Solar PV Area & Output

Module count, row spacing, land area and annual energy for fixed-tilt and tracking arrays.

1. What this check does

Converts between DC capacity and area. For fixed-tilt arrays it finds the row pitch that keeps one row from shading the next during a chosen window around solar noon on the winter solstice, and from that the ground coverage ratio (GCR). Tracking arrays use a GCR you enter or a typical default. With the plane-of-array insolation for the site it estimates annual energy, specific yield, capacity factor and, optionally, avoided CO₂.

2. Inputs used

Target DC kW, or the available area.
Module rating (W at STC), length along the slope and width, and how many modules are stacked up the slope in a row.
Mounting (fixed, single-axis, dual-axis), latitude, and for fixed arrays the tilt and the shade-free window.
Optional: plane-of-array insolation from NREL PVWatts or the NSRDB, performance ratio, DC/AC ratio, and a grid emission factor from EPA eGRID.

3. Formulas and assumptions

Sun position (winter solstice, solar time)

Elevation

\sin\alpha = \sin\phi\sin\delta + \cos\phi\cos\delta\cos h

φ = |latitude|, δ = −23.45°, h = 15° per hour from noon.

Azimuth

\cos\gamma = \dfrac{\sin\alpha\sin\phi - \sin\delta}{\cos\alpha\cos\phi}

From due south (north in the southern hemisphere).

Row spacing and area

Row pitch

D = L\cos\beta + \dfrac{L\sin\beta\,\cos\gamma}{\tan\alpha} \qquad \mathrm{GCR} = \dfrac{L}{D}

β tilt; L slope length = modules up × module length.

Modules

N = \left\lceil \dfrac{\mathrm{kW} \times 1000}{W} \right\rceil \quad\text{or}\quad N = \left\lfloor \dfrac{\text{Area}\cdot \mathrm{GCR}}{A_{\text{module}}} \right\rfloor

Capacity, land

\mathrm{kW_{dc}} = \dfrac{N\,W}{1000} \qquad \mathrm{kW_{ac}} = \dfrac{\mathrm{kW_{dc}}}{\mathrm{DC/AC}} \qquad \text{Land} = \dfrac{N\,A_{\text{module}}}{\mathrm{GCR}}

Energy

Annual energy

E = \mathrm{kW_{dc}} \cdot \mathrm{POA} \cdot 365 \cdot \mathrm{PR}\quad (\mathrm{kWh/yr})

Yield, CF

\text{Yield} = \dfrac{E}{\mathrm{kW_{dc}}} \qquad \mathrm{CF} = \dfrac{E}{8760\,\mathrm{kW_{dc}}}

CO₂

\mathrm{CO_2} = \dfrac{E}{1000}\cdot \mathrm{EF}\cdot \dfrac{0.4536}{1000}\quad (\mathrm{t/yr})

EF in lb/MWh (EPA eGRID).

Rows face due south (north in the southern hemisphere) on flat ground; slopes, azimuth offsets and edge effects are ignored.
The declination of −23.45° is the solstice value; the shade-free window is in solar time, not clock time.
Tracker GCR defaults are 0.35 (single-axis) and 0.2 (dual-axis), typical screening values chosen by RokBench; enter your layout value when known.
Performance ratio default 0.80 is a RokBench screening assumption covering temperature, soiling, wiring, mismatch, inverter and availability losses. NREL PVWatts models these explicitly and is the better source.
The plane-of-array insolation you enter must match the mounting and tilt. "Fill from coordinates" uses NASA POWER climatology (2001–2020): for fixed tilt it interpolates NASA's values for 0°, latitude − 15°, latitude, latitude + 15° and 90°; for trackers it uses the fixed optimal-tilt value, which leaves out tracker gain and so understates energy.

4. What is NOT checked

Fire code roof setbacks and access pathways, and structural loading.
String sizing, NEC 690 conductors, overcurrent protection and rapid shutdown.
Inverter clipping (flagged above DC/AC 1.5), interconnection limits and export rules.
Shading from terrain, trees and nearby objects; snow and bifacial gain.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

NREL PVWatts Calculator and the National Solar Radiation Database (NSRDB) — U.S. DOE public data
NASA Langley Research Center (LaRC) POWER Project — climatology API (public data)
EPA eGRID2023 — emission rates by grid subregion and the Power Profiler ZIP code table (public data); non-baseload rates are EPA's suggested simple estimate of emissions avoided
NEC 2023 Article 690 — solar photovoltaic systems
Duffie & Beckman, Solar Engineering of Thermal Processes — solar geometry

6. Validation cases

Hand-calculated cases run on every change. See Validation.

7. Known issues and changes

See the Changelog. Try the tool: Solar PV Area & Output.