# What Is The Solar Constant Per Square Foot?

## What is the Solar Constant?

The solar constant is defined as the amount of incoming solar radiation per unit area that would be incident on a plane perpendicular to the rays, at a distance of one astronomical unit (AU) from the Sun (94,500,000 miles or 150,000,000 km) (Definition of solar constant – Merriam-Webster). It represents the mean solar electromagnetic radiation (solar irradiance) per unit area and includes all types of solar radiation, not just the visible light. The solar constant incorporates all different wavelengths of solar radiation, including infrared, ultraviolet, and radio waves.

The value of the solar constant is measured by satellite as 1,361 watts per square meter (W/m2). However, it varies by about 6.9% throughout the year depending on the Earth’s distance from the Sun. It is lowest in early July when the Earth is farthest from the Sun, and highest in early January when the Earth is closest. The solar constant is important for solar power because it represents the maximum power that could theoretically be obtained from the Sun. Knowledge of the solar constant allows engineers to design solar panels and calculate potential solar energy generation.

## Calculating the Solar Constant

The solar constant represents the amount of incoming solar radiation per unit area that would be incident on a plane perpendicular to the rays, at a distance of one astronomical unit (AU) from the Sun (1 AU is the average distance between the Earth and Sun or about 150 million kilometers)1. It includes all types of solar radiation, not just the visible light. The currently accepted value of the solar constant is 1,361 watts per square meter (W/m2).

The solar constant is calculated by taking the total solar irradiance (solar power per unit area) at 1 AU from the Sun and dividing it by the cross-sectional area of a sphere centered on the Sun with a radius of 1 AU. This provides the radiation per unit area on a spherical surface enveloping the Sun. The calculation involves the solar luminosity (total power output of the Sun) and the astronomical unit:

Solar Constant = Solar Luminosity / Surface Area of Sphere at 1 AU

The key variables involved are:

• Solar luminosity: 3.846×1026 W
• Radius of 1 AU: 149,597,870.7 km

Plugging these values into the equation yields the solar constant of ~1,361 W/m2. Small variations in solar luminosity and the Earth-Sun distance lead to minor fluctuations around this average value2.

## Units of the Solar Constant

The solar constant represents the amount of incoming solar electromagnetic radiation per unit area. It is measured on a surface perpendicular to the rays of the sun at the average distance of the Earth from the Sun.

The standard SI unit used for the solar constant is watts per square meter (W/m2). This unit represents the rate at which solar energy is received per unit area.

Some other common units used for the solar constant include:

• Btu per square foot per hour (Btu/ft2/hr) – Used mainly in the United States
• Calories per square centimeter per minute (cal/cm2/min) – Represents the amount of solar energy in terms of heat
• Langleys per minute (Ly/min) – A langley is equivalent to one calorie per square centimeter

The average value of the solar constant is approximately 1.366 kilowatts per square meter (kW/m2). In other units, this equates to:

• 437.4 Btu/ft2/hr
• 0.433 cal/cm2/min
• 1.956 Ly/min

The solar constant is a useful measure for calculating the amount of solar energy received at the Earth’s surface after accounting for various losses in the atmosphere. Knowing the solar constant in different units aids solar energy calculations and system design.

## Average Solar Constant Value

The solar constant is the amount of incoming solar radiation per unit area that would be incident on a plane perpendicular to the sun’s rays at a distance of one astronomical unit (AU) outside the earth’s atmosphere. An astronomical unit is the average distance between the Earth and the Sun, about 92.96 million miles (150 million km).

According to Byjus, the average value of the solar constant is approximately 1,366 watts per square meter (W/m2). This value represents the mean total electromagnetic radiation emitted by the sun over all wavelengths per unit area and is considered the standard benchmark for solar irradiance outside the earth’s atmosphere.

However, the solar constant varies slightly throughout the year due to the earth’s elliptical orbit and its axial tilt. The observed values range from approximately 1,322 W/m2 around July 4 to 1,414 W/m2 around January 4, a difference of about 6.9%. But on average across a full year, the solar constant equals roughly 1,360 W/m2.

Knowing the average solar constant allows scientists to calculate the maximum potential solar energy available at the top of the earth’s atmosphere for conversion into other energy forms like heat or electricity. It provides an upper limit on available solar radiation before accounting for absorption and scattering in the atmosphere.

## Variations in the Solar Constant

The solar constant, the amount of incoming solar radiation per unit area measured above the atmosphere, is not actually constant. There are several factors that cause the solar constant to vary over time.

One cause of variation is the elliptical shape of Earth’s orbit around the Sun. Because of this elliptical orbit, Earth’s distance from the Sun ranges annually between 91 million miles at perihelion (closest approach) to 94.5 million miles at aphelion (farthest distance). This 7% change in distance leads to an approximate 6.9% variation in the solar constant received at the top of Earth’s atmosphere.

The 11 year solar cycle also contributes to variation in the solar constant. As the Sun moves through its natural 11 year cycle of activity, changing levels of sunspots and faculae cause subtle changes in solar irradiance. Measurements indicate the solar constant decreases about 0.1% from solar maximum to solar minimum due to these cyclical changes in solar activity.

Other phenomena like solar flares and the 27 day solar rotation also introduce short-term fluctuations in the solar constant. However, the elliptical orbit and solar cycle account for the predominant variations.

## Importance for Solar Power

The solar constant is critically important for estimating and calculating the potential power output from solar photovoltaic panels. The solar constant represents the maximum power available per unit area just above the Earth’s atmosphere. This can be used to calculate the potential solar irradiation available at any location after accounting for atmospheric absorption and reflection, solar panel efficiency, orientation, and tracking capabilities. Knowing the available solar resource is key for properly sizing solar PV systems to meet electrical demand.

Specifically, the solar constant value of approximately 1,366 watts per square meter outside the atmosphere provides an upper limit and benchmark for calculations. This peak irradiance value must then be reduced based on the location’s atmosphere, weather patterns, latitude, and panel characteristics to determine the usable solar resource available. While the available solar irradiation varies greatly by geography and local conditions, the solar constant provides a consistent starting point for engineering analysis and financial modeling of solar power systems. Overall, the solar constant is foundational for determining and optimizing the potential electrical output from solar photovoltaics worldwide.

## Solar Constant Per Square Foot

The solar constant represents the amount of solar energy per second received on a unit area of surface perpendicular to the rays of the Sun at the average Sun-Earth distance outside the atmosphere. It has an accepted modern value of approximately 1366 watts per square meter (W/m2).

To convert the solar constant into per square foot units, we need to convert meters to feet and watts to BTU/hour.

One square meter is equivalent to 10.764 square feet. So the solar constant per square foot is:

1366 W/m2 x (10.764 ft2/m2) = 14683.824 W/ft2

To convert watts to BTU/hour, we multiply by 3.412:

14683.824 W/ft2 x 3.412 = 50030.174 BTU/hr/ft2

Therefore, the solar constant per square foot is approximately 50030 BTU/hr/ft2.

This value represents the total solar energy received per hour on each square foot of area oriented perpendicular to the Sun outside the Earth’s atmosphere, at the average Earth-Sun distance. Knowing the solar constant per square foot allows us to calculate potential solar energy collection for photovoltaic or solar thermal systems.

Several factors affect the amount of solar radiation reaching the Earth’s surface, known as surface irradiance. These include:

Latitude – Areas closer to the equator receive more direct irradiance from the sun than areas farther away. This is because the sun’s rays hit the equator more directly.

Season – More radiation reaches the Earth’s surface during summer months than winter. In the northern hemisphere, irradiance peaks around the summer solstice in June and decreases towards the winter solstice in December. [1]

Time of Day – Irradiance is highest when the sun is directly overhead and decreases as the sun’s angle above the horizon lessens. Irradiance peaks at solar noon and is lowest at sunrise and sunset.

Cloud Cover – Clouds reflect and absorb incoming solar radiation, reducing surface irradiance significantly on cloudy days versus clear days. Thick, low-lying clouds have the greatest impact.

Altitude – Higher elevations receive more irradiance because there is less atmosphere for the sunlight to pass through. Irradiance increases by about 4% for every 1,000 ft rise in elevation.

Air Pollution – Particles from sources like smog, smoke, and haze scatter and absorb radiation, reducing surface irradiance, especially UV radiation.

## Applications and Uses

The solar constant has several important applications in science and engineering. For example, it is used to calculate the theoretical maximum power available from solar panels at any given location on Earth (https://www.e-education.psu.edu/eme812/node/644). Knowing the solar constant allows solar panel engineers to properly size systems to meet energy demands.

In climate science, measuring variations in the solar constant over time provides information about changes in solar activity and any potential impacts on Earth’s climate (https://www.noaa.gov/measuring-solar-constant). Satellite measurements by NASA and NOAA track total solar irradiance and detect subtle changes over years or decades.

The solar constant also has applications in spacecraft and satellite design. Engineers must account for the solar energy absorbed and radiated by a spacecraft’s surfaces. Knowledge of the solar constant in space enables proper thermal management and temperature control of sensitive electronics and payloads.

Weather forecasting and modeling relies in part on accurate measurements of incoming solar radiation. The solar constant provides a baseline for estimating solar energy at the top of the atmosphere for a given location and time.

In the future, improved measurements of the solar constant may further our understanding of solar variability and the interaction between the Sun and Earth’s climate. Continued monitoring is important for identifying long-term trends and potential impacts on renewable energy production.

## Future Measurement and Research

The measurement of the solar constant and monitoring its potential variability has been identified as crucial for understanding climate change and the availability of solar energy. Several studies have been examining future plans to continue measuring and studying the solar constant.

The Solar Futures Study conducted by the U.S. Department of Energy in 2021 analyzed pathways for significantly increasing solar power generation in the United States and discussed the importance of continued solar resource monitoring and forecasting. As solar becomes a larger contributor to the energy mix, accurately measuring and predicting available solar resources will be critical.

NASA’s Climate and Radiation Lab is developing the Compact Total Irradiance Monitor (CTIM) to be launched in 2023, which will extend the 40-year record of solar irradiance measurements (Phys.org). The CTIM instrument will be smaller, lighter, and cheaper than previous sensors while still providing high-accuracy measurements.

Overall, research indicates strong interest in sustaining long-term solar irradiance datasets and developing improved measurement technologies. As the world transitions to renewable energy, ongoing solar resource monitoring and forecasting will be essential for effective planning and operation of solar power systems.