Solar PV Inter-Row Spacing Calculator

Two consecutive rows at 25° tilt, pitch 3.93 m, clear distance 1.86 m and worst-case design-day shadow reach 1.86 m.

Geometric shadow intersection only. Times are local clock times derived from solar time using longitude, time zone and the equation of time.

All values recalculated with the same engine for each pitch variation.

• →Why this pitch — 1. Solar geometry — declination -23.45° and equation of time 1.03 min for Winter solstice (21 Dec) give a solar-noon altitude of 37.95° at latitude 28.6°. 2. Table geometry — 1 × 2.28 m portrait module(s) plus gaps give a slope length of 2.28 m, height H = 0.964 m and projection D = 2.066 m. 3. Shadow geometry — the perpendicular shadow reach x = H·cos(γs − γ)/tanα peaks at 1.862 m inside the required window. 4. Pitch — the selected objective (Balanced (shadow-free across the required window)) sets P = D + x_design = 3.928 m, leaving 1.862 m of clear ground between rows. 5. GCR — D / P = 2.066 / 3.928 = 0.526 (52.6%). 6. Shading check — the maximum geometric shaded fraction inside the window is 0% against the accepted 0%.
• →Land utilisation, balanced and low-shading pitches are three explicit design objectives, not standards; pick the one that matches the project's land cost, yield target and O&M access requirement.
• →Winter-solstice sizing is a widely used design criterion, not a code requirement — for high-latitude or land-constrained sites an equinox or annual-yield-optimised pitch may be more economic.
• →Engineering-grade preliminary calculation. Final design must be verified against project-specific site conditions, manufacturer datasheets, applicable standards and utility requirements.
• →This calculator provides preliminary geometric row-spacing and shading estimates. Final PV plant layout should be validated using detailed topographical survey data, equipment geometry, site constraints and detailed PV simulation software such as PVsyst or an equivalent engineering tool.

Design day: Winter solstice (21 Dec) (day 355). Declination -23.45°, equation of time 1.03 min, longitude 77.2°, time zone UTC+5.5.
Table geometry: 1 module(s) portrait up the slope → slope length 2.28 m, height 0.964 m, horizontal projection 2.066 m, lower edge 0.5 m, upper edge 1.46 m.
Worst-case shadow reach in the required window occurs at 09:00 AM clock time: 1.862 m perpendicular to the rows.
Selected objective "Balanced (shadow-free across the required window)" → pitch 3.928 m, clear distance 1.862 m, GCR 0.526.
Expert instant 09:00 AM: solar time 08:40 AM, hour angle -50.04°, altitude 19.07°, zenith 70.93°, azimuth 131.92° from north, shadow reach 1.862 m.
Shading figures are geometric shaded fractions of the collector slope height. They are not electrical yield losses — module/string electrical mismatch is not modelled here.

Designs are stored privately in this browser — nothing is uploaded.

• Table slope length L = n·l + (n−1)·g (l = module side up the slope)
• Vertical height H = L·sinβ · Horizontal projection D = L·cosβ
• Declination δ = 23.45·sin(360(284+n)/365) ; EoT = 9.87sin2B − 7.53cosB − 1.5sinB
• Solar time = clock + 4(λ − 15·TZ) + EoT ; hour angle ω = 15(t_solar − 12)
• sinα = sinφ·sinδ + cosφ·cosδ·cosω ; azimuth from north γs
• Perpendicular shadow reach x = H·cos(γs − γ_array) / tan(α)
• Row pitch P = D + x_design · Clear distance C = P − D
• GCR = D / P · Geometric shaded fraction f = (x − C)/x for x > C

Inter-row spacing is a geometric problem: the vertical height of a tilted table casts a shadow whose horizontal reach depends on the solar altitude and on how far the sun's azimuth is from the direction the array faces. The pitch is the horizontal projection of the table plus the shadow reach you choose to design out. The calculator computes solar declination, the equation of time, solar time, hour angle, altitude and azimuth for the selected design date and location, so the shadow length, pitch, GCR, shadow-free window and hourly shading table all come from the same engine.

1. 1.Table slope length Ln·l + (n−1)·g2.28 m
2. 2.Vertical height HL·sinβ0.964 m
3. 3.Horizontal projection DL·cosβ2.066 m
4. 4.Solar declination δCooper, day 355-23.45°
5. 5.Equation of timeSpencer1.03 min
6. 6.Solar altitude at solar noonasin(sinφsinδ + cosφcosδcosω)37.95°
7. 7.Solar azimuth at solar noonfrom true north180°
8. 8.Shadow reach at solar noonH·cos(γs−γ)/tanα1.236 m
9. 9.Worst-case shadow reach in the required windowmax over 09:00 AM–03:00 PM1.862 m
10. 10.Minimum geometric pitchD + x(noon)3.302 m
11. 11.Balanced pitchD + max x(window)3.928 m
12. 12.Low-shading pitchD + max x(window)·(1+15%)4.207 m
13. 13.Selected pitchBalanced (shadow-free across the required window)3.928 m
14. 14.Inter-row clear distanceP − D1.862 m
15. 15.Ground coverage ratioGCR = D / P0.526 (52.6%)

• •Worked example (same engine, same formulas): latitude 28.60° N, longitude 77.20° E, UTC+5:30, one portrait module 2.28 m long, 25° tilt, array azimuth 180°, winter solstice, required shadow-free window 09:00–15:00.
• •Step 1 — Solar geometry: day 355, declination −23.45°, equation of time ≈ +1.6 min, solar-noon altitude ≈ 37.9°.
• •Step 2 — Table geometry: L = 2.28 m, H = 2.28·sin25° = 0.964 m, D = 2.28·cos25° = 2.066 m.
• •Step 3 — Shadow: at solar noon x = H/tan(α) ≈ 1.24 m; the worst reach inside 09:00–15:00 is larger because the sun is lower and off-axis.
• •Step 4 — Pitch: P = D + x_design, so the balanced pitch is the projection plus the worst window shadow.
• •Step 5 — GCR: GCR = D / P, reported as a ratio and a percentage.
• •Step 6 — Shading check: the hourly table reports the geometric shaded fraction of row height at each hour and the achievable shadow-free window.
• •Run the calculator with these inputs to see the exact runtime values — the worked example uses the same engine, so the numbers agree.

• • Fixed-tilt array with identical, parallel, evenly spaced rows.
• • Uniform single-plane terrain; slope is applied as a simplified adjustment to the effective solar altitude.
• • Both rows share the same lower-edge ground clearance, so clearance cancels in the shadow geometry.
• • Representative row geometry — end-of-row and edge effects are not modelled.
• • No external obstruction or horizon shading is modelled.
• • Preliminary geometric shading only; electrical mismatch and yield losses are not calculated.
• • Solar position is computed from the entered latitude, longitude, time zone and design date (Cooper declination, Spencer equation of time).
• • Winter-solstice sizing is a design criterion (assumption), not a universal requirement.