Solar Panel Output Calculator (Monthly and Annual kWh from System Size, Peak Sun Hours, Direction and Tilt)

Enter the system size (kW) and choose a city preset (or type in the solar radiation) to see the monthly and yearly output. Choosing the roof direction and tilt fills in the correction factor.

System size (kW)

Performance ratio K

Roof direction

Tilt (°)

Direction and tilt factor (%)

City preset (solar radiation)

How to enter solar radiation

Yearly average solar radiation (kWh/m²/day)

January

February

March

April

May

June

July

August

September

October

November

December

The presets are monthly averages of solar radiation on a south-facing surface tilted 30° (kWh/m²/day, also called peak sun hours), from US typical-year weather data. A blank performance ratio is treated as 0.73, and a blank correction factor as 100% (due south, 30° tilt). A year is 365 days (January 31, February 28, and so on).

Result and graph

Enter the system size and the solar radiation for your area in the fields on the left and press "Calculate". The monthly and yearly output and a chart will appear here.

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What you can do on this page
What is this calculation used for?
How to Use
Formula
Symbols and terms
- Symbols
- Terms
Good to know before you start
How to calculate it in Excel
How to calculate it in Google Sheets
How to calculate it in Python
How to write it in LaTeX and other math languages (copy and paste)
How to have ChatGPT do the calculation
DataChef Features
Related Features
NumberChef Calculators List

What you can do on this page

Enter the system size (kW) and the solar radiation for your area, and you get the monthly and yearly output (kWh), the yearly output per kW, and the monthly and daily averages on the spot
Choose a simple mode with one yearly average, or a monthly mode with values for January to December. Presets fill in typical values for Seattle, Los Angeles, Phoenix, Denver, Dallas, Chicago, Atlanta, Miami and New York
Pick the roof direction (south, southeast/southwest, east/west) and tilt (0 to 40°), and a correction factor relative to due south at 30° (= 100%) is filled in for you. You can change the number freely
The performance ratio (one factor for inverter, heat, dirt and wiring losses) starts at 0.73 and can be changed. A bar chart of the monthly output is also shown
A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page

This page calculates only the energy output (kWh). It does not use electricity rates or export (net metering) credits. To turn the yearly output into dollars, enter the yearly kWh on the "Annual kWh to Cost Calculator" page; for the cost of a single appliance, use the "Electricity Cost Calculator". The preset values are typical values from public US solar data. Sunlight varies a lot by location, even within one state, so choose the nearest city or enter the value for your own address. Real output also changes with weather, shade, snow and panel aging.

What is this calculation used for?

Checking whether the "yearly production" on a solar quote makes sense

A solar quote or proposal shows an "estimated yearly production" in kWh. Enter the same system size and your area's solar radiation here and calculate it yourself. You can see whether the number comes from standard assumptions (solar radiation and losses) or from quite optimistic ones.
As a guide, the yearly output per kW for due south at 30° is about 1,100 kWh in Seattle and about 1,800 kWh in Phoenix. If a quote in Chicago shows 2,000 kWh per kW, ask about the solar radiation and loss figures; if a quote in Phoenix shows 1,000 kWh per kW, ask about shade or direction. Output changes with weather and shade, so the result is only what the system makes under the conditions you entered.

Estimating the output of an east or west roof when you have no south-facing roof

Splitting panels between the east and west sides of a gable roof, or putting them on a southeast roof, is common. The table of correction factors shows that east or west (30° tilt) still gets about 85% of due south, and southeast or southwest about 96%.
Before deciding that solar will not work because the roof does not face south, calculate the output with the real direction and tilt. Then you can compare with numbers whether to add more panels to make up the difference or to use another side of the roof.

Knowing the monthly ups and downs to plan your electricity use or a battery

The monthly mode shows the yearly pattern: more output from spring to late summer and less in the short days of winter (and even less where snow covers the panels). With the Atlanta values, May makes about 60% more than December, and in cloudy-winter Seattle, August makes more than four times as much as December.
Knowing this pattern helps you plan. For example, "summer afternoons can cover the air conditioning" or "in winter most of the electricity will come from the grid". If your utility has net metering, summer surplus credits may carry over to winter bills, depending on the rules. It is also a starting point when you think about the size of a home battery.

Comparing your home's yearly electricity use with the solar output

Add up 12 months of kWh from your electric bills (many utilities also show this online) to get your home's yearly use. The average US home uses about 10,800 kWh a year. A 7 kW system in Atlanta makes about 9,700 kWh a year, so by amount alone it covers about 90% of an average home's use.
But solar only produces during the day, and you still use electricity at night. How much this lowers your bill depends on how your utility credits the electricity you send to the grid (net metering, net billing and so on) and on fixed charges, so equal output and use does not always mean a zero bill.

Finding out why the output is lower than expected

If the output you see in the monitoring app after installation is lower than calculated, enter the actual solar radiation for that month into this formula. You can then tell whether the gap comes from the weather or from something else (shade, dirt, snow, a faulty device or panel aging).
For example, if May produced only half the calculated output, the weather alone is hard to blame. That is a sign to ask the installer about shade from trees or buildings, dirty panels or the condition of the inverter.

Formula

Correcting solar radiation for roof direction and tilt

Standard notation (the usual math form)

$H_{m}$ $=$ $H_{m,0}$ $\times$ $\dfrac{f}{100}$

In words (symbols replaced with words)

③ $H_m$: solar radiation on the panels (kWh/m²/day) $=$ ① $H_{m,0}$: solar radiation at due south, 30° tilt (kWh/m²/day) $\times$ ② $f$: correction factor (%) ÷ 100

The formula in words

① Take the $H_{m,0}$: solar radiation at due south, 30° tilt (from a preset or solar data)

② multiply it by the $f$: correction factor (%) divided by 100

③ and you get the $H_m$: solar radiation on your actual roof (direction and tilt)

Quick example

In an area with 5.0 kWh/m²/day at due south and 30° tilt, the solar radiation on an east-facing roof (30° tilt, correction factor 85%) is

$H_m$: solar radiation on the panels $=$ at due south, 30° (5.0) $\times$ correction factor (85%) ÷ 100

$5.0 \times \dfrac{85}{100} = 4.25$

Key idea

Solar panels make more electricity the more directly they face the sun. In the Northern Hemisphere, including the US, the sun crosses the southern sky, so a panel facing due south and tilted about 30° gets close to the most sunlight over a year in much of the country. This calculator uses that as 100% and treats other directions as a relative value (the correction factor). The correction factors used here are as follows (for tilts of 0°, 10°, 20°, 30° and 40°, in that order). South: 88%, 95%, 99%, 100%, 99% Southeast / Southwest: 88%, 93%, 96%, 96%, 95% East / West: 88%, 88%, 87%, 85%, 82% Flat (0°) is about 88% in any direction. Even an east or west roof gets around 85% of due south, so a home without a south-facing roof can still use solar. North-facing roofs lose much more, so they are not in this table. These are rough values for mid-latitudes such as most of the continental US; the real values change a little with latitude and local weather.

Monthly output (kWh)

Standard notation (the usual math form)

$E_{m}$ $=$ $H_{m}$ $\times$ $K$ $\times$ $P$ $\times$ $D_{m}$ $\div$ $G_{s}$

In words (symbols replaced with words)

⑥ $E_m$: monthly output (kWh) $=$ ① $H_m$: solar radiation on the panels (kWh/m²/day) $\times$ ② $K$: performance ratio $\times$ ③ $P$: system size (kW) $\times$ ④ $D_m$: days in the month $\div$ ⑤ $G_s$: standard irradiance (1 kW/m²)

The formula in words

① Take the $H_m$: solar radiation on the panels (per day)

② multiply it by the $K$: performance ratio (the factor that takes off the losses)

③ and by the $P$: system size (kW) to get the output for one day,

④ multiply by the $D_m$: days in the month to get a whole month,

⑤ divide by the $G_s$: standard irradiance (1 kW/m²) to make the unit kWh,

⑥ and you get the $E_m$: monthly output (kWh)

Quick example

In January (31 days) with 4.0 kWh/m²/day (Atlanta, due south at 30°), a 7 kW system with a performance ratio of 0.73 produces

$E_1$: January output (kWh) $=$ solar radiation (4.0) $\times$ performance ratio (0.73) $\times$ system size (7 kW) $\times$ days (31) $\div$ standard irradiance (1 kW/m²)

$4.0 \times 0.73 \times 7 \times 31 \div 1 = 633.64 \approx 633.6$

Key idea

This formula is the simple method of JIS C 8907, the Japanese standard for estimating solar output, and it is the same idea as the common US rule of thumb "system size × peak sun hours × derate factor". A system size of $P$ kW is the output when the panels receive the standard irradiance of 1 kW/m². So dividing the solar radiation $H_m$ (kWh/m²/day) by $G_s$ (1 kW/m²) turns it into hours: how many hours a day the panels work as if at full power. These are the peak sun hours. Multiply by the system size $P$ and you get the output for one day with no losses (kWh). In real life there are losses. Panels make less power when they get hot, the inverter loses a few percent when it changes DC to AC, and dirt and wiring lose a little more. The performance ratio $K$ puts all of these into one number (the default here, 0.73, means about 27% loss). A typical breakdown is heat loss (about 10% over a year, or 0.9; 15% to 20% in summer and only a few percent in winter), inverter loss (about 5% to 10%, or 0.9 to 0.95) and other losses such as dirt, wiring and aging (about 10%, or 0.9). $0.9 \times 0.9 \times 0.9 \approx 0.73$ is where the default comes from. For US cities, the free PVWatts calculator with its default settings gives yearly results that match $K$ of about 0.73 to 0.8 (lower in hot climates). If you know the real performance of a system, or you use it in a cold climate or with high-efficiency equipment, change $K$. In the monthly mode, the yearly output is the sum of $E_m$ for January through December.

Yearly output (from the yearly average solar radiation)

Standard notation (the usual math form)

$E_{\mathrm{year}}$ $=$ $H$ $\times$ $K$ $\times$ $P$ $\times$ $365$ $\div$ $G_{s}$

In words (symbols replaced with words)

⑥ $E_{\mathrm{year}}$: yearly output (kWh) $=$ ① $H$: yearly average solar radiation (kWh/m²/day) $\times$ ② $K$: performance ratio $\times$ ③ $P$: system size (kW) $\times$ ④ days in a year (365) $\div$ ⑤ $G_s$: standard irradiance (1 kW/m²)

The formula in words

① Take the $H$: yearly average solar radiation (per day)

② multiply it by the $K$: performance ratio

③ and by the $P$: system size (kW) to get the output on an average day,

④ multiply by the days in a year (365) to get a whole year,

⑤ divide by the $G_s$: standard irradiance (1 kW/m²) to make the unit kWh,

⑥ and you get the $E_{\mathrm{year}}$: yearly output (kWh)

Quick example

For a 7 kW system with a performance ratio of 0.73, facing due south at 30° in an area with a yearly average of 5.2 kWh/m²/day (typical of Atlanta), the yearly output is

$E_{\mathrm{year}}$: yearly output (kWh) $=$ yearly average solar radiation (5.2) $\times$ performance ratio (0.73) $\times$ system size (7 kW) $\times$ 365 days $\div$ standard irradiance (1 kW/m²)

$5.2 \times 0.73 \times 7 \times 365 \div 1 = 9698.78 \approx 9699$

Key idea

The simple mode uses this formula for the yearly output. The yearly output divided by the system size $P$, called the yearly output per kW (kWh/kW/yr), is a yardstick for comparing places and setups. In the US, due south at 30°, it runs from about 1,100 kWh/kW/yr in Seattle to about 1,800 in Phoenix (in the example above, $9699 \div 7 \approx 1386$). If the output on a quote is far from this range for your area, it is a good reason to ask about the solar radiation and loss figures behind it. The monthly average is the yearly output divided by 12, and the daily average is the yearly output divided by 365. The monthly mode adds up the output of each month, so it also reflects the different number of days in each month (31, 28, and so on).

Solar output is basically "solar radiation on the panels (kWh/m²/day) × performance ratio K × system size (kW) × days ÷ standard irradiance (1 kW/m²)". The solar radiation for due south at 30° is first multiplied by the direction and tilt factor to get the value for your roof. Calculate each month and add them up for the yearly output, or, with a yearly average, just multiply by 365 days.

Symbols and terms

Symbols

$H_m$	H sub m	The average daily solar radiation on the actual panel surface (its direction and tilt), in kWh/m²/day. $H$ is the usual symbol for solar radiation: in solar energy, the energy per area (irradiation) is written $H$ and the power per area (irradiance) is written $G$. The small $m$ stands for month and shows which month the value is for.
$H_{m,0}$	H sub m zero	The monthly solar radiation on a surface facing due south at 30° (the preset or public solar data). The small $0$ means "the base value before correction".
$f$	f	The direction and tilt correction factor (%), compared with due south at 30° (= 100). From the first letter of "factor".
$K$	K	The performance ratio: one factor for the losses from heat, the inverter, dirt, wiring and so on. The default in this calculator is 0.73. The letter $K$ is often used for a coefficient.
$P$	P	The system size: the total rated power of the solar panels, in kW. From the first letter of "power".
$D_m$	D sub m	The number of days in the month (31 for January, 28 for February). From the first letter of "days"; the small $m$ stands for the month.
$G_s$	G sub s	The standard irradiance: the light intensity used in the test that sets a panel's rated power (Standard Test Conditions), fixed at 1 kW/m². $G$ is the usual symbol for irradiance (from "global irradiance") and $s$ stands for standard.
$E_m$	E sub m	The monthly output, in kWh. From the first letter of "energy"; the small $m$ stands for the month.
$E_{\mathrm{year}}$	E sub year	The yearly output (kWh). In the monthly mode it is the sum of $E_1$ through $E_{12}$; in the simple mode it comes straight from the yearly average solar radiation.
$H$	H	The yearly average solar radiation on the panels (kWh/m²/day), used in the simple mode. It is the monthly $H_m$ averaged over a year.

Terms

solar radiation	The amount of energy in sunlight that reaches the ground (or a roof). This calculator uses kWh per square meter per day (kWh/m²/day). It is larger in sunnier places and seasons. It is also called solar insolation.
plane-of-array radiation	The solar radiation on a tilted surface such as a roof, instead of on flat ground. Because the sun's height changes with the seasons, a surface facing south and tilted about 30° gets more sunlight over a year than a flat one. Weather data for "global horizontal" radiation is for a flat surface, so using it as is gives a lower output estimate.
kWh/m²/day	The unit of solar radiation - the energy (kWh) that reaches 1 m² of surface in one day. The same number can be read as "how many hours of strong 1 kW/m² sunlight per day" (peak sun hours).
peak sun hours	Solar radiation (kWh/m²/day) divided by the standard irradiance (1 kW/m²), in hours. It tells how many hours a day the panels work as if at full power. Multiply it by the system size (kW) to get the output for one day with no losses (kWh). In Japan this is called "equivalent sunshine hours".
system size	The total rated power of all the solar panels (kW), the basic number for the size of a solar system, as in "a 7 kW system". With 400 W panels, 18 panels make 7.2 kW.
rated power	The power (W) one panel makes under Standard Test Conditions (irradiance of 1 kW/m², panel temperature of 25°C (77°F) and so on). The "400 W" on a spec sheet is this value. On a real roof, heat and sunlight are different, so the panel runs below this most of the time.
Standard Test Conditions (STC)	The fixed conditions for measuring panel power: irradiance of 1 kW/m², panel temperature of 25°C (77°F) and a set type of light. $G_s$ (1 kW/m²) in the formula is the irradiance under these conditions.
performance ratio	A factor that shows how much of the "ideal output" (from solar radiation and system size) a system really produces. It covers heat loss, inverter loss, dirt, wiring loss and so on. For homes it is about 0.7 to 0.8, and the default in this calculator is 0.73. It is also called the derate factor.
inverter	The device that changes the DC power from the panels into the AC power used in a home. A few percent is lost in this change, and that is one of the losses in the performance ratio.
azimuth	The compass direction the panels face. In the US, due south produces the most, east or west about 85% of that, and north much less. In this calculator, choosing a direction fills in the correction factor.
tilt angle	The angle of the panels. Flat is 0°. Many home roofs are about 20° to 30°. Roof pitch in the US is written as rise per 12 inches of run - 4/12 is about 18°, 6/12 about 27° and 8/12 about 34°.
yearly output per kW	The yearly output (kWh) divided by the system size (kW), in kWh/kW/yr. It lets you compare systems of different sizes and different places. In the US, due south at 30°, it is about 1,100 in Seattle to about 1,800 in Phoenix. It is also called specific yield.
degradation	The slow drop in panel output over the years, usually said to be about 0.5% a year. It is not in this calculator's formula. For long-term estimates, make the performance ratio a little smaller or apply a degradation rate separately.

Good to know before you start

Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
If you get stuck, going back over these topics is the quickest way forward.

Multiplying and dividing decimals (Grades 5–6)	Being able to multiply decimals, as in $4.0 \times 0.73 \times 7$ Being able to find a "per kW" value by division, as in $9699 \div 7$
Percents (Grades 6–7)	Being able to turn a percent into a decimal, as in "85% is 0.85 times the whole" Knowing that "whole × percent = part" (solar radiation at due south × correction factor = solar radiation on your roof)
Units and combined units (Grades 5–8)	Knowing that k (kilo) means 1,000 times, so $1\,\mathrm{kW} = 1000\,\mathrm{W}$ Being able to read a combined unit such as "kWh/m²/day" as "kWh per square meter per day"
Power and energy (middle school physical science)	Telling apart power (W, kW), how fast electricity is made or used, and energy (Wh, kWh), the total amount made or used Knowing that energy = power × time (system size in kW × peak sun hours = output in kWh)
The sun's path and the seasons (elementary and middle school science)	Knowing that the sun rises in the east, crosses the southern sky and sets in the west (so a south-facing surface gets the most light in the US) Knowing that the sun is high in summer and low in winter (so tilting the panels a little collects more sunlight over a year)

How to calculate it in Excel

Copy the whole table below and paste it into cell A1 in Excel. It works as is.

Table to correct solar radiation for direction and tilt

Solar radiation at due south, 30° (kWh/m²/day)	5.0
Direction and tilt factor (%)	85
Solar radiation on the panels (kWh/m²/day)	=B1*B2/100

Table to find the monthly output

Solar radiation on the panels (kWh/m²/day)	4.0
Performance ratio K	0.73
System size (kW)	7
Days in the month	31
Standard irradiance (kW/m²)	1
Monthly output (kWh)	=B1B2B3*B4/B5

Table to find the yearly output (from the yearly average)

Yearly average solar radiation (kWh/m²/day)	5.2
Performance ratio K	0.73
System size (kW)	7
Yearly output (kWh)	=B1B2B3*365
Yearly output per kW (kWh/kW/yr)	=B4/B3
Monthly average output (kWh/month)	=B4/12
Daily average output (kWh/day)	=B4/365

Table to find the monthly and yearly output (Atlanta, 7 kW)

January solar radiation (kWh/m²/day)	4.0
February solar radiation (kWh/m²/day)	4.5
March solar radiation (kWh/m²/day)	5.0
April solar radiation (kWh/m²/day)	5.9
May solar radiation (kWh/m²/day)	6.1
June solar radiation (kWh/m²/day)	5.8
July solar radiation (kWh/m²/day)	5.9
August solar radiation (kWh/m²/day)	5.8
September solar radiation (kWh/m²/day)	5.7
October solar radiation (kWh/m²/day)	5.4
November solar radiation (kWh/m²/day)	4.5
December solar radiation (kWh/m²/day)	3.8
Performance ratio K	0.73
System size (kW)	7
January output (kWh)	=B1$B$13$B$14*31
February output (kWh)	=B2$B$13$B$14*28
March output (kWh)	=B3$B$13$B$14*31
April output (kWh)	=B4$B$13$B$14*30
May output (kWh)	=B5$B$13$B$14*31
June output (kWh)	=B6$B$13$B$14*30
July output (kWh)	=B7$B$13$B$14*31
August output (kWh)	=B8$B$13$B$14*31
September output (kWh)	=B9$B$13$B$14*30
October output (kWh)	=B10$B$13$B$14*31
November output (kWh)	=B11$B$13$B$14*30
December output (kWh)	=B12$B$13$B$14*31
Yearly output (kWh)	=SUM(B15:B26)
Yearly output per kW (kWh/kW/yr)	=B27/B14

After pasting, the upper cells in column B are your inputs and the green formula cells are calculated automatically.
The first table applies the east/west correction (85%) to 5.0 at due south and 30°, and B3 shows 4.25. The second table is the monthly output for 4.0, K = 0.73, 7 kW and 31 days, and B6 shows 633.64 (kWh).
The third table finds the yearly output from a yearly average of 5.2. B4 shows 9698.78 (about 9,699 kWh) and B5 shows 1385.54 (about 1,386 kWh per kW).
The fourth table uses the monthly values for Atlanta to find the output for each of the 12 months and adds them up. The yearly output in B27 is about 9,704 kWh, and B28 is about 1,386 kWh/kW/yr. The monthly formulas refer to B13 and B14 with fixed references such as "$B$13", so changing the factor and system size recalculates all 12 months at once.

How to calculate it in Google Sheets

Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.

Table to correct solar radiation for direction and tilt

Solar radiation at due south, 30° (kWh/m²/day)	5.0
Direction and tilt factor (%)	85
Solar radiation on the panels (kWh/m²/day)	=B1*B2/100

Table to find the monthly output

Solar radiation on the panels (kWh/m²/day)	4.0
Performance ratio K	0.73
System size (kW)	7
Days in the month	31
Standard irradiance (kW/m²)	1
Monthly output (kWh)	=B1B2B3*B4/B5

Table to find the yearly output (from the yearly average)

Yearly average solar radiation (kWh/m²/day)	5.2
Performance ratio K	0.73
System size (kW)	7
Yearly output (kWh)	=B1B2B3*365
Yearly output per kW (kWh/kW/yr)	=B4/B3
Monthly average output (kWh/month)	=B4/12
Daily average output (kWh/day)	=B4/365

Table to find the monthly and yearly output (Atlanta, 7 kW)

January solar radiation (kWh/m²/day)	4.0
February solar radiation (kWh/m²/day)	4.5
March solar radiation (kWh/m²/day)	5.0
April solar radiation (kWh/m²/day)	5.9
May solar radiation (kWh/m²/day)	6.1
June solar radiation (kWh/m²/day)	5.8
July solar radiation (kWh/m²/day)	5.9
August solar radiation (kWh/m²/day)	5.8
September solar radiation (kWh/m²/day)	5.7
October solar radiation (kWh/m²/day)	5.4
November solar radiation (kWh/m²/day)	4.5
December solar radiation (kWh/m²/day)	3.8
Performance ratio K	0.73
System size (kW)	7
January output (kWh)	=B1$B$13$B$14*31
February output (kWh)	=B2$B$13$B$14*28
March output (kWh)	=B3$B$13$B$14*31
April output (kWh)	=B4$B$13$B$14*30
May output (kWh)	=B5$B$13$B$14*31
June output (kWh)	=B6$B$13$B$14*30
July output (kWh)	=B7$B$13$B$14*31
August output (kWh)	=B8$B$13$B$14*31
September output (kWh)	=B9$B$13$B$14*30
October output (kWh)	=B10$B$13$B$14*31
November output (kWh)	=B11$B$13$B$14*30
December output (kWh)	=B12$B$13$B$14*31
Yearly output (kWh)	=SUM(B15:B26)
Yearly output per kW (kWh/kW/yr)	=B27/B14

These formulas use only multiplication, division and the SUM function, so the same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace column B with the solar radiation and system size for your area.

How to calculate it in Python

capacity_kw = 7            # system size P (kW)
design_factor = 0.73       # performance ratio K
orientation_percent = 100  # direction and tilt factor f (%). 100 for due south at 30 degrees
standard_irradiance = 1    # standard irradiance Gs (kW/m2)

# Monthly solar radiation at due south, 30 degrees tilt (kWh/m2/day). Example: Atlanta
irradiation_south30 = [4.0, 4.5, 5.0, 5.9, 6.1, 5.8, 5.9, 5.8, 5.7, 5.4, 4.5, 3.8]
days_in_month = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

yearly_kwh = 0
for month, (h0, days) in enumerate(zip(irradiation_south30, days_in_month), start=1):
    h = h0 * orientation_percent / 100                       # solar radiation on the panels Hm
    monthly_kwh = h * design_factor * capacity_kw * days / standard_irradiance  # monthly output Em
    yearly_kwh += monthly_kwh
    print(f"Month {month:2d}: {monthly_kwh:.1f} kWh")

print(f"Yearly output: {yearly_kwh:.0f} kWh")
print(f"Yearly output per kW: {yearly_kwh / capacity_kw:.0f} kWh/kW/yr")
print(f"Monthly average: {yearly_kwh / 12:.1f} kWh/month, daily average: {yearly_kwh / 365:.2f} kWh/day")

Runs with the standard library only. Change the first four values (system size, performance ratio, correction factor and standard irradiance) and the list of monthly solar radiation to your own conditions and run it. With the example values, it prints a yearly output of about 9,704 kWh and about 1,386 kWh/kW/yr.

How to write it in LaTeX and other math languages (copy and paste)

Correcting solar radiation for roof direction and tilt

Hₘ = Hₘ,₀ × f ÷ 100

H_{m} = H_{m,0} \times \frac{f}{100}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>H</mi><mi>m</mi></msub>
    <mo>=</mo>
    <msub><mi>H</mi><mrow><mi>m</mi><mo>,</mo><mn>0</mn></mrow></msub>
    <mo>&#xD7;</mo>
    <mfrac><mi>f</mi><mn>100</mn></mfrac>
  </mrow>
</math>

H_m = H_(m,0) * f / 100

irradiation = baseIrradiation*factor/100

H_m := H_m0*f/100;

H_m = H_m0*f/100;

H_m = H_(m,0)×f/100

Monthly output (kWh)

Eₘ = Hₘ × K × P × Dₘ ÷ Gₛ

E_{m} = \frac{H_{m} \times K \times P \times D_{m}}{G_{s}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>E</mi><mi>m</mi></msub>
    <mo>=</mo>
    <mfrac>
      <mrow>
        <msub><mi>H</mi><mi>m</mi></msub>
        <mo>&#xD7;</mo>
        <mi>K</mi>
        <mo>&#xD7;</mo>
        <mi>P</mi>
        <mo>&#xD7;</mo>
        <msub><mi>D</mi><mi>m</mi></msub>
      </mrow>
      <msub><mi>G</mi><mi>s</mi></msub>
    </mfrac>
  </mrow>
</math>

E_m = (H_m * K * P * D_m) / G_s

monthlyEnergy = irradiation*designFactor*capacity*days/standardIrradiance

E_m := H_m*K*P*D_m/G_s;

E_m = H_m*K*P*D_m/G_s;

E_m = (H_m×K×P×D_m)/G_s

Yearly output (from the yearly average solar radiation)

E_year = H × K × P × 365 ÷ Gₛ

E_{\mathrm{year}} = \frac{H \times K \times P \times 365}{G_{s}}

<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
  <mrow>
    <msub><mi>E</mi><mtext>year</mtext></msub>
    <mo>=</mo>
    <mfrac>
      <mrow>
        <mi>H</mi>
        <mo>&#xD7;</mo>
        <mi>K</mi>
        <mo>&#xD7;</mo>
        <mi>P</mi>
        <mo>&#xD7;</mo>
        <mn>365</mn>
      </mrow>
      <msub><mi>G</mi><mi>s</mi></msub>
    </mfrac>
  </mrow>
</math>

E_"year" = (H * K * P * 365) / G_s

yearlyEnergy = irradiation*designFactor*capacity*365/standardIrradiance

E_year := H*K*P*365/G_s;

E_year = H*K*P*365/G_s;

E_year = (H×K×P×365)/G_s

How to have ChatGPT do the calculation

You are a calculation assistant for solar panel output. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing).

A 7 kW solar system is installed on a roof facing due south with a 30° tilt. The performance ratio is 0.73 and the standard irradiance is 1 kW/m².
The monthly solar radiation at due south and 30° tilt (kWh/m²/day), from January, is 4.0, 4.5, 5.0, 5.9, 6.1, 5.8, 5.9, 5.8, 5.7, 5.4, 4.5, 3.8.
Find the monthly output (kWh) as "solar radiation × performance ratio × system size × days in the month ÷ standard irradiance" (a year is 365 days, February has 28 days).
Find each of the following:
1. The monthly output for January through December (kWh, to 1 decimal place)
2. The yearly output (kWh) and the yearly output per kW (kWh/kW/yr)
3. The monthly and daily average output

Show the formulas you used and the numbers from the execution result.

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\(H_m\)	H sub m	The average daily solar radiation on the actual panel surface (its direction and tilt), in kWh/m²/day. \(H\) is the usual symbol for solar radiation: in solar energy, the energy per area (irradiation) is written \(H\) and the power per area (irradiance) is written \(G\). The small \(m\) stands for month and shows which month the value is for.
\(H_{m,0}\)	H sub m zero	The monthly solar radiation on a surface facing due south at 30° (the preset or public solar data). The small \(0\) means "the base value before correction".
\(f\)	f	The direction and tilt correction factor (%), compared with due south at 30° (= 100). From the first letter of "factor".
\(K\)	K	The performance ratio: one factor for the losses from heat, the inverter, dirt, wiring and so on. The default in this calculator is 0.73. The letter \(K\) is often used for a coefficient.
\(P\)	P	The system size: the total rated power of the solar panels, in kW. From the first letter of "power".
\(D_m\)	D sub m	The number of days in the month (31 for January, 28 for February). From the first letter of "days"; the small \(m\) stands for the month.
\(G_s\)	G sub s	The standard irradiance: the light intensity used in the test that sets a panel's rated power (Standard Test Conditions), fixed at 1 kW/m². \(G\) is the usual symbol for irradiance (from "global irradiance") and \(s\) stands for standard.
\(E_m\)	E sub m	The monthly output, in kWh. From the first letter of "energy"; the small \(m\) stands for the month.
\(E_{\mathrm{year}}\)	E sub year	The yearly output (kWh). In the monthly mode it is the sum of \(E_1\) through \(E_{12}\); in the simple mode it comes straight from the yearly average solar radiation.
\(H\)	H	The yearly average solar radiation on the panels (kWh/m²/day), used in the simple mode. It is the monthly \(H_m\) averaged over a year.

Multiplying and dividing decimals (Grades 5–6)	Being able to multiply decimals, as in \(4.0 \times 0.73 \times 7\) Being able to find a "per kW" value by division, as in \(9699 \div 7\)
Percents (Grades 6–7)	Being able to turn a percent into a decimal, as in "85% is 0.85 times the whole" Knowing that "whole × percent = part" (solar radiation at due south × correction factor = solar radiation on your roof)
Units and combined units (Grades 5–8)	Knowing that k (kilo) means 1,000 times, so \(1\,\mathrm{kW} = 1000\,\mathrm{W}\) Being able to read a combined unit such as "kWh/m²/day" as "kWh per square meter per day"
Power and energy (middle school physical science)	Telling apart power (W, kW), how fast electricity is made or used, and energy (Wh, kWh), the total amount made or used Knowing that energy = power × time (system size in kW × peak sun hours = output in kWh)
The sun's path and the seasons (elementary and middle school science)	Knowing that the sun rises in the east, crosses the southern sky and sets in the west (so a south-facing surface gets the most light in the US) Knowing that the sun is high in summer and low in winter (so tilting the panels a little collects more sunlight over a year)

Solar Panel Output Calculator (Monthly and Annual kWh from System Size, Peak Sun Hours, Direction and Tilt)

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How to have ChatGPT do the calculation

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Finds the energy use and cost per day, week, month and year from one appliance's wattage, duty cycle and hours of use

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