Solar Panel Calculator

Solar Panel Sizing: Equations, Variables, Worked Examples, and Pro Tips

Solar panel sizing is the process of translating your energy needs into a practical array size (kWdc), number of modules, and—in some cases—battery capacity. Whether you’re planning a grid-tied rooftop system to offset utility bills or an off-grid install for a cabin or RV, the core idea is the same: estimate daily energy demand, apply realistic losses, and divide by site-specific peak sun hours (PSH) to determine the required array wattage. This article explains the equations, the meaning of each variable, limitations you should consider, and includes step-by-step examples you can mirror after using the calculator above.

\( \displaystyle \textbf{Required DC Array Power}:\quad P_{\mathrm{req,DC}}=\frac{E_{\mathrm{day}}}{\mathrm{PSH}\cdot \eta_{\mathrm{sys}}} \)

Here \(E_{\mathrm{day}}\) is average daily energy use (Wh/day), \(\mathrm{PSH}\) is peak sun hours (h/day) for your location and tilt, and \(\eta_{\mathrm{sys}}\) is an overall system derate capturing temperature, wiring, mismatch, soiling, and inverter efficiency. Once you have \(P_{\mathrm{req,DC}}\), the number of panels is a straightforward division by module nameplate \(P_{\mathrm{mod}}\).

Core Equations for Solar Panel Sizing

\( \displaystyle P_{\mathrm{req,DC}}=\frac{E_{\mathrm{day}}}{\mathrm{PSH}\cdot \eta_{\mathrm{sys}}} \quad\text{(DC side array size in W)} \)

\( \displaystyle N_{\mathrm{panels}}=\left\lceil \frac{P_{\mathrm{req,DC}}}{P_{\mathrm{mod}}} \right\rceil \quad\text{(panel count, round up)} \)

\( \displaystyle P_{\mathrm{AC}}\approx P_{\mathrm{req,DC}}\cdot \eta_{\mathrm{inv}} \quad\text{(expected AC power under STC-like irradiance)} \)

\( \displaystyle E_{\mathrm{month}} \approx P_{\mathrm{req,DC}}\cdot \overline{\mathrm{PSH}}_{\mathrm{month}}\cdot \eta_{\mathrm{sys}}\cdot 30 \quad\text{(monthly energy estimate)} \)

If your calculator also handles batteries, you may see the following relationships for autonomy and depth of discharge (DoD):

\( \displaystyle C_{\mathrm{batt}}(\text{Wh})=\frac{E_{\mathrm{day}}\cdot \text{Days}_\mathrm{aut}}{\mathrm{DoD}} ,\qquad C_{\mathrm{batt}}(\text{Ah})=\frac{C_{\mathrm{batt}}(\text{Wh})}{V_{\mathrm{sys}}} \)

What Each Variable Means

\(E_{\mathrm{day}}\) — Average daily energy consumption (Wh/day). Use real bills or a load list.
\(\mathrm{PSH}\) — Peak sun hours (h/day), i.e., the equivalent full-sun hours; depends on location, tilt, and shading.
\(\eta_{\mathrm{sys}}\) — Total system efficiency (0–1). Typical ranges: 0.72–0.85 for grid-tie; 0.60–0.80 for off-grid.
\(P_{\mathrm{mod}}\) — Module nameplate power at STC (W), e.g., 400–450 W for many modern residential panels.
\(\eta_{\mathrm{inv}}\) — Inverter efficiency (0–1), commonly 0.96–0.98 for quality string inverters and microinverters.
\(\text{Days}_\mathrm{aut}\) — Desired battery autonomy (days) for off-grid or backup use.
\(\mathrm{DoD}\) — Allowable depth of discharge (0–1); e.g., 0.8 for LiFePO₄ with 80% usable capacity.
\(V_{\mathrm{sys}}\) — Nominal battery bus voltage (e.g., 24 V or 48 V).

Typical System Derate (\(\eta_{\mathrm{sys}}\)) Components

Loss Component	Typical Range	Notes
Module temperature	−5% to −15%	Hot rooftops reduce output; use temperature coefficient.
Soiling	−0% to −5%	Dust, pollen, bird droppings; varies by climate/cleaning.
Wiring/mismatch	−1% to −3%	Connector and gauge choices matter.
Inverter efficiency	−2% to −4%	High-quality inverters minimize conversion loss.
Shading/soiling events	project-specific	Seasonal trees, chimneys, or snow can be significant.

How to Size a Solar Array (Step-by-Step)

Quantify daily energy use \(E_{\mathrm{day}}\). From utility bills, take annual kWh and divide by 365; or build a load list (device watts × hours per day).
Find site-specific PSH. Use the calculator’s location input or a PSH map/library; select the planned tilt/azimuth.
Choose a realistic system derate \(\eta_{\mathrm{sys}}\). Start with 0.75–0.8 for grid-tie, lower for off-grid or hotter climates.
Compute required DC array wattage. Use \(P_{\mathrm{req,DC}}=E_{\mathrm{day}}/(\mathrm{PSH}\cdot\eta_{\mathrm{sys}})\).
Pick a module wattage \(P_{\mathrm{mod}}\) and round up panel count. \(N_{\mathrm{panels}}=\lceil P_{\mathrm{req,DC}}/P_{\mathrm{mod}}\rceil\).
Check roof area and stringing. Confirm the physical layout fits setbacks and that string voltages/currents meet inverter specs.
Iterate with constraints. Adjust tilt, derate, or module choice to meet energy and budget goals.

Worked Examples You Can Mirror

Example 1 — Grid-Tied Home, No Battery

A homeowner uses \(E_{\mathrm{day}}=24{,}000\ \text{Wh/day}\) (≈720 kWh/month). Local peak sun hours at the planned tilt are \(\mathrm{PSH}=5.2\ \text{h/day}\). They assume \(\eta_{\mathrm{sys}}=0.78\).

\( \displaystyle P_{\mathrm{req,DC}}=\frac{24{,}000}{5.2\times 0.78}=5{,}915\ \text{W} \approx 5.92\ \text{kWdc}. \)

Using 415 W modules:

\( \displaystyle N_{\mathrm{panels}}=\left\lceil \frac{5{,}915}{415}\right\rceil=\lceil 14.25\rceil=15\ \text{panels}. \)

A 15-module, ~6.2 kWdc system gives headroom for hotter months and minor soiling while targeting annual offset.

Example 2 — Off-Grid Cabin with Two Days Autonomy

A cabin’s measured load is \(E_{\mathrm{day}}=3{,}600\ \text{Wh/day}\). Seasonal PSH averages \(\mathrm{PSH}=4.0\). Because off-grid adds controller and battery losses, select \(\eta_{\mathrm{sys}}=0.68\).

\( \displaystyle P_{\mathrm{req,DC}}=\frac{3{,}600}{4.0\times 0.68}=1{,}324\ \text{W}. \)

With 200 W portable panels, \(N_{\mathrm{panels}}=\lceil 1{,}324/200\rceil=7\) panels. For batteries (48 V system), 2 days autonomy and 80% DoD:

\( \displaystyle C_{\mathrm{batt}}(\text{Wh})=\frac{3{,}600\times 2}{0.8}=9{,}000\ \text{Wh},\qquad C_{\mathrm{batt}}(\text{Ah})=\frac{9{,}000}{48}\approx 188\ \text{Ah}. \)

A 48 V, ~200 Ah LiFePO₄ bank would meet these goals with margin.

Example 3 — Temperature Coefficient Check

Module nameplate is at STC (cell 25 °C). In hot climates, NOCT conditions push cell temperature higher, reducing output by the temperature coefficient \(\gamma\) (e.g., −0.34%/°C). If expected cell temperature is 45 °C, the 20 °C rise implies:

\( \displaystyle \Delta P \approx \gamma \times \Delta T = (-0.0034)\times 20 = -6.8\% \)

Incorporate this in \(\eta_{\mathrm{sys}}\) or increase array size to maintain target production.

How to Use These Equations (and When They Break Down)

Budgeting and feasibility: Early-stage sizing lets you estimate how many panels fit the energy goal and if your roof area suffices.
Module selection trade-offs: Higher-watt modules reduce count but can be larger and heavier; ensure they fit setbacks and rafters.
String design: After panel count, check open-circuit voltage at lowest expected temperatures and operating current at highest irradiance against inverter limits.
Limitations: Monthly PSH varies; snow, shading, or seasonal loads can change energy needs. For precise design, use monthly PSH and include shading simulations.
Battery nuance: Storage adds charge-controller and round-trip losses; temperature derating and inverter idle loads also matter.

Pro Tips and Common Pitfalls

Use energy, not power: Size from Wh/day, not just peak watts. A short-lived high load could be fine if the daily energy is modest.
Be honest about losses: Overly optimistic \(\eta_{\mathrm{sys}}\) yields under-performing arrays. Start conservative (0.75–0.8 grid-tie).
Consider future growth: New EV or heat pump? Add a margin now so you don’t rapidly outgrow the array or inverter.
Temperature matters: Hot rooftops reduce output; choose racking with good airflow or slightly oversize the array.
Verify roof structure and setbacks: Especially with heavier bifacial or glass-glass modules.
Shade is multiplicative: Partial shade on a string can disproportionately reduce output without module-level power electronics.

Solar Panel Sizing: Frequently Asked Questions

How many solar panels do I need for a typical home?

Divide your daily Wh by (\(\mathrm{PSH}\cdot \eta_{\mathrm{sys}}\)) to get array watts, then divide by panel wattage. Many U.S. homes land between 12–24 modern panels depending on usage, PSH, and losses.

What are peak sun hours (PSH)?

PSH is the equivalent number of hours per day when solar irradiance averages 1,000 W/m². It collapses seasonal and angular effects into a simple factor; higher PSH means fewer panels for the same energy goal.

Do I size to monthly or annual energy?

For grid-tie, annual energy is common; for off-grid or high winter loads, use the worst-month PSH and loads, or consider a generator/utility backup.

How does temperature affect panel output?

Most modules lose ~0.3–0.4% per °C above 25 °C cell temperature. Hot climates need more array power or better ventilation to hit targets.

Is bigger always better?

Oversizing adds cost and may exceed service-panel limits or incentives. Optimize for your offset goal, interconnection constraints, and roof space.

What efficiency should I assume?

For first-pass estimates: 0.75–0.8 for grid-tie; 0.6–0.75 for off-grid with batteries. Fine-tune using local temperature, shading, and specific inverter/module data.

Key Takeaways

Start with energy: Use daily Wh, not peak watts, to capture real usage.
Use the master sizing equation: \(P_{\mathrm{req,DC}}=E_{\mathrm{day}}/(\mathrm{PSH}\cdot\eta_{\mathrm{sys}})\).
Round up and verify: Compute panel count, then confirm space, electrical limits, and stringing.
Account for the real world: Temperature, shading, soiling, and seasonal swings justify conservative derates or extra capacity.
Batteries add complexity: Include autonomy, DoD, voltage, and round-trip efficiency if you need storage.

With these equations and examples, you can interpret the calculator’s results, sanity-check design options, and communicate clearly with installers or inspectors. The workflow is simple—measure energy, find PSH, pick a realistic derate, solve for DC watts, and translate that into a panel count and layout that fits your roof and goals.