Solar Calculations Math Tutorial for Solar Energy Power Systems

Electricity can be a mystery to folks who have never had any experience working with it, or for folks who took physics in high school and can't remember much of anything other than that the battery made the light bulb glow.

Basic electric calculations for off grid solar applications are not that hard, but you have to know the terminology.  Here it is.  Don't quit now, it's really pretty easy, but you have to learn the vocabulary for it to make sense.  Electricity can be visualized very easily using a water analogy, or in some cases, horsepower, gas tank size and miles per gallon might be a better way to conceptualize electricity.

Electrical Current (Flow)

Current is a measure of electron flow, measured in electrons (charge) moving per second.  The unit of measurement is Amperes or 'Amps', named after André-Marie Ampère.  The amount of Amps represents the amount of charge flowing past a point in a particular time period.

When dealing with solar panels or batteries, connecting them in parallel will increase the available current.

Water Flow

The amount of flow of water in a garden hose is a good analogy to current flow.  A common measurement unit of water flow is gallons per minute or gpm or g/m.  SI units would be liters per minute, lpm or l/m.  A flow rate of 5 gpm would fill a 5 gallon bucket in 1 minute.  A flow rate of 1 gpm would fill a 5 gallon bucket in 5 minutes.

Electrical Voltage (Pressure)

Voltage is the measure of the force of the moving electrons.  The unit of measurement is Volts named after Alessandro Volta.  It's the pressure which causes electrical current to flow.  The amount of Volts represents the amount of pressure available to push the electrons thru the wire and load.

When dealing with solar panels or batteries, connecting them together in series will increase the voltage (pressure).  Three solar panels of 32V each connected in series creates 96V of pressure at the terminals.  In storage systems, connecting 2-12V batteries in series makes 24V and 4-12V batteries in series makes 48V.

Water Pressure

The amount of water pressure feeding a garden hose is a good analogy to voltage.  A common measurement unit of water pressure is pounds per square inch, PSI.  SI units would be Pascals or Newtons/ square meter (Pa or N/m2).  Imagine using your thumb to plug the end of the garden hose completely.  It's very easy to do when the water pressure is 5-10psi, but if you try to do it with 50-80psi, the standard city water pressure, it is much harder than it seems like it would be.  Even if you try to turn down the hose faucet valve to minimal flow, sooner or later the pressure will build up to 80 psi and you will not be able to keep your thumb over the end of the hose.  That's pressure.

Power (rate of energy production/use)

Watts is a measure of power, describing the amount of energy converted by an electrical circuit.  When generating power with an electrical generator such as a solar panel, we take the Volts x Amps and get Watts produced.  When consuming power such as with a light or water pump, we take the Volts x Amps and get Watts consumed.  Watts is measured at a specific point in time, so for instance, a 300W solar panel will produce 300W at any given point in time when in full sunlight.  If you accumulate that 300W over the time of an hour you will have generated 300 Watt-hours of energy.  This is the measure of total energy storage like in the size of your battery system.

When configuring a solar system adding panels will increase the available power by the panel power no matter how the panels are configured.  The sample to the right shows a 3S2P or 3 Series (panels), 2 Parallel (strings) to make the array.

Note that a solar array rated for 900W of power, i.e. 96V @ 9.4 A, is only the potential power availability.  The solar array will only produce as much power as is consumed at any given point in time.


The power of the water coming out of the hose is Watts.  Put your thumb over the end of the hose and see how far you can squirt.  The harder you squeeze the farther you can squirt?  The water flow is still a couple of gallons per minute.  In the same way, if you increase the Volts (pressure), a small amount of Amps (flow) can turn into a lot of Watts.

Horsepower and Watts are a measure of the same thing and the units can be converted where 1HP = 746Watts.  One way to visualize this is that a strong person can push a car over a flat street, but not very fast.  A strong athlete is able to produce about 0.3hp, whereas your car engine would be in the range of 100hp.  You can see both a person and the car engine can both move the car 1 block, but one of them is much faster.

Note that an engine rated for 100HP of power is only the potential power availability.  The engine will only produce as much power as is needed at any given point in time, such as accelerating or towing a trailer.

Energy (ability to do work)

While it is very easy to confuse power and energy, and often times the 2 words are used interchangeably, they are not the same thing.  Battery capacity is a measure of the total energy needed to charge the batteries, or the total energy available when they are fully charged.  If the total battery capacity is 1800Wh (Watt-hours), then, in theory, you can use an 1800W (~2.5hp) motor for 1 hour before the battery is drained.  By the same token, you could use a smaller 100W motor for 18 hours.  They both will use the same amount of energy, i.e. 1800 x 1 = 100 x 18, but will use it at different rates (power).

Similar to the power example above, for the purposes of energy storage, it does not matter how the batteries are configured.  Four 12V batteries rated for 1800Wh each will give a total of 6000Wh of energy storage whether they are all connected in parallel, all connected in series, or a combination of both.

Similar to solar panels, batteries can be configured in strings and parallel strings.

  • Four 12V, 100A batteries in series is called a 4S or 4S1P configuration
    • the total voltage is 4 x 12V = 48V.
    • the total available current is 1 x 100A = 100A.
    • the total available power is 48V x 100A = 4800W.
  • Four 12V, 100A batteries in parallel is called a 4P or 1S4P configuration
    • the total voltage is 1 x 12V = 12V.
    • the total available current is 4 x 100A = 400A.
    • the total available power is 12V x 400A = 4800W.
  • Four 12V, 100A batteries in series/parallel is called a 2S2P configuration
    • the total voltage is 2 x 12V = 24V.
    • the total available current is 2 x 100A = 200A.
    • the total available power is 24V x 200A = 4800W.


Gas tank size

A very easy way to visualize the amount of energy storage is by the size of a gas tank.  You can imagine that driving on the freeway you would be able to go a certain distance on a 10 gallon tank of gas.  If you had 20 gallons of gas, you would be able to go 2 times further before a refill.

In a similar fashion, with the same 10 gallons of gas you would be able to go much further with a motorcycle than a muscle car.  The 40hp motorcycle engine uses the gas as a slower rate than a 400hp muscle car engine.

Advanced Terms and Concepts


The electrical resistance to flow is measured in Ohms, named after Georg Ohm, written with the symbol Ω.  Electrical resistance has the effect of pushing in the opposite direction as the voltage (pressure), therefore decreasing the flow.  It is conceivable that the resistance could be so high that the flow can be reduced to near zero.  Very closely related to wire resistance is ampacity described below.  Ohms is related to pressure and flow with the following equation:

1Ω = 1V/1A.


Backpressure (Resistance)

When determining how much resistance there is to flow, for instance the depth of water in a well, the backpressure or height the water has to be lifted is called head pressure.  The pressure of the pump in psi must be greater than the backpressure of the water column in the pipe.  As an example, if your water depth was 231 feet down and your pump was 10 feet below the water level, the total head pressure pushing against the pump would be 231 feet or 100psi (2.31feet of head {of water} = 1psi).  That means if your pump can produce just 100psi you would never be able to get any water out of the well because the water is pushing on the pump just as hard as the pump is pushing on the water.  The pump must be sized to produce more than 100psi just to overcome the water column backpressure and more if there is a pressure tank or a tall tank.

Flow and Pressure Rating

The current carrying capacity of a wire is called its ampacity.  Because resistance in wires is dissipated as heat, you would want as large of wires as practicable.  If too much current flows in a wire, the heat cannot be dissipated into the air fast enough and the wire gets hot.  When it gets hot the insulation starts to melt, and if 2 different wires touch they can create a spark and start a fire.

The voltage rating of a wire is similar to the pressure rating of a hydraulic hose.  The type of insulation on a wire is directly related to its voltage rating.  Car jumper cables, even though they have a large ampacity, do not need to have a high voltage rating because the vast majority of vehicles use a 12V starting battery.  Photovoltaic (PV) wire has a much thicker and tougher insulation with a higher voltage rating because even residential solar systems can reach 300, 600 or 1000V.  The thicker and tougher insulation prevents sparking thru the insulation, has good abrasion resistance and very good UV sunlight resistance.

Flow and Pressure Rating

Water and hydraulic hoses also have flow and pressure ratings.  You likely won't find the pressure rating on a garden hose because city water pressure is relatively low at around 50-80 psi.  When working with hydraulic hoses where greater pressure (PSI) is present, it becomes very important to use the properly rated hose.  A garden hose will not last very long as a replacement hose for the hydraulic cylinder on a backhoe bucket because these pressures can reach 2000psi or much higher on newer equipment.  And you can easily see that the diameter of the hose will allow more fluid to flow, similar to ampacity of a wire.

Solar Calculations Math

All of these electrical units of measure are used together to determine the Volts, Amps, Watts and Watt-hours for any particular solar electric application. 

There are a lot of other nuances to consider when sizing equipment for a specific application.  The trade off include cost vs. desired outcome, available rooftop or battery storage physical limitations, wire sizing and electrical efficiencies, seasonal or climate tendencies that may affect solar power generation, or even product availability.


Getting the most out of your panel

The IV (pronounced eye-vee, as in the symbols of units of measurement for current and voltage) curve of a panel describes the practical current output at a given voltage.  Ideally, a power source would be able to supply infinite current at any given voltage, but practical power supplies, including solar panels, have limits.

For solar panels, the IV curve is used to determine at which current and voltage level the most power is produced by the panel.  Since power is determined by the voltage times the current, the maximum power would be the area under the IV curve that has the maximum area.  The blue line represents the area of that curve and the top of the blue line would be the greatest power production.  

MPPTs or Maximum Point Power Trackers use complex electronics in the form of a DC to DC converter with input and output measurements to try to maximize the input loading of the tracker to cause the maximum power point of the solar panel to be achieved.  It should be noted that the power point of a panel can change rapidly due to fluctuating cloud conditions, temperature, precipitation, tree shading etc.  Good MPPT converters take hundreds or thousands of measurements per second in an attempt to compensate for this.

On the vast majority of panels, the Voc (Open Circuit Voltage), Isc (Short Circuit Current), Vmp and Imp (Voltage and Current at Maximum Power) are specified.  The differences between panels with regard to these parameters is one reason why it is important to use the same model number of panel when building strings and arrays.  Dissimilar parameters would make it difficult for the MPPT to make the adjustments necessary to track maximum power.  If adding on to your array, it is important to try to match the parameters between panels as closely as possible if the same model number of panel is not available.

Peak Solar Hours

A peak sun hour is defined as one hour in which the intensity of solar irradiance (sunlight) reaches an average of 1,000 watts (W) of energy per square meter (roughly 10.5 square feet).

Another way to look at it is that a peak sun hour is the equivalent of 1000 W/m² of sunlight for an hour.

A peak sun hour represents the amount of sunlight for which most solar panels are rated at their output, that is, a 300W panel is specified to produce 300W when the amount of solar irradiation hitting the earths surface is 1000W/m^2.  Solar panels are only likely to receive around that much sunlight when facing directly towards the sun when the sun is at its strongest, at midday. 

High Quality Chart

Solar Hours/Day

If there are a number of peak sun hours per day, what's the terms solar hours/day used for?

The answer is that there is at least one other factor that is a major contributor to how much power your panels can actually produce.  This factor is the angle at which the sun hits the solar panel.  For the nerdiest of you, the equivalent ratio is the cosine of the angles, along each edge of the panel, normal to a plane on the surface of the earth.  In visual terms, it is the ratio of the size of the shadow being cast by the solar panel when a piece of cardboard is placed behind the panel and the cardboard is oriented perfectly perpendicular to the sun.

In the illustration with the solar panels at different angles, one can see the difference in the size of the shadow cast.  Now imagine that the angle of the panels is fixed, but the sun moves to change the angle, along with a piece of cardboard behind the panel that is always facing the sun.  The same shape of shadow will be cast.  The smaller the shadow, the smaller the effective area that is being hit with sunlight, and hence a reduction in power output.

The table below gives you a rough idea of what this boils down to.



Equivalent Solar Hours/Day
Alabama  3.5 – 4
Alaska  2 – 3
Arizona 7 – 8
Arkansas  3.5 – 4
California 5 - 7.5
Colorado  5 – 6.5
Connecticut  3
Florida  4
Georgia  4 – 4.5
Idaho  4 – 4.5
Illinois 3 – 4
Indiana  2.5 – 4
Iowa  4
Kansas 4 – 5.5
Kentucky  3 – 4
Louisiana  4 – 4.5
Maine  3 – 3.5
Maryland  3 – 4
Massachusetts  3
Michigan  2.5 – 3.5
Minnesota 4
Mississippi  4 – 4.5
Missouri  4 – 4.5
Montana  4 – 5
Nebraska  4.5 – 5
Nevada  6 – 7.5
New Hampshire  3 – 3.5
New Jersey  3.5 – 4
New Mexico 6 – 7
New York  3 – 3.5
North Carolina  4 – 4.5
North Dakota  4 – 4.5
Ohio  2.5 – 3.5
Oklahoma  4.5 – 5.5
Oregon  3 – 5
Pennsylvania  3
Rhode Island  3.5
South Carolina 4 – 4.5
South Dakota  4.5 – 5
Tennessee  4
Texas  4.5 – 6
Utah  6 – 7
Vermont  3 – 3.5
Virginia 3.5 – 4
Washington  2.5 – 5
West Virginia 3
Wisconsin  3.5
Wyoming  5.5 – 6
High Quality Chart

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