) energy.
- Electric current - A flow of electrically charged particles such as electrons with a conductor or a circuit. See Conduction, Electricity.
- Electricity - 1. The behavior of negative and positive charges (electrons and protons) due to their attraction and repulsion. 2. The flow of electrons; electric current. See Electrical (Electromagnetic) energy, Electric current.
- Electron - 1. A subatomic particle with a negative electric charge that orbits the nucleus of an atom. 2. The basic particle that makes up an electric current.
- Energy - 1. The ability to organize or change matter. 2. The ability to do work. See British thermal unit, Calorie, Joule, and Kilowatt-hour for units of energy. One unit can be converted to another.
- First law of thermodynamics - Energy cannot be created or destroyed; it can only be converted from one form to another. For example, the potential chemical energy in coal can be converted in thermal energy.
- Heat - The transfer of energy from one object at a higher temperature to another object at a lower temperature. Heat can be transferred by conduction, convection, or radiation. Although technically incorrect, the word heat is often used to mean "thermal energy." See Thermal energy.
- Horsepower (abbrev. hp) - A unit of power. One horsepower equals 550 foot-pounds per second of 746 watts. See Power.
- Joule - A unit of energy. One joule equals 0.2388 calories or 0.0009481 Btu.
- Kilocalorie - (abbrev. Cal, kcal; also Calorie [written with a capital C], Food Calorie, Large calorie) 1. A unit of energy equal to 1,000 calories, 4,187 joules, or 3.969 Btu. 2.The amount of energy needed to raise the temperature of one kilogram of water one degree Celsius. See Calorie, Food calorie.
- Kilowatt - (abbrev. KW; pl. Kilowatts) - A unit of power equal to 1,000 watts. See Watt.
- Kilowatt-hour (abbrev. KWh; pl. Kilowatt-hours) - 1. A unit of energy equal to 3,413 Btu or 3,600,000 joules. 2. An amount of energy that results from the steady production or consumption of one kilowatt of power for a period of one hour.
- Kinetic energy - The energy possessed by a moving object. The formula for kinetic energy is 1/2 (mass) x (velocity)2.
- Leaking electricity - The energy used by an appliance when the appliance is in its lowest power mode (typically when the appliance is off). A variety of appliances, especially those with remote control devices, consume electricity even after they are turned off. Other appliances, including those with built-in clocks, never stop using electricity.
- Photovoltaic cell - A device that converts solar energy directly into electricity. For example, photovoltaic cells provide electricity for handheld calculators, watches, battery chargers, homes, and satellites.
- Photovoltaics - Of, or related to, the use of photovoltaic (solar) cells for producing electricity. See Photovoltaic cell.
- Potential energy - The energy in matter due to its position or the arrangement of its parts. Forms of potential energy include chemical, elastic, electrical (electromagnetic), gravitational, nuclear, and thermal energy. Potential energy is often referred to as "stored" energy. Some scientists and energy educators avoid the word stored because it might lead to the misunderstanding that energy is a substance. Click here to see further information about this and other possible energy misconceptions.
- Power - 1. The rate at which energy is transferred or converted per unit of time. 2. The rate in which work is done. See Horsepower, Kilowatt, Megawatt, Watts for units of power.
- Resistance - The opposition of electric current by a material or electrical device. Electrical energy is converted into thermal and other forms of energy when work is done by a current to overcome a resistance.
- Second Law of Thermodynamics - 1. Each time energy is converted from one form to another, some of the energy is always degraded to a lower-quality, more dispersed, less useful form. 2. No system can convert energy from one form to another useful for with 100 percent efficiency. 3. Energy cannot be spontaneously transferred from a cold body to a hot body. 4. The entropy of a system increases over time.
- Solar cell - See Photovoltaic cell.
- Solar energy - Energy transferred from the sun to Earth in the form of electromagnetic radiation.
- Sound - Mechanical energy vibrations transmitted as waves through a solid, liquid, or a gas that can be detected by the human ear.
- Sound energy - See Sound.
- Standby energy - See Leaking electricity.
- Stored energy - See Potential energy.
- Switch - A device used to open or close an electric circuit or to divert electric current from one part of a circuit to another.
- System - 1. A group of interacting, interrelated, or interdependent parts made up of matter and energy that form a complex whole. 2. Anything that uses matter and energy to organize, maintain, or change itself (e.g., the sun, a glass of water, a frog, a city).
- Temperature - The level or degree of thermal energy in a substance, an object, or the surrounding environment as measured on a standard scale. In other words, temperature refers to whether something is hot or cold. It is the measurement of how fast the molecules are moving back and forth.
- Therm - (pl. Therms) A unit describing the energy contained in natural gas. One therm equals 100,000 Btu. See Btu.
- Thermal energy - The total internal kinetic and potential energy of an object due to the random motion of its atoms and molecules. An object that feels hot has more thermal energy inside it than it does after it has cooled down. Although technically incorrect, the word "heat" is often used to mean thermal energy. See Heat.
- Volt - (abbrev. V; pl. Volts) A unit of voltage (potential difference). One volt is equal to performing one joule of work to move or separate one coulomb (6.25 x 1,018) of electrons.
- Watt - (abbrev. W; pl. Watts) - A unit of power. One watt equals the production or use of one joule of energy per second. See Joule, Kilowatt, Megawatt, Power.
- Work - The transfer of energy from one object or system to another by applying a force over a distance. The formula for work is (force) x (distance).
