How to Calculate Solar Insolation

••• fhm/Moment/GettyImages

Stepping outside and letting the sunlight fall onto your face is a good feeling. Figuring out how much sunlight it actually is means calculating something called the ​solar insolation​. The solar insolation also give you a way of determining physical weathering in dry regions like deserts.

Solar Insolation Calculation

Solar insolation​ is the amount of solar radiation over the size of a surface area over time. The photovoltaic generators which create electrical energy from incoming sunlight measure insolation as ​average irradiance​ in kilowatt per square meter (kW/m2).

Sometimes another variation that uses a time component is used, kilowatt-hours over kilowatt-peak-year kWh/(kWp*year). This means you can create a solar irradiance formula by measuring the ​power of sunlight over a specific area through a certain amount of time​.

Scientists also use the term ​flux​ to refer to solar radiation per unit of horizontal area over a certain region. This is similar to magnetic flux, the amount of magnetic field passing through a two-dimensional surface are, but, in this case, flux of solar insolation may also vary depending on how far away the Earth is.

You can measure the flux density at the tip of the atmosphere by


for ​FO​ solar flux density at the highest point of the atmosphere and solar zenith angle ​θ0​, the angle between your zenith and the center of the Sun's disc. Your zenith is the line going straight vertically into the atmosphere when you're standing somewhere on Earth.

Solar insolation can also be measured as the f​lux divided by a horizontal surface area​. These quantities also hold use in calculating the rate at which energy from the sun reaches the Earth's surface. The solar irradiance formula has shown scientists that the solar irradiance at the highest point of the atmosphere changes by about 7% throughout the year from 1.412 kW/m2 in January to 1.321 kW/m2 in July, because of how the Earth moves closer and farther away from the sun.

Air Mass in Solar Insolation

You can also determine the direct component of solar radiation by the formula ​1.353 x .7M​ for air mass factor ​M​ which is ​(1/cosθ​​0​​).678​ for zenith angle ​θ0.​ The ​air mass​ is the proportion of how much of the atmosphere the sunlight has to travel at the single moment and how much atmosphere the sunlight would have to pass through if the sun was directly overheard.

This means, if the sun were directly above your head, the air mass would be 1 as the two values of the proportion would be equal. When the sun is very high in the sky, the value for cos ​θ​​0​ is relatively small and negligible.

The ​direct​ part of solar radiation is how much radiation comes directly from the sun​. Diffused radiation​ is how much the sky and atmosphere diffuse the radiation. ​Reflected radiation​ is the amount reflected back by bodies of water on Earth.

Other Solar Insolation Calculation Methods

You can use the the online Calculation of Solar Insolation by PV Education to calculate solar insolation. Make sure you understand the variables and equations behind the calculator. Any insolation calculator such as this one takes into account the position of the sun in space and the maximum solar insolation on a surface at a particular angle.

The calculator uses the solar insolation as a factor dependent upon the latitude and the day of the year. This lets it perform the calculation by taking into account the theory of the solar system as well as experimental results.

Properties Related to Solar Insolation

These observations of sunlight give scientists other quantities they can calculate such as the solar constant S, given by


with the current distance between the sun and Earth ​r​ and average distance between the sun and Earth ​r0.​ This gives scientists a more straightforward way of determining how the motion between the sun and the Earth affects sunlight. Solar flux density ​F​ can also be calculated as the change in solar heating at the highest point of the atmosphere per unit area over a difference in time, given by ​dQ/dt​. This is pertinent for engineering solar cells that take advantage of changes in sunlight throughout the day in producing electrical energy.

More advanced and nuanced calculators can take into account specific features like weather effects to predict the solar insolation on various days. Other useful properties of sunlight include the Direct Normal Irradiance (​DNI​), the amount of solar radiation that an object or area experiences over the size of the area itself.

The incoming sunlight must be perpendicular to the surface when performing this calculation. These factors, like solar insolation, are dependent upon atmosphere, angle of the sun and distance between the sun and the Earth so more advanced calculations can describe them to make more meaningful measurements.

Solar Radiation Calculation vs. Insolation

While using calculators to give you solar insolation values, you should understand the underlying physics behind solar insolation itself. There are a few simple mathematical equations that can describe solar insolation. This can help you learn more about how solar insolation is used in fields of study that harness the power of sunlight.

Solar insolation is closely related to solar radiation itself, but insolation gives you a more precise way of calculating the radiation on a single object relevant to energy rather than just taking a measurement of sunlight itself.

Solar radiation is the electromagnetic light that comes directly from the sun. This generally ranges from visible light to ultraviolet rays and in some cases it even extends to X-rays and infrared waves. This means solar radiation gives you a reliable way of determining the light that supports life on Earth. The atmosphere surrounding the planet typically deflects other more harmful components of the sun's radiation.

You can use a solar radiation calculation to determine the nuclear fusion reactions of the sun itself. These phenomena produce the helium of the sun from 700 million tons of hydrogen per second. Einstein's famous equation ​E = mc2​ describes this process that breaks the atomic bonds between hydrogen atoms for energy of the reaction ​E​ in joules, mass lost in the process ​m​ in kg and speed of light ​c​ (3.8 x 108 m/s). The fusion process is how the sun produces the electromagnetic waves of radiation itself.

Uses of Solar Insolation Research

Solar system designs rely on solar insolation to measure how powerful they need to be as effective as possible. Engineers working on these designs use solar insolation to determine how to estimate how much energy photovoltaic systems should produce.

Data related to solar insolation is also helpful for identifying, interpreting and comparing types of physical weather on Earth due to the Earth's orbit around the sun. This extends to carbonate or siliciclastic-carbonate ramps, geological features of sloping from a low gradient to shallow water shorelines in figuring out how the Earth traps heat from the Sun in forming these features.

Finally, construction engineers need to take into account the radiation and solar insolation when creating buildings to withstand the temperature and heat of the sun.


About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.