# 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 (that's me) 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.

AmpsAmps is a measure of energy flow, measured in electrons moving per second. The amount of Amps represents the amount of charge flowing past a point in a particular time period.

VoltsVolts is a measure of the force of the moving electrons. It's the pressure which causes electrical current to flow. It is also used to describe the amount of energy stored, like a 12 volt battery.

WattsWatts is a measure of power. It describes the amount of energy converted by an electrical circuit.

OhmsOhms is a measure of electrical resistance. It you have a wire with two conductors, like a lamp cord, and connect one conductor to the positive and the other to the negative pole of a 12 volt battery (like jump starting a car), the smaller the wire diameter and the longer length of the wire the greater the Ohms, which causes the Volts delivered to decrease. An increased resistance measured in Ohms causes a reduction in current aka Volts.

The Good Old Garden Hose ExampleGet your garden hose and turn on the water so that it is flowing at the rate of a couple of gallons a minute, so that you could fill up a 5 gallon bucket in 2-3 minutes.

The rate of flow of the water, which is pretty slow, is equivalent to **Amps**. The lower the flow the lower the amps.

The force of the water coming out of the hose is the **Volts**. The lower the force, the lower the volts.

The power (energy) 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, a small amount of Amps can turn into a lot of Watts.

If you link together 2 or 3 or 4 garden hoses without changing the setting on the faucet, what you will see is that the rate of flow goes down because the resistance of the water passing though the hose reduces the flow. This same effect is measured in **Ohms** in electrical circuits.

All of these electrical units of measure are used together to determine the Volts, Amps and Watts for any particular solar electric application. I am not going to talk about Ohms or Ohms Law. Ohms is not important for calculating solar component sizing. Ohms IS important when you start looking at the available Volts and wire sizes and the distances between components like batteries, solar panels, charge controllers and inverters. The lower the Volts and the greater the distance traveled, the bigger the wire that is needed.

Volts x Amps = Watts

This is the starting point for doing the math.

Convert Watts to Amps: Amps = Watts / Volts (slash = divide)12 Watts / 12 Volts = 1 Amp

Convert Amps to Watts: Watts = Amps x Volts1 Amp x 12 Volts = 12 Watts

Convert Watts to Volts: Volts = Watts / Amps120 Watts / 10 Amps = 12 Volts

Convert Volts to Watts: Watts = Amps x Volts12 Amps x 12 Volts = 144 Watts

Energy Measurements Over Time

When you are trying to figure out what size solar panels you need, and how much battery storage, and what size charge controller or inverter you need for any particular solar energy application, the time that the sun shines on your panels, the time between sunny days (cloudy weather), the time that you what to be able to operate whatever you are going to power with your solar energy - everything is about time.

So, watts and amps are measured by time for any given voltage. The voltage of your off grid system is a given based on what you decide - you are going to have a 12 volt system, or a 24 volt system, or a 48 volt system based on the batteries you decide to use.

Watt-Hours Used to measure energy inflow from your solar panel and outflow from the devices you are powering Watt-Hours per day or other time period

Amp-Hours Used to measure energy storage and outflow in batteries and energy inflow from your solar panel.

A Simple Load Analysis

I have two 10 watt 12 volt LED lights I want to operate for 4 hours per night. 10 watts x 2 x 4 hours = 80 watt-hours.

80 watt-hours divided by 12 volts = 6.67 amp hours. Because we can only use half the energy in a lead acid battery without harming the battery, the minimum battery size is 6.67 amps x 2 = 13.34 amp hours.

I want my system to be reliable if we have four consecutive days of cloudy weather, 4 days of autonomy x 13.34 = 53.36 amp hours for the battery. Sun Xtender makes a 56 amp hour AGM battery, PXV-560T.

This installation is in a location that gets 5 hours of full sun (insolation) per day. To recharge the battery for one day of use we need 13.34 amps in 5 hours = 2.67 amps from a 12 volt solar panel. Most load calculations include a discount factor for the inefficiency of recharging the battery. 20 percent is typical. 2.67 / 0.8 = 3.34 amps. We have a 60 watt solar panel that has an Imp (amps maximum power point) of 3.49. Look at the 60 watt panel top of the page.

The 60 watt solar panel has a short circuit amp rating (Isc) of 3.86 amps. 3.86 x 1.25 = 4.83. I can use a 5 amp or larger charge controller with this panel to charge the battery. If I want to make sure I am getting the best efficiency available for charging the battery, I would use a small MPPT charge controller like the Genasun 5 amp for lead acid.

Summary

Solar energy math calculations for system sizing can be done with a simple calculator using the basic formulas shown here.

If you want to see an example already in the website, read my page about CPAP battery backup emergency solar power.

When you calculate your loads, you will quickly see the advantage of using the most energy efficient devices you can find, like our SunDanzer solar refrigerators and freezers for example. High efficiency refrigerators and other appliances like Vari-Cyclone super energy efficient ceiling fans, Pico portable LED lights and other electrical devices used around the house are less expensive than solar electric components. If you can downsize your loads through efficiency, your solar system will be less costly and easier to justify from a return on investment perspective.

Learn more, download the Successful Off Grid System Design Primer. Or, download the Successful Off Grid System Design Primer with Excel Workbook in a ZIP file.

Please contact us today for more information or assistance with your solar applications.