Voltage Loss Formulas:
Voltage loss in a wire is synonymous to pressure loss in a pipe.
Electric current flows in a wire, just like water in a pipe, and creates a loss. The loss
is a function of:
 The diameter of the wire  The smaller the diameter, the larger the loss.
 The length of the wire  The longer the wire, the larger the loss.
 The type of metal used in the wire  The higher the resistance, the
larger the loss. Copper and Aluminum wires are the most common types, with copper having
the lower resistance.
Voltage Loss is calculated using "OHM'S LAW", as
follows:


E = IR 

Where: 

E
is the Voltage Loss, in volts 



I
is the current flowing through the wire,
in amperes 



R
is the resistance of the wire, in ohms 

For singlephase circuits, the
formula for Voltage Loss is:
Voltage Loss = Amps X Wire Resistance per
1,000 feet X Distance in thousands of feet X 2 Wires
For threephase circuits, the
formula for Voltage Loss is:
Voltage Loss = .866 X Amps X Wire
Resistance per 1,000 feet X Distance in thousands of feet X 2 Wires
Example:
A controller in a city park will be installed 4,200 feet away (this is
the total trench length) from the 115 VAC power source. What is the voltage loss using 14
AWG wire? Is this size wire large enough?
1. 
From the catalog of the controller manufacturer we find that the
controller will consume 0.25 amperes when two valves are activated. 
2. 
From the chart below, the resistance for 14 AWG wire is 2.525
ohms/thousand feet. 


COPPER
WIRE RESISTANCE (OHMS PER 1000' OF WIRE) 
WIRE
GAUGE (AWG) 
18 
16 
14 
14/12 
14/10 
12 
10 
8 
6 
4 
2 
1/0 
2/0 
6.385 
4.016 
2.525 
2.057 
1.762 
1.588 
.999 
.628 
.395 
.249 
.156 
.098 
.078 


3. 
From the formula for singlephase circuits: 

Voltage Loss = Amps X Wire Resistance per 1,000 feet X Distance in
thousands of feet X 2 Wires 

Voltage Loss = 0.25 amps X 2.525 ohms/MFT X 4.2 MFT X 2 Wires 

Voltage Loss = 5.3025 or approximately 5.3 volts 
4. 
To determine if this is acceptable, we subtract the 5.3 volt loss form
the 115 VAC at the source. The voltage at the controller is 115  5.3 = 109.7 volts.
This is within the controller manufacturer's requirements of 105  120 volts,
and is therefore acceptable. 
The same formula can be used to try other sizes of wire.
If you need help, please check with your closest
Paige
Electric representative.