What is the rolling sphere method?

It is a geometric design method where an imaginary sphere of a fixed radius is rolled over a structure and its air terminals. Any surface the sphere can touch is exposed to a direct strike, while areas in the sphere's shadow are protected.

What sphere radius does NFPA 780 use?

NFPA 780 commonly uses a 150 ft (about 46 m) rolling sphere for ordinary structures. IEC 62305 uses smaller spheres for higher protection levels: 20 m for Level I, 30 m for Level II, 45 m for Level III and 60 m for Level IV.

How is the protective radius of one terminal found?

From rolling-sphere geometry, the protective radius on the surface equals the square root of (2 times R times h minus h squared), where R is the sphere radius and h the terminal height. The sphere rests on the tip and the roof, touching the roof at that distance.

Why does spacing between terminals matter?

Between two terminals the sphere sags downward by R minus the square root of (R squared minus half-the-spacing squared). If that sag drops below the height of an object at the midpoint, the object is exposed and you must add a terminal or reduce the spacing.

Does a smaller sphere give more protection?

Yes. A smaller radius sphere dips less and touches fewer points, so it demands more, closely spaced air terminals and yields a higher protection level. Larger spheres are permitted for ordinary structures with a lower required protection level.

Lightning Protection Rolling Sphere Calculator

The rolling sphere method is the standard way to lay out lightning air terminals on a structure. You imagine a sphere of a defined radius rolled across the roof and its terminals; wherever it touches is a potential strike point, and the shadow it casts is the protected zone. This calculator applies the geometry from NFPA 780 and IEC 62305 to size protective radii and check the gap between terminals.

How it works

For a single air terminal of height h standing on a flat roof, the rolling sphere of radius R rests on the tip and the roof, contacting the surface at a horizontal distance:

d = sqrt(2 × R × h − h²)

Any point on the roof within d of the terminal base is shielded. Between two equal terminals spaced s apart, the sphere can dip into the gap by a sag of:

sag = R − sqrt(R² − (s / 2)²)

The protected zone height at the midpoint is the terminal height minus this sag. If an object there rises above that line, it is exposed.

Worked example

With the NFPA 780 ordinary sphere (R = 150 ft) and a 10 ft terminal:

d = sqrt(2 × 150 × 10 − 10²) = sqrt(2900) ≈ 53.9 ft

Two such terminals 40 ft apart produce a sag of:

sag = 150 − sqrt(150² − 20²) = 150 − sqrt(22100) ≈ 1.34 ft

so the protected line at the midpoint sits about 10 − 1.34 = 8.66 ft above the roof — anything shorter than that at the midpoint is protected.

Tips and notes

Choosing a smaller sphere (a higher protection level) shrinks the protective radius and forces tighter terminal spacing, which is appropriate for structures with sensitive contents. Always pair the air-terminal layout with a complete down-conductor, bonding and grounding system per NFPA 780, and treat tall masts with the separate single-mast protective-cone model rather than the surface-radius formula above.