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Solar Panel Calculator

Size a solar system from your electricity use and count the panels it needs. Or estimate what a given system makes in a year.

Level: Grades 6–7

  • Common Core standard 6.RP.A.3.bSolve unit rate problems including those involving unit pricing and constant speed.
  • Common Core standard 6.RP.A.3.cFind a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
Printable worksheet

Solar Panel Calculator

Know the answer you need? Pick an input to work backward.

Inputs
What do you want to find?

Look for the kWh figure on your utility bill. A 12-month total evens out the seasons.

Yearly average for your site. Solar resource maps and installer quotes list this figure.

The share of rated output left after losses from the inverter, wiring, heat and dirt.

The rated power (Pmax) on the panel's spec sheet.

Result

System size needed

8.22 kW

Covering 10,800 kWh a year needs about 8.22 kW, or 21 panels of 400 W.

Panels at 400 W
21
Size with whole panels
8.4 kW
Annual production with whole panels
11,038 kWh/yr
Annual energy to produce
10,800 kWh/yr
Specific yield
1,314 kWh per kW per year

See the step-by-step solution ↓

Step-by-step solution

  1. Turn your monthly use into a yearly total: monthly use × 12

    900 kWh×12=10,800 kWh

  2. Spread the yearly target over 365 days, because sun hours are given per day

    10,800 kWh365=29.589 kWh

  3. Divide by the useful sun hours each day (sun hours × efficiency) to get the system size in kW

    29.589 kWh4.5 h×0.8=8.2192 kW

  4. Count the panels: the size in watts divided by each panel's watts, rounded up because panels come whole

    8,219.18 W400 W=20.548=→=21

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how big a solar system you need to cover your electric bill, and how many panels that takes. You size it by working backward from the energy you use. Your utility bill tells you how many kilowatt-hours (kWh) you use. Your location tells you how many hours of full-strength sunshine a panel gets on an average day. And real-world losses shave a share off the panels' rated output. Divide the energy you need each day by the useful sun hours, and you have the system's size in kilowatts (kW).

This calculator does that sizing for you. It turns the result into a whole number of panels at the wattage you choose. It works the other way too. Give it a system size, and it estimates the yearly, monthly and daily energy that system should make. Every regional and equipment figure is an input you can swap for your own.

Where it's used

Why this math matters outside the classroom:

  • Sizing a system. A home using 10,950 kWh a year with 5 sun hours and a 0.8 derate needs about 10,950 ÷ (365 × 5 × 0.8) = 7.5 kW.
  • Panel count. A 7.5 kW system built from 400 W panels needs 7,500 ÷ 400 = 18.75, so 19 panels.
  • Off-grid cabins. Off-grid cabin owners size a small array to cover lights and a fridge on the shortest days of the year.
  • Checking quotes. Homeowners check an installer's yearly production estimate against their own sun-hour figures.

Grade level and standards: Grades 6–7; Common Core State Standards for Mathematics 6.RP.A.3.b, 6.RP.A.3.c. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose whether you want the system size for your use, or the output of a system you already have in mind.
  2. Enter your electricity use from your bill, monthly or yearly, and the share of it you want solar to cover. In production mode, enter the system's DC size in kW instead.
  3. Replace the example peak sun hours, typical efficiency and example panel wattage with figures for your site and your chosen panel.
  4. Read the system size, the panel count, and the output of the rounded-up system. The working shows each multiplication.

What the inputs mean

Electricity use
Bills usually show the kWh used in the billing period, and many also chart the last 12 months. A yearly total is better than a single month. Heating, cooling and daylight change how much you use across the seasons.
Share of that use to cover with solar
100% aims to match your yearly use. Choose less for a partial system, or more if you expect to add an electric car or heat pump.
System size (DC rating)
The total DC rating of the system: number of panels × panel wattage ÷ 1,000.
Peak sun hours per day (example: 4.5)
Peak sun hours are the hours per day that would give the same energy if the sun shone at full strength (1,000 W/m²) the whole time. They depend on how far north or south you are, the climate, and the tilt and direction of the roof. The default of 4.5 is only an example. Solar maps from national energy agencies, and installer quotes, give a figure for your address.
System efficiency / derate factor (typical: 80%)
Also called the performance ratio or derate factor. It rolls up the losses from the inverter (the box that turns panel power into household power), wiring, heat, dust, shade and panels that don't quite match. Around 75% to 85% is typical for a well-installed system. An installer's output estimate hints at the figure they used.
Panel wattage (example: 400 W)
The panel's rated power under standard test conditions. Its spec sheet lists it as Pmax or rated power.

Formula and method

annual use = monthly use × 12
daily energy = annual use × share to cover ÷ 365
system size (kW) = daily energy (kWh) ÷ (peak sun hours × efficiency)
panels = ceiling(system size × 1,000 ÷ panel watts)
annual production (kWh) = system size × peak sun hours × efficiency × 365

A 1 kW system makes 1 kWh in one peak sun hour, before losses. So kilowatts times sun hours gives kilowatt-hours per day. Multiplying by the efficiency takes off the losses between the panels' label rating and the energy that reaches your meter.

Panels only come in whole units, so the count is rounded up. That's what "ceiling" means in the formula. The calculator then reports the size and output of that rounded-up system. It's a little larger than the exact need.

The specific yield (kWh per kW per year) is sun hours × efficiency × 365. It's a handy figure for comparing sites, because it doesn't depend on how big the system is.

Worked example

A household uses 900 kWh a month and wants to cover all of it. The site gets an example 4.5 peak sun hours, efficiency is a typical 80%, and the chosen panels are rated 400 W.

  1. Annual use: 900 × 12 = 10,800 kWh.
  2. Daily energy: 10,800 ÷ 365 = 29.589 kWh per day.
  3. System size: 29.589 ÷ (4.5 × 0.8) = 29.589 ÷ 3.6 = 8.22 kW.
  4. Panels: 8,219 W ÷ 400 W = 20.55, rounded up to 21 panels.
  5. 21 panels × 400 W = 8.4 kW, which produces 8.4 × 4.5 × 0.8 × 365 = 11,037.6 kWh a year.

Result: The household needs about 8.22 kW of panels, which is 21 panels of 400 W. That system should make roughly 11,038 kWh a year, slightly more than the 10,800 kWh used.

Understanding the result

The system size is a starting point for talks with installers, not a final design. Roof area, shade, which way the roof faces and local rules on sending power to the grid all change the final size.

Output changes with the seasons. Summer months can make two or three times as much as winter months. So a system sized to match yearly use will make extra in summer and fall short in winter. Whether that evens out depends on how your utility credits the power you send back.

If the panel count looks too large for your roof, a higher-wattage panel lowers the count. It doesn't lower the total kW you need.

Assumptions and limitations

  • A year is 365 days, and a month is one twelfth of a year.
  • Peak sun hours are a yearly average for the panels' actual tilt and direction.
  • Efficiency is one factor covering all losses. Panels slowly wearing out over time isn't modeled.
  • System size is the DC (panel) rating. Inverter size and AC rating aren't calculated.
  • No location data is built in. The answer is only as good as the sun hours and efficiency you enter.
  • Shade from trees, chimneys or nearby buildings can cut output far more than the efficiency figure suggests.
  • Battery storage, net metering rules (how your utility credits extra power), costs and incentives are outside what this calculator covers.

Frequently asked questions

Where do I find my peak sun hours?

Public solar maps let you look up the average daily solar energy for a location. It's usually given in kWh per square meter per day, and that number equals peak sun hours. An installer's quote also hints at a value. Divide its first-year kWh estimate by the system size and by 365. Then divide by the efficiency they assumed.

Why does the calculator round the panel count up?

You can't install part of a panel. Rounding down would leave the system short of your target. So the count is rounded up, and the calculator shows how much the slightly larger system makes.

What efficiency or derate factor should I use?

The 80% default is a typical round figure for a grid-tied system with a modern inverter. Hot climates, dusty sites, long cable runs or partial shade push it lower. If an installer gave you an output estimate, you can work out the factor they used and enter that instead.

Does a higher-wattage panel make more energy?

Per panel, yes. But the energy you need sets the total kW. A 450 W panel just means fewer panels for the same system size. That helps when roof space is tight.

Can I size for more than 100% of my use?

Yes, up to 200%. That's useful if you expect to use more power, for example after buying an electric car. But some utilities limit how much you may send back to the grid.

How this calculator is checked

Method: Standard peak-sun-hour sizing method: energy = DC rating × peak sun hours × derate factor; rearranged for size. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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